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Descriptive Statistics
16: Descriptive Statistics
· For additional ancillary materials related to this chapter, please visit thePoint.
Statistical analysis enables researchers to organize, interpret, and communicate numeric information. Mathematic skill is not required to grasp statistics—only logical thinking ability is needed. In this book, we underplay computation. We focus on explaining which statistics to use in different situations and on how to understand what statistical results mean.
Statistics can be descriptive or inferential. Descriptive statistics are used to describe and synthesize data (e.g., a percentage). When a percentage or other descriptive statistic is calculated from population data, it is called a parameter . A descriptive index from a sample is a statistic . Research questions are about parameters, but researchers calculate statistics to estimate them and use inferential statistics to make inferences about the population. This chapter discusses descriptive statistics, and Chapter 17 focuses on inferential statistics. First we discuss levels of measurement because the analyses that can be performed depend on how variables are measured.
LEVELS OF MEASUREMENT
Scientists have developed a system for classifying measures. The four levels of measurement are nominal, ordinal, interval, and ratio.
Nominal Measurement
The lowest level of measurement is nominal measurement , which involves assigning numbers to classify characteristics into categories. In previous chapters, we referred to nominal measurement as categorical. Examples of variables amenable to nominal measurement include gender, blood type, and marital status.
Numbers assigned in nominal measurement have no quantitative meaning. If we code males as 1 and females as 2, the number 2 does not mean “more than” 1. The numbers are only symbols representing different values of gender. We easily could use 1 for females, 2 for males.
Nominal measurement provides no information about an attribute except equivalence and nonequivalence. If we were to “measure” the gender of Nate, Alan, Mary, and Anna by assigning them the codes 1, 1, 2, and 2, respectively, this means Nate and Alan are equivalent on the gender attribute but are not equivalent to Mary and Anna.
Nominal measures must have categories that are mutually exclusive and collectively exhaustive. For example, if we were measuring marital status, we might use these codes: 1 = married, 2 = separated or divorced, 3 = widowed. Each person must be classifiable into one and only one category. The requirement for collective exhaustiveness would not be met if there were people in a sample who had never been married.
Numbers in nominal measurement cannot be treated mathematically. It is not meaningful to calculate the average gender of a sample, but we can compute percentages. In a sample of 50 patients with 30 men and 20 women, we could say that 60% were male and 40% were female.
Ordinal Measurement
Ordinal measurement involves sorting people based on their relative ranking on an attribute. This measurement level goes beyond categorization: Attributes are ordered according to some criterion. Ordinal measurement captures not only equivalence but also relative rank.
Consider this ordinal scheme for measuring ability to perform activities of daily living: (1) completely dependent, (2) needs another person’s assistance, (3) needs mechanical assistance, (4) completely independent. The numbers signify incremental ability to perform activities of daily living. People coded 4 are equivalent to each other with regard to functional ability and, relative to those in the other categories, have more of that attribute.
Ordinal measurement does not, however, tell us anything about how much greater one level is than another. We do not know if being completely independent is twice as good as needing mechanical assistance. Nor do we know if the difference between needing another person’s assistance and needing mechanical assistance is the same as that between needing mechanical assistance and being completely independent. Ordinal measurement tells us only the relative ranking of the attribute’s levels.
As with nominal measures, mathematic operations with ordinal-level data are restricted—for example, averages are usually meaningless. Frequency counts, percentages, and several other statistics to be discussed later are appropriate for ordinal-level data.
Interval Measurement
Interval measurement occurs when researchers can assume equivalent distance between rank ordering on an attribute. The Fahrenheit temperature scale is an example: A temperature of 60°F is 10°F warmer than 50°F. A 10°F difference similarly separates 40°F and 30°F, and the two differences in temperature are equivalent. Interval-level measures are more informative than ordinal ones, but interval measures do not communicate absolute magnitude. For example, we cannot say that 60°F is twice as hot as 30°F. The Fahrenheit scale uses an arbitrary zero point: Zero degrees does not signify an absence of heat. Most psychological and educational tests are assumed to yield interval-level data.
Interval scales expand analytic possibilities—in particular, interval-level data can be averaged meaningfully. It is reasonable, for example, to compute an average daily body temperature for hospital patients. Many statistical procedures require interval measurements.
Ratio Measurement
Ratio measurement is the highest measurement level. Ratio measures provide information about ordering on the critical attribute, the intervals between objects, and the absolute magnitude of the attribute because they have a rational, meaningful zero. Many physical measures provide ratio-level data. A person’s weight, for example, is measured on a ratio scale. We can say that someone who weighs 200 pounds is twice as heavy as someone who weighs 100 pounds.
Because ratio measures have an absolute zero, all arithmetic operations are permissible. Statistical procedures suitable for interval-level data are also appropriate for ratio-level data. In previous chapters, we called variables that were measured on either the interval or ratio scale as continuous.
Example of Different Measurement Levels: Grønning and colleagues (2014) tested the effect of a nurse-led education program for patients with chronic inflammatory polyarthritis. Gender (male/female) and diagnosis (psoriatic, rhematoid, or unspecified arthritis) were measured as nominal-level variables. Education (10 years, 11–12 years, 13+ years) was operationalized as an ordinal measurement in this particular study. Many outcomes (e.g., self-efficacy, coping, pain, hospital anxiety and depression) were measured on an interval-level scale. Several variables were measured on a ratio level (e.g., age, number of hospital admissions).
Comparison of the Levels
The four levels of measurement form a hierarchy, with ratio scales at the top and nominal measurement at the base. Moving from a higher to a lower level of measurement results in an information loss. For example, if we measured a woman’s weight in pounds, this would be a ratio measure. If we categorized the weights into three groups (e.g., under 125, 125 to 175, and 176+), this would be an ordinal measure. With this scheme, we would not be able to differentiate a woman who weighed 125 pounds from one who weighed 175 pounds—we have much less information with the ordinal information. This example illustrates another point: With information at one level, it is possible to convert data to a lower level, but the converse is not true. If we were given only the ordinal measurements, we could not reconstruct actual weights.
It is not always easy to identify a variable’s level of measurement. Nominal and ratio measures usually are discernible, but the distinction between ordinal and interval measures is more problematic. Some methodologists argue that most psychological measures that are treated as interval measures are really only ordinal measures. Although instruments such as Likert scales produce data that are, strictly speaking, ordinal, many analysts believe that treating them as interval measures results in too few errors to warrant using less powerful statistical procedures.
TIP: In operationalizing variables, it is best to use the highest measurement level possible because they are more powerful and precise. Sometimes, however, group membership is more informative than continuous scores, especially for clinicians who need “cut points” for making decisions. For example, for some purposes, it may be more relevant to designate infants as being of low versus normal birth weight (nominal level) than to use actual birth weight values (ratio level). But it is best to measure at the higher level and then convert to a lower level, if appropriate.
FREQUENCY DISTRIBUTIONS
When quantitative data are unanalyzed, it is not possible to discern even general trends. Consider the 60 numbers in Table 16.1 , which are fictitious scores of 60 preoperative patients on a six-item measure of anxiety—scores that we will consider as interval level. Inspection of the numbers does not help us understand patients’ anxiety.
TABLE 16.1: Patients’ Anxiety Scores
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A set of data can be described in terms of three characteristics: the shape of the distribution of values, central tendency, and variability. Central tendency and variability are dealt with in subsequent sections.
Constructing Frequency Distributions
Frequency distributions are used to organize numeric data. A frequency distribution is a systematic arrangement of values from lowest to highest, together with a count of the number of times each value was obtained. Our 60 anxiety scores are shown in a frequency distribution in Table 16.2 . We can readily see the highest and lowest scores, the most common score, where the bulk of scores clustered, and how many patients were in the sample (total sample size is typically depicted as N ). None of this was apparent before the data were organized.
Frequency distributions consist of two parts: observed score values (the Xs) and the frequency of cases at each value (the f s). Scores are listed in order in one column, and corresponding frequencies are listed in another. The sum of numbers in the frequency column must equal the sample size. In less verbal terms, ∑f = N, which means the sum of (signified by Greek sigma, ∑) the frequencies (f) equals the sample size (N).
It is useful to display percentages for each value, as shown in column 3 of Table 16.2 . Just as the sum of all frequencies should equal N, the sum of all percentages should equal 100.
Frequency data can also be displayed graphically. Graphs for displaying interval- and ratio-level data include histograms and frequency polygons , which are constructed in a similar fashion. First, score values are arrayed on a horizontal dimension, with the lowest value on the left, ascending to the highest value on the right. Frequencies or percentages are displayed vertically. A histogram is constructed by drawing bars above the score classes to the height corresponding to the frequency for that score. Figure 16.1 shows a histogram for the anxiety score data. Frequency polygons are similar, but dots connected by straight lines are used to show frequencies. A dot corresponding to the frequency is placed above each score ( Figure 16.2 ).
BASIC SAMPLING CONCEPTS
We begin by reviewing some terms associated with sampling—terms that are used primarily (but not exclusively) in quantitative research.
Populations
A population (the “P” of PICO questions) is the entire aggregation of cases in which a researcher is interested. For instance, if we were studying American nurses with doctoral degrees, the population could be defined as all U.S. citizens who are registered nurses (RNs) and who have a PhD, DNSc, DNP, or other doctoral-level degree. Other possible populations might be all patients who had cardiac surgery in Princess Alexandria Hospital in 2015, all women with irritable bowel syndrome in Sweden, or all children in Canada with cystic fibrosis. Populations are not restricted to humans. A population might consist of all hospital records in a particular hospital or all blood samples at a particular laboratory. Whatever the basic unit, the population comprises the aggregate of elements in which the researcher is interested.
It is sometimes useful to distinguish between target and accessible populations. The accessible population is the aggregate of cases that conform to designated criteria and that are accessible for a study. The target population is the aggregate of cases about which the researcher would like to generalize. A target population might consist of all diabetic people in New York, but the accessible population might consist of all patients with diabetes who attend a particular clinic. Researchers usually sample from an accessible population and hope to generalize to a target population.
TIP: Many quantitative researchers fail to identify their target population or to discuss the generalizability of the results. The population of interest needs to be carefully considered in planning and reporting a study.
Eligibility Criteria
Researchers must specify criteria that define who is in the population. Consider the population American nursing students. Does this population include students in all types of nursing programs? How about RNs returning to school for a bachelor’s degree? Or students who took a leave of absence for a semester? Do foreign students enrolled in American nursing programs qualify? Insofar as possible, the researcher must consider the exact criteria by which it could be decided whether an individual would or would not be classified as a member of the population. The criteria that specify population characteristics are the eligibility criteria or inclusion criteria. Sometimes, a population is also defined in terms of characteristics that people must not possess (i.e., exclusion criteria ). For example, the population may be defined to exclude people who cannot speak English.
In thinking about ways to define the population and delineate eligibility criteria, it is important to consider whether the resulting sample is likely to be a good exemplar of the population construct in which you are interested. A study’s construct validity is enhanced when there is a good match between the eligibility criteria and the population construct.
Of course, eligibility criteria for a study often reflect considerations other than substantive concerns. Eligibility criteria may reflect one or more of the following:
· Costs. Some criteria reflect cost constraints. For example, when non-English-speaking people are excluded, this does not usually mean that researchers are uninterested in non-English speakers but rather that they cannot afford to hire translators or multilingual data collectors.
· Practical constraints. Sometimes, there are other practical constraints, such as difficulty including people from rural areas, people who are hearing impaired, and so on.
· People’s ability to participate in a study. The health condition of some people may preclude their participation. For example, people with cognitive impairments, who are in a coma, or who are in an unstable medical condition may need to be excluded.
· Design considerations. As noted in Chapter 10 , it is sometimes advantageous to define a homogeneous population as a means of controlling confounding variables.
The criteria used to define a population for a study have implications for the interpretation and generalizability of the findings.
Example of Inclusion and Exclusion Criteria: Schallom and colleagues (2015) studied the relationship between gastric reflux and pulmonary aspiration in hospitalized patients receiving gastric tube feedings. To be eligible, patients had to have a confirmed gastric location of a feeding tube, be mechanically ventilated, and be aged 18 years or older. Patients were excluded if they were pregnant, had a documented history of GERD, had any airborne infectious disease, or had oral trauma.
Samples and Sampling
Sampling is the process of selecting cases to represent an entire population, to permit inferences about the population. A sample is a subset of population elements , which are the most basic units about which data are collected. In nursing research, elements most often are humans.
Samples and sampling plans vary in quality. Two key considerations in assessing a sample in a quantitative study are its representativeness and size. A representative sample is one whose key characteristics closely approximate those of the population. If the population in a study of patients who fall is 50% male and 50% female, then a representative sample would have a similar gender distribution. If the sample is not representative of the population, the study’s external validity and construct validity are at risk.
Certain sampling methods are less likely to result in biased samples than others, but a representative sample can never be guaranteed. Researchers operate under conditions in which error is possible. Quantitative researchers strive to minimize errors and, when possible, to estimate their magnitude.
Sampling designs are classified as either probability sampling or nonprobability sampling. Probability sampling involves random selection of elements. In probability sampling, researchers can specify the probability that an element of the population will be included in the sample. Greater confidence can be placed in the representativeness of probability samples. In nonprobability samples , elements are selected by nonrandom methods. There is no way to estimate the probability that each element has of being included in a nonprobability sample, and every element usually does not have a chance for inclusion.
Strata
Sometimes, it is useful to think of populations as consisting of subpopulations, or strata . A stratum is a mutually exclusive segment of a population, defined by one or more characteristics. For instance, suppose our population was all RNs in the United Kingdom. This population could be divided into two strata based on gender. Or, we could specify three strata of nurses younger than 30 years of age, nurses aged 30 to 45 years, and nurses 46 years or older. Strata are often used in sample selection to enhance the sample’s representativeness.
Staged Sampling
Samples are sometimes selected in multiple phases, in what is called multistage sampling . In the first stage, large units (such as hospitals or nursing homes) are selected. Then, in the next stage, individuals are sampled. In staged sampling, it is possible to combine probability and nonprobability sampling. For example, the first stage can involve the deliberate (nonrandom) selection of study sites. Then, people within the selected sites can be selected through random procedures.
Sampling Bias
Researchers work with samples rather than with populations because it is cost-effective to do so. Researchers seldom have the resources to study all members of a population. It may be possible to obtain reasonably accurate information from a sample, but data from samples can be erroneous. Finding 100 people willing to participate in a study may be easy, but it is usually hard to select 100 people who are an unbiased subset of the population. Sampling bias refers to the systematic over- or underrepresentation of a population segment on a characteristic relevant to the research question.
As an example of consciously biased selection, suppose we were investigating patients’ responsiveness to nurses’ touch and decide to recruit the first 50 patients meeting eligibility criteria. We decide, however, to omit Mr. Z from the sample because he has been hostile to nursing staff. Mrs. X, who has just lost a spouse, is also bypassed. These decisions to exclude certain people do not reflect bona fide eligibility criteria. This can lead to bias because responsiveness to nurses’ touch (the outcome variable) may be affected by patients’ feelings about nurses or their emotional state.
Sampling bias often occurs unconsciously, however. If we were studying nursing students and systematically interviewed every 10th student who entered the nursing school library, the sample would be biased in favor of library-goers, even if we are conscientious about including every 10th student regardless of age, gender, or other traits.
TIP: Internet surveys are attractive because they can be distributed to geographically dispersed people. However, there is an inherent bias in such surveys, unless the population is defined as people who have easy access to, and comfort with, a computer and the Internet.
Sampling bias is partly a function of population homogeneity. If population elements were all identical on key attributes, then any sample would be as good as any other. Indeed, if the population were completely homogeneous—exhibited no variability at all—then a single element would be sufficient. For many physiologic attributes, it may be safe to assume reasonably high homogeneity. For example, the blood in a person’s veins is relatively homogeneous and so a single blood sample is adequate. For most human attributes, however, homogeneity is the exception rather than the rule. Age, health status, stress, motivation—all these attributes reflect human heterogeneity. When variation occurs in the population, then similar variation should be reflected, to the extent possible, in a sample.
TIP: One easy way to increase a study’s generalizability is to select participants from multiple sites (e.g., from different hospitals, nursing homes, communities). Ideally, the different sites would be sufficiently divergent that good representation of the population would be obtained.
NONPROBABILITY SAMPLING
Nonprobability sampling is less likely than probability sampling to produce representative samples. Despite this fact, most studies in nursing and other health disciplines rely on nonprobability samples.
Convenience Sampling
Convenience sampling entails using the most conveniently available people as participants. For example, a nurse who conducts a study of teenage risk-taking at a local high school is relying on a convenience sample. The problem with convenience sampling is that those who are available might be atypical of the population with regard to critical variables.
Sometimes, researchers seeking people with certain characteristics place an advertisement in a newspaper, put up signs in clinics, or post messages on online social media. These “convenient” approaches are subject to bias because people select themselves as volunteers in response to posted notices and likely differ from those who do not volunteer.
Snowball sampling (also called network sampling or chain sampling) is a variant of convenience sampling. With this approach, early sample members (called seeds) are asked to refer other people who meet the eligibility criteria. This approach is often used when the population involves people who might otherwise be difficult to identify (e.g., people who are afraid of hospitals).
Convenience sampling is the weakest form of sampling. In heterogeneous populations, there is no other sampling approach in which the risk of sampling bias is greater. Yet, convenience sampling is the most commonly used method in many disciplines.
Example of a Convenience Sample: Krueger and colleagues (2015) studied fetal response (fetal heart rate and movement) to live and recorded maternal speech following a history of fetal exposure to a passage spoken by the mother. The study participants were a convenience sample of 21 pregnant women.
TIP: Rigorous methods of sampling hidden populations, such as the homeless or injection drug users, are emerging. Because standard probability sampling is inappropriate for such hidden populations, a method called respondent-driven sampling (RDS), a variant of snowball sampling, has been developed. RDS, unlike traditional snowballing, allows the assessment of relative inclusion probabilities based on mathematical models (Magnani et al., 2005). McCreesh and colleagues (2012) have undertaken a recent evaluation of RDS.
Quota Sampling
A quota sample is one in which the researcher identifies population strata and determines how many participants are needed from each stratum. By using information about population characteristics, researchers can ensure that diverse segments are represented in the sample, in the proportion in which they occur in the population.
Suppose we were interested in studying nursing students’ attitude toward working with AIDS patients. The accessible population is a school of nursing with 500 undergraduate students; a sample of 100 students is desired. The easiest procedure would be to distribute questionnaires in classrooms through convenience sampling. Suppose, however, that we suspect that male and female students have different attitudes. A convenience sample might result in too many men or women. Table 12.1 presents fictitious data showing the gender distribution for the population and for a convenience sample (second and third columns). In this example, the convenience sample overrepresents women and underrepresents men. We can, however, establish “quotas” so that the sample includes the appropriate number of participants from both strata. The far-right column of Table 12.1 shows the number of men and women required for a quota sample for this example.
Data Collection in Quantitative Research
13: Data Collection in Quantitative Research
· For additional ancillary materials related to this chapter, please visit thePoint.
Both the study participants and those collecting the data are constrained during the collection of structured quantitative data. The goal is to achieve consistency in what is asked and how answers are reported, in an effort to reduce biases and facilitate analysis. Major methods of collecting structured data are discussed in this chapter. We begin by discussing broad planning issues.
DEVELOPING A DATA COLLECTION PLAN
Data collection plans for quantitative studies ideally yield accurate, valid, and meaningful data. This is a challenging goal, typically requiring considerable time and effort to achieve. Steps in developing a data collection plan are described in this section. (A flowchart illustrating the sequence of steps is available in the Toolkit of the accompanying Resource Manual.)
Identifying Data Needs
Researchers usually begin by identifying the types of data needed for their study. In quantitative studies, researchers may need data for the following purposes:
· 1. Testing hypotheses, addressing research questions. Researchers must include one or more measures of all key variables. Multiple measures of some variables may be needed if a variable is complex or if there is an interest in corroboration.
· 2. Describing the sample. Information should be gathered about major demographic and health characteristics. We advise gathering data about participants’ age, gender, race or ethnicity, and education (or income). This information is critical in interpreting results and understanding the population to whom findings can be generalized. If the sample includes participants with a health problem, data on the nature of that problem also should be gathered (e.g., severity, treatments, time since diagnosis).
TIP: Asking demographic questions in the right way is more difficult than you might think. Because the need to collect information about sample characteristics is nearly universal, we have included a demographic form and guidelines in the Toolkit of the accompanying Resource Manual. The demographic questionnaire can be adapted as needed.
· 3. Controlling confounding variables. Several approaches to controlling confounding variables require measuring those variables. For example, for analysis of covariance, variables that are statistically controlled must be measured.
· 4. Analyzing potential biases. Data that can help to identify potential biases should be collected. For example, researchers should gather information that would help them understand selection or attrition biases.
· 5. Understanding subgroup effects. It is often desirable to answer research questions for key subgroups of participants. For example, we may wish to know if a special intervention for pregnant women is equally effective for primiparas and multiparas. In such a situation, we would need to collect data about the participants’ childbearing history.
· 6. Interpreting results. Researchers should try to anticipate alternative results and then consider what types of data would help in interpreting them. For example, if we hypothesized that the presence of school-based clinics in high schools would lower the incidence of sexually transmitted diseases among students but found that the incidence remained constant after the clinic opened, what type of information would help us interpret this result (e.g., information about the students’ frequency of intercourse, number of partners, and so on)?
· 7. Assessing treatment fidelity. In intervention studies, it is useful to monitor treatment fidelity and to assess whether the intended treatment was actually received.
· 8. Assessing costs. In intervention studies, information about costs and financial benefits of alternative treatments is often useful.
· 9. Obtaining administrative information. It is usually necessary to gather administrative data—for example, dates of data collection and contact information in longitudinal studies.
The list of possible data needs may seem daunting, but many categories overlap. For example, participant characteristics for sample description are often useful for bias analysis, for controlling confounders, or for creating subgroups. If resource constraints make it impossible to collect the full range of variables, then researchers must prioritize data needs.
TIP: In prioritizing data needs, it may be useful to develop a matrix so that data collection decisions can be made in a systematic way. Such a matrix can help to identify “holes” and redundancies. A partial example of such a matrix is included in the Toolkit of the Resource Manual for you to use and adapt.
Selecting Types of Measures
After data needs have been identified, the next step is to select a data collection method (e.g., self-report, records) for each variable. It is not unusual to combine self-reports, observations, physiologic, or records data in a single study.
Data collection decisions must also be guided by ethical considerations (e.g., whether covert data collection is warranted), cost constraints, availability of assistants to help with data collection, and other issues discussed in the next section. Data collection is often the costliest and most time-consuming portion of a study. Because of this, researchers often have to make a few compromises about the type or amount of data collected.
Selecting and Developing Instruments
Once preliminary data collection decisions have been made, researchers should determine if there are instruments available for measuring study variables, as will often be the case. Potential data collection instruments should then be assessed. The primary consideration is conceptual relevance: Does the instrument correspond to your conceptual definition of the variable? Another important criterion is whether the instrument will yield high-quality data. Approaches to evaluating data quality of quantitative measures are discussed in Chapter 14 . Additional factors that may affect decisions in selecting an instrument are as follows:
· 1. Resources. Resource constraints sometimes prevent the use of the highest quality measures. There may be some direct costs associated with the measure (e.g., some scales must be purchased), but the biggest expense is for compensating the people collecting the data if you cannot do it single-handedly. In such a situation, the instrument’s length may determine whether it is a viable option. Also, it is often advantageous to pay a participant stipend to encourage participation. Data collection costs should be carefully considered, especially if the use of expensive methods means that you will be forced to cut costs elsewhere (e.g., using a smaller sample).
· 2. Availability and familiarity. You may need to consider how readily available various instruments are. Data collection strategies with which you have had experience are often preferable to new ones because administration is usually smoother and more efficient in such cases.
· 3. Population appropriateness. Instruments must be chosen with the characteristics of the target population in mind. Characteristics of special importance include participants’ age and literacy levels. If there is concern about participants’ reading skills, the readability of a prospective instrument should be assessed. If participants include members of minority groups, you should strive to find instruments that are culturally appropriate. If non-English-speaking participants are included in the sample, then the selection of an instrument may be based on the availability of a translated version.
· 4. Norms and comparisons. It may be desirable to select an instrument that has relevant norms. Normsindicate the “normal” values on the measure for a specified population and thus offer a good comparison. Also, it may be advantageous to select an instrument because it was used in other similar studies to facilitate interpretation of study findings.
· 5. Administration issues. Some instruments have special requirements. For example, obtaining information about the developmental status of children may require the skills of a professional psychologist. Some instruments require stringent conditions with regard to the time of administration, privacy of the setting, and so on. In such a case, requirements for obtaining valid measures must match attributes of the research setting.
· 6. Reputation. Instruments designed to measure the same construct often differ in the reputation they enjoy among specialists in a field, even if they are comparable with regard to documented quality. Thus, it may be useful to seek the advice of knowledgeable people, preferably ones with personal, direct experience using the instruments.
If existing instruments are not suitable for some variables, you may be faced with either adapting an instrument or developing a new one. Creating a new instrument should be a last resort, especially for novice researchers, because it is challenging to develop accurate and valid measuring tools (see Chapter 15 ).
If you are fortunate to locate a suitable instrument, your next step likely will be to obtain the authors’ permission to use it. In general, copyrighted materials require permission. Instruments that have been developed under a government grant are often in the public domain and may not require permission. When in doubt, it is best to obtain permission. By contacting the instrument’s author for permission, you can also request more information about the instrument and its quality. (A sample letter requesting permission to use an instrument is in the Toolkit. )
TIP: In finalizing decisions about instruments, it may be necessary to consider the trade-offs between data quality and data quantity (i.e., the number of instruments or questions). If compromises have to be made, it is usually preferable to forego quantity—especially because long instruments tend to depress participant cooperation.
Pretesting the Data Collection Package
Researchers who develop a new instrument usually subject it to rigorous pretesting so that it can be evaluated and refined. Even when the data collection plan involves existing instruments, however, it is wise to conduct a pretest with a small sample of people (usually 10 to 20) who are similar to actual participants.
One purpose of a pretest is to see how much time it takes to administer the entire instrument package. Typically, researchers use multiple instruments and it may be difficult to estimate how long it will take to administer the complete set. Time estimates are often required for informed consent purposes, for developing a budget, and for assessing participant burden.
Pretests can serve many other purposes, including the following:
· Identifying parts of the instrument package that are hard for participants to read or understand
· Identifying questions that participants find objectionable or offensive
· Assessing whether the sequencing of questions or instruments is sensible
· Evaluating training needs for data collectors
· Evaluating whether the measures yield data with sufficient variability
With regard to the last purpose, researchers need to ensure that there is sufficient variation on key variables with the instruments they select. In a study of the link between depression and a miscarriage, for example, depression would be compared for women who had or had not experienced a miscarriage. If the entire pretest sample looks very depressed (or not at all depressed), however, it may be advisable to pretest a different measure of depression.
Example of Pretesting: Nyamathi and colleagues (2012) studied the factors associated with depressive symptoms in a sample of 156 homeless young adults. The study involved collecting an extensive array of data via self-reports. All of the instruments had been previously tested, modified, and validated for homeless populations, including pretests to evaluate clarity and sensitivity to the population.
Developing Data Collection Forms and Procedures
After the instrument package is finalized, researchers face several administrative tasks, such as the development of various forms (e.g., screening forms to assess eligibility, informed consent forms, records of attempted contacts with participants). It is prudent to design forms that are attractively formatted, legible, and inviting to use, especially if they are to be used by participants themselves. Care should also be taken to design forms to ensure confidentiality. For example, identifying information (e.g., names, addresses) is often recorded on a page that can be detached and kept separate from other data.
TIP: Whenever possible, try to avoid reinventing the wheel. It is inefficient and unnecessary to start from scratch—not only in developing instruments but also in creating forms, training materials, and so on. Ask seasoned researchers if they have materials you could borrow or adapt.
In most quantitative studies, researchers develop data collection protocols that spell out procedures to be used in data collection. These protocols describe such things as the following:
· Conditions for collecting the data (e.g., Can others be present during data collection? Where must data collection occur?)
· Specific procedures for collecting the data, including requirements for sequencing instruments and recording information
· Information for participants who ask routine questions about the study (i.e., answers to FAQs). Examples include the following: How will the information from this study be used? How did you get my name? How long will this take? Who will have access to this information? Can I see the study results? Whom can I contact if I have a complaint? Will I be paid or reimbursed for expenses?
· Procedures to follow in the event that a participant becomes distraught or disoriented or for any other reason cannot complete the data collection
Researchers also need to decide how to actually gather, record, and manage their data. Technologic advances continue to offer new options—some of which we discuss later in the chapter. Some suggestions about new technology for data collection are offered by Courtney and Craven (2005), Guadagno et al. (2004), and Hardwick et al. (2007).
TIP: Document all major actions and decisions as you develop and implement your data collection plan. You may need the information later when you write your research report, request funding for a follow-up study, or help other researchers with a similar study.
STRUCTURED SELF-REPORT INSTRUMENTS
The most widely used data collection method by nurse researchers is structured self-report, which involves a formal instrument. The instrument is an interview schedule when questions are asked orally in face-to-face or telephone interviews. It is called a questionnaire or an SAQ (self-administered questionnaire) when respondents complete the instrument themselves, either in a paper-and-pencil format or on a computer. This section discusses the development and administration of structured self-report instruments.
Types of Structured Questions
Structured instruments consist of a set of questions (often called items ) in which the wording of both the questions and, in most cases, response options are predetermined. Participants are asked to respond to the same questions, in the same order, and with a fixed set of response options. Researchers developing structured instruments must devote careful effort to the content, form, and wording of questions.
Open and Closed Questions
Structured instruments vary in degree of structure through different combinations of open-ended and closed-ended questions. Open-ended questions allow people to respond in their own words, in narrative fashion. The question “What was your biggest challenge after your surgery?” is an example of an open-ended question. In questionnaires, respondents are asked to give a written reply to open-ended items, and so adequate space must be provided to permit a full response. Interviewers are expected to quote oral responses verbatim or as closely as possible.
Closed-ended (or fixed-alternative) questions offer response options, from which respondents choose the one that most closely matches the appropriate answer. The alternatives may range from a simple yes or no (“Have you smoked a cigarette within the past 24 hours?”) to complex expressions of opinion or behavior.
Both open- and closed-ended questions have certain strengths and weaknesses. Good closed-ended items are often difficult to construct but easy to administer and, especially, to analyze. With closed-ended questions, researchers need only tabulate the number of responses to each alternative to gain descriptive information. The analysis of open-ended items is more difficult and time-consuming. The usual procedure is to develop categories and code open-ended responses into the categories. That is, researchers essentially transform open-ended responses to fixed categories in a post hoc fashion so that tabulations can be made.
Closed-ended items are more efficient than open-ended questions, that is, respondents can answer more closed- than open-ended questions in a given amount of time. In questionnaires, participants may be less willing to compose written responses than to check off a response alternative. Closed-ended items are also preferred if respondents are unable to express themselves well verbally. Furthermore, some questions are less intrusive in closed form than in open form.
4: Measurement and Data Quality
· For additional ancillary materials related to this chapter, please visit thePoint.
In quantitative studies, an ideal data collection procedure is one that measures a construct accurately, soundly, and with precision. Biophysiologic methods have a higher chance of success in attaining these goals than self-report or observational methods, but no method is flawless. In this chapter, we discuss criteria for evaluating the quality of data obtained by measuring constructs with structured instruments. We note that the field of measurement in health fields is evolving; a fuller discussion of the new directions and controversies, and a more detailed presentation of statistical issues in measurement, is provided in Polit and Yang (2015). We begin by discussing principles of measurement.
MEASUREMENT
Quantitative studies obtain data through the measurement of constructs. Clinicians also require that phenomena of interest be measured. Measurement involves assigning numbers to represent the amount of an attribute present in a person or object. Attributes are not constant: They vary from day to day or from one person to another. Variability is presumed to be capable of a numeric expression signifying how much of an attribute is present. The purpose of assigning numbers is to differentiate between people with varying degrees of the attribute.
Rules and Measurement
Measurement involves assigning numbers according to rules. Rules are necessary to promote consistency and interpretability. The rules for measuring temperature, weight, and other physical attributes are familiar to us. Rules for measuring constructs such as nausea or quality of life, however, have to be invented. Whether the data are collected by observation, self-report, or some other method, researchers must specify criteria for assigning numeric values to the characteristic of interest. When researchers or clinicians invent a set of rules to gauge a construct, they create a measure of the construct. Measures yield scores —numeric values that communicate how much of an attribute is present or whether it is present at all.
The rules for measuring constructs must be evaluated to see if they are good rules. It is not enough to have rules—the rules must yield quantitative information that truly and accurately corresponds to different amounts of the targeted trait. New measurement rules reflect hypotheses about how attributes vary. The adequacy of the hypotheses—that is, the worth of the measurements—needs to be assessed empirically.
Researchers (and clinicians) work with fallible measures. Instruments that measure psychosocial phenomena by means of self-reports or observation are more error-prone than physical measures, but few measurements are error-free.
Advantages of Measurement
What exactly does measurement accomplish? Consider how handicapped health care professionals would be in the absence of measurement. For example, what if there were no measures of body temperature or blood pressure? A major strength of measurement is that it removes subjectivity and guesswork. Because measurement is based on explicit rules, resulting information tends to be objective—that is, it can be independently verified. Two people measuring a person’s weight using the same scale would likely get identical results. Most measures incorporate mechanisms for minimizing subjectivity.
Measurement also makes it possible to obtain reasonably precise information. Instead of describing Alex as “rather tall,” we can depict him as being 6 feet 3 inches tall. With precise measures, researchers can differentiate among people with different degrees of an attribute.
Finally, measurement is a language of communication. Numbers are less vague than words. If a researcher reported that the average oral temperature of a sample of patients was “high,” different readers might interpret the sample’s physiologic state differently. However, if the researcher reported an average temperature of 99.8°F, there would be no ambiguity.
Theories of Measurement
Psychometrics is the branch of psychology concerned with the theory and methods of psychological measurement. Health measurement has been strongly influenced by psychometrics, although differences in aims and conceptualizations have begun to emerge. When new measures are developed and tested, researchers often say that they are undertaking a psychometric assessment.
Within psychometrics (and health measurement), two theories of measurement have been influential. Classical test theory (CTT) is a psychometric theory of measurement that has been dominant until fairly recently. CTT has been used as a basis for developing multi-item measures of health constructs and is also appropriate for conceptualizing all types of measurements (e.g., biophysiologic measures). An alternative measurement theory ( item response theory or IRT ) gaining in popularity is discussed in Chapter 15 . Unlike CTT, IRT is an appropriate framework only for multi-item scales and tests.
Errors of Measurement
Procedures for obtaining measurements, as well as the objects being measured, are susceptible to influences that can alter the resulting data. Some influences can be controlled or minimized, and attempts should be made to do so, but such efforts are rarely completely successful.
Instruments that are not perfectly accurate yield measurements containing some error. Within classical test theory, an observed (or obtained ) score can be conceptualized as having two parts—an error component and a true component. This can be written as follows:
Obtained score = True score ± Error
or
XO = XT ± XE
The first term in the equation is an observed score—for example, a score on an anxiety scale. XT is the value that would be obtained with an infallible measure. The true score is hypothetical—it can never be known because measures are not infallible. The final term is the error of measurement . The difference between true and obtained scores results from factors that distort the measurement.
Decomposing obtained scores in this manner highlights an important point. When researchers measure an attribute, they are also measuring attributes that are not of interest. The true score component is what they wish to isolate; the error component is a composite of other factors that are also being measured, contrary to their wishes. We illustrate with an exaggerated example. Suppose a researcher measured the weight of 10 people on a spring scale. As participants step on the scale, the researcher places a hand on their shoulders and applies pressure. The resulting measures (the XOs) will be biased upward because scores reflect both actual weight (XT) and pressure (XE). Errors of measurement are problematic because their value is unknown and also because they often are variable. In this example, the amount of pressure applied likely would vary from one person to the next. In other words, the proportion of true score component in an obtained score varies from one person to the next.
Many factors contribute to errors of measurement. Some errors are random, while others are systematic, reflecting bias. Common sources of measurement error include the following:
· 1. Transient personal factors. A person’s score can be influenced by such personal states as fatigue or mood. In some cases, such factors directly affect the measurement, as when anxiety affects pulse rate measurement. In other cases, personal factors alter scores by influencing people’s motivation to cooperate, act naturally, or do their best.
· 2. Situational contaminants. Scores can be affected by the conditions under which they are produced. A participant’s awareness of an observer’s presence (reactivity) is one source of bias. Environmental factors, such as temperature, lighting, and time of day, are potential sources of measurement error.
· 3. Response-set biases. Relatively enduring characteristics of people can interfere with accurate measurements. Response sets such as social desirability or acquiescence are potential biases in self-report measures ( Chapter 13 ).
· 4. Administration variations. Alterations in the methods of collecting data from one person to the next can result in score variations unrelated to variations in the target attribute. For example, if some physiologic measures are taken before a feeding and others are taken after a feeding, then measurement errors can potentially occur.
· 5. Instrument clarity. If the directions on an instrument are poorly understood, then scores may be affected. For example, questions in a self-report instrument may be interpreted differently by different respondents, leading to a distorted measure of the variable.
· 6. Item sampling. Errors can be introduced as a result of the sampling of items used in the measure. For example, a nursing student’s score on a 100-item test of critical care nursing knowledge will be influenced by which 100 questions are included. A person might get 94 questions correct on one test but 92 right on another similar test.
TIP: The Toolkit section of Chapter 14 of the Resource Manual includes a list of suggestions for enhancing data quality and minimizing measurement error in quantitative studies.
Major Types of Measures
Measurements for nursing research and practice can vary in a number of ways. For example, measurements can vary in terms of information source (i.e., self-reports, observation, etc.), complexity (e.g., a simple visual analog scale or a multidimensional scale with dozens of items), and type of scores they yield (e.g., continuous scores, categorical scores). Some measures are designed to be generic—that is, broadly applicable across different clinical or nonclinical populations; other measures are specific—that is, designed for use with specific groups of people. For example, there are self-efficacy scales that are generic, but there are many disease-specific self-efficacy scales (e.g., for diabetes or asthma).
Static and Adaptive Measures
Multi-item measures also differ with regard to whether they are static or adaptive. A static measure is administered in a comparable manner for everyone being measured. For a static composite scale, people complete an entire set of items and then are scored based on responses to all items. Most health-related measures are static. As an example, a widely used generic measure of depression is called the Center for Epidemiologic Studies Depression Scale, the CES-D (Radloff, 1977). Total scores on the CES-D rely on responses to the same 20 questions for everyone. Much of this book uses static scales to illustrate key measurement concepts.
An adaptive measure, by contrast, involves using responses to early questions to guide the selection of subsequent questions. Dynamic adaptive measures are becoming popular as a way to obtain precise information about an attribute with minimum respondent burden. Adaptive testing has its origin in measurement advances from item response theory. Item banks with hundreds of items have been created for broad health topics, such as physical function, pain, or sleep disturbance. The most important example of item banking is PROMIS® (Patient Reported Outcomes Measurement Information System), developed with support from the U.S. National Institutes of Health (Cella et al., 2007). An approach called computerized adaptive testing (CAT) uses these item banks to create measurements that are tailored to individuals. With such tailoring, the set of items used to measure a construct can be different for each patient. Despite item differences, cross-patient comparisons can be made because the testing places people along a dimension of interest.
Reflective Scales and Formative Indexes
An important distinction is whether a multi-item measure is formative or reflective, which concerns the nature of the relationship between a construct and the measure of the construct. Constructs are not directly observable—they must be inferred by the effects they have on observables, such as responses to items on a patient-reported outcome (PRO) or behaviors witnessed and recorded on an observational scale. Most health scales are reflective scales : The items are viewed as reflections of the construct. For example, on the CES-D, it is presumed that a person’s underlying level of depression causes him or her to respond in a certain way to the items about sleep disturbance, sadness, and so on. The items on a reflective scale share a common cause—in this case, level of depression. Items on reflective scales are expected to be interrelated because they all reflect (are caused by) the construct.
Not all multi-item instruments, however, are reflective. A multi-item measure can be conceptualized as having items that “cause” or define the attribute (rather than being the effect of the attribute). Such measures are called formative measures. Several writers advocate using the term scale for multi-item reflective measures, and the term index for multi-item formative measures (DeVellis, 2012; Streiner, 2003). A formative index involves constructs that are formed by its components, rather than causing them.
A good illustration of a formative index is the Holmes-Rahe Social Readjustment Scale, which is a measure of stress. Psychiatrists Holmes and Rahe studied whether stressful life events might cause illness and devised an index that asked patients to indicate which of 43 life events they had experienced in the previous year (Holmes & Rahe, 1967). Examples of life event items include death of a spouse, pregnancy, and change in residence. The life events are assigned different weights or “life change units” (e.g., 100 for death of a spouse, 20 for a change in residence), and the units are then added together. The sum of life change units defines the construct of stressful life events. The items are not the “effect” of the construct—for example, having high stress does not “cause” the death of a spouse or a residential move.
Because the items on an index are not caused by an underlying construct, they are not necessarily intercorrelated. In fact, items with modest correlations that capture different aspects of an attribute are often desired in a formative index. Many screening tools are formative and are composed of components that independently predict an outcome.
The development of reflective scales and formative indexes is necessarily different. For example, because the items on a formative index define the attribute, the specific items matter very much. If the item “I had crying spells” on the CES-D scale was removed, for example, the other 19 items could carry most of the burden of measuring depression. But if the item “Death of a spouse” was removed from the Holmes-Rahe index, the score would misrepresent the stress levels of people who had lost a spouse. Another consequence of having noncorrelated items on a formative index is that some of the standard assessment methods associated with CTT are not appropriate, as we explain later in this chapter.
TIP: Formative indexes are seldom created using standard psychometric approaches. Formative indexes are sometimes developed within the field of clinimetrics, which is devoted to the development of measures of clinical phenomena. Polit and Yang (2015) have written a chapter on clinimetrics in their measurement book.
MEASUREMENT PROPERTIES: AN OVERVIEW
In making decisions about how to measure their constructs, careful researchers select instruments that are known to be psychometrically sound—that is, ones that have good measurement properties . Psychometricians have traditionally focused on two measurement properties when assessing the quality of a measure: reliability and validity. Measurement experts in health disciplines, however, have taken a broader view of the measurement properties of an instrument.
A Measurement Taxonomy
The field of health measurement was in some turmoil for many years with regard to measurement terminology and definitions. Recently, a working group in the Netherlands used a Delphi-type approach with a panel of health measurement experts to identify key measurement properties and to develop a taxonomy and definitions of those properties. The result was the creation of COSMIN , the Consensus-based Standards for the selection of health Measurement Instruments (Mokkink et al., 2010a, 2010b; Terwee et al., 2012). (Information about COSMIN can be accessed at http://www.cosmin.nl .) Polit and Yang (2015), building on the groundbreaking COSMIN work, made small modifications to the taxonomy to more clearly incorporate a time perspective. A graphic depiction of the Polit-Yang measurement taxonomy is shown in Figure 14.1 .
In this taxonomy, there are four measurement property domains. Two are cross-sectional—that is, they concern the quality of measurements at one point in time. These cross-sectional domains are reliabilityand validity, the properties used for decades by psychometricians. Two other domains in the taxonomy concern longitudinal measurement—that is, the quality of measurements capturing changes over time. These two domains are called the reliability of change scores and responsiveness. New measures that are likely to be used to measure a construct at a single point and to assess how the construct changed over time ideally would be evaluated for all four measurement properties. The taxonomy also incorporates another concept—interpretability—that has relevance for both point-in-time scores and change scores.
Each measurement property can be evaluated by estimating measurement parameters that quantify the degree to which the scores on the measure have desirable properties. These estimates are the means by which conclusions can be drawn about an instrument’s quality. Estimates of measurement properties are relevant for particular applications and particular populations, and so researchers need to carefully consider the comparability of their sample to the sample used in measurement assessments of a given instrument.
TIP: The Toolkit for Chapter 14 in the accompanying Resource Manual includes a summary table that specifies measurement parameters that are relevant under different scenarios.
The four measurement property domains and the two interpretability aspects correspond to six key measurement questions, which we illustrate with an example. Suppose we were testing the effects of a nurse-led support program for family caregivers of patients with dementia and one of our outcome variables was depression. Suppose that we found that a participant in the intervention group had a score of 20 on the CES-D at baseline (high level of depression) and a score of 15 (less depression) at a 6-month follow-up. Six questions we could ask, corresponding to the elements in the measurement taxonomy, are as follows:
· 1. Reliability: Is the score of 20 at baseline the right score for this patient—is it a dependable score value?
· 2. Validity: Is the scale truly measuring the construct depression, or is it measuring something else?
· 3. Interpretation of a score: What does a score of 20 mean? Is it high or low?
· 4. Reliability of change: Is the change from 20 to 15 a real change, or does it merely reflect random fluctuations in measurement?
· 5. Responsiveness: Does the change from 20 to 15 correspond to a commensurate improvement in degree of depression?
· 6. Interpretation of a change score: What does a 5-point improvement mean? Is the improvement large enough to be considered clinically significant?
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