Statistical Test Selection and Analysis

J Wound Ostomy Continence Nurs. 2008;35(6):561-568. Published by Lippincott Williams & Wilkins SPOTLIGHT ON RESEARCH From the Center for Clinical Investigation Statistical Test Selection and Analysis Demystifying a Mysterious Process Janice M. Beitz Introduction Modern healthcare practice mandates that registered nurses and nursing students be able to critique and utilize patient-related research. Critique of newly published research contains many components, one of the most challenging being the statistical analysis or selection processes. Based on personal experiences as a student and teacher in graduate and undergraduate nursing research courses, doctoral education in psychometrics, and generating and publishing research, I believe that quantitative statistical analysis can intimidate some nurses because of what has been called metacognitive inhibition. 1 Metacognition is an internal cognitive process whereby people know their personal learning processes and recognize difficult tasks when they see them. 2 Usually learners (eg, nurses) use metacognitive skills without difficulty. In the case of statistical analysis and statistics usage, the inherent abstract and sometimes complex nature of the subject makes neophyte researchers and neophyte users of research struggle for a metacognitive perspective. WOC nurses and other healthcare clinicians need not be intimidated by statistical analysis because metacognitive components do pervade its structure. Following certain guidelines and answering crucial questions can help the nurse see the big picture and gain facility with the content. I have termed these questions and guidelines the statistical cognitive schema. 1 Thankfully many authors have written about and offered suggestions for teaching and learning the selection and analysis of statistical tests. Facilitating approaches have included critical concepts development and graphic organizers, 3 linking the research question(s) and hypothesis(es) to the analysis, 4 instructional strategies incorporating situated cognition (real-world) application exercises, 5 practice and drill problems, 6 emphasis on exploration of students statistical thinking and grasp of fundamental, foundational ideas of statistics, 7 incorporating digital analysis of research problems using a laptop computer, 8 designing tables on statistical test selection, 9 following guidelines and using golden rules, 10 creating a top ten list of recommendations for teaching and learning statistical analysis and inference, 11 and selecting statistical tests in light of type I error. 12 A recent study analyzed statistical test selection in reverse. Zellner and colleagues 13 scrutinized all quantitative research articles published in 13 nursing journals in 2000. They identified 10 primary statistics that were used most often (representing 80% of all statistical measures used in the 462 articles reviewed). The statistics included mean, frequency distribution, standard deviation, range, percentiles, percentages and quartiles, t test (dependent and independent), analysis of variance (ANOVA) (all kinds), correlation, the Cronbach, and 2. The authors suggest that neophyte and experienced nurses should clearly understand these basic statistical analyses to optimally interpret published healthcare research and also to conduct research. The ultimate metacognitive questions for the WOC nurse are as follows: (1) Do the researcher(s) use the appropriate statistical tests in this study? (2) What question do they answer? and (3) How does a WOC nurse researcher select the correct analytic tests and processes? I believe that the greatest amount of confusion surrounding quantitative analysis and statistical test selection relates to applying statistics to actual situations. WOC nurse investigators who are determining their analytic approach would start with their research question and design to determine the appropriate statistical test. Heuristic devices can be used to further ease the selection process. To facilitate answering the question of what test should be used to answer this research question in the context of the design, I have developed several helpful aids. First of all, there is what the author calls the statistical cognitive schema. 1 These are questions Janice M. Beitz, PhD, RN, CS, CNOR, CWOCN, CRNP, Professor of Nursing, WOCNEP Codirector, School of Nursing and Health Sciences, La Salle University, Philadelphia, Pennsylvania. Corresponding author: Janice M. Beitz, PhD, RN, CS, CNOR, CWOCN, CRNP, School of Nursing and Health Sciences, La Salle University, 1900 W Olney Ave, Philadelphia, PA 19141 (beitz@lasalle.edu). Copyright 2008 by the Wound, Ostomy and Continence Nurses Society J WOCN November/December 2008 561

562 Beitz J WOCN November/December 2008 TABLE 1. Descriptive and Inferential Statistics: Applications Term Definition a Real-World Application Descriptive Statistics: Measures of Central Tendency (Centrality) Mean Median Mode The arithmetic average; sum of measures divided by the number of measures; a trustworthy estimate of population parameters for normally distributed data when used with confidence intervals and/or SD Middle value of an ordered set of numbers; 50% of distribution is below median; find middle value of an odd set of ordered numbers or compute mean of 2 middle values for an even set of ordered numbers Most frequently occurring value; if all measures are different, no mode exists; if 2 numbers occur with equal frequency, called bimodal A WOC nurse wishes to know the average result for a class of 50 staff registered nurses on a pressure ulcer knowledge test A WOC nurse wishes to know the value of the 50th percentile rank in an ordered distribution of results on a skin care test given to licensed practical nurses and nurses aides A WOC nurse researcher wants to know the most frequent response in a 5-point survey, helping the nurse spot clustering of responses Descriptive Statistics, Measures of Dispersion (Spread) Variance SD Range Quartiles (interpercentile measures) Percentiles (not percentages) z score (standard score) SE, SEM The square of the SD; sum of the squared deviation of each value from the mean divided by n 1; not used as often as SD in healthcare Commonly used measure of variability for normally distributed data; square root of the variance; tells variability around the mean; can use to plot sample raw scores in terms of normal curve Difference between the maximum value (highest measure) and minimum value (lowest measure); highly sensitive to extreme values Interquartile range range of values extending from 25th to 75th percentile; find median (50th percentile) 1st quartile is middle values of all scores below median; 3rd quartile is same distance above Tells the relative position of a given score in a distribution of scores, allows researcher to compare scores on separate tests that have different means and SDs; calculated by number of scores less than a given score divided by total number of scores multiplied by 100; can convert raw score to z score to percentile using a conversion table Standard score expresses a score in terms of its distance from the mean and in terms of the normal curve. z score is calculated by subtracting mean score from the raw score and dividing by the SD of the distribution of scores A statistical index of the probability that a given sample mean is representative of all means from data repeatedly drawn A WOC nurse wants a general sense of how scores were distributed in a standardized staff development test on ostomy care A WOC nurse researcher wants to know how much on average nurse externs test scores vary around the mean score on a skin and wound care module final examination A WOC nurse tracking WOC patient census data wants to know the spread of patients served monthly during the last 12 mo A WOC nurse wants to know how many patients from ICU and on WOC service were in the highest and lowest quartiles in terms of critical care acuity ratings A WOC nurse researcher wants to compare an individual student s score on 2 standardized different tests; a test on WOC knowledge and a comprehensive National Council Licensure EXamination-Registered Nurse preparation test A WOC researcher wants to know a patient s relative performance on 2 different valid and reliable physiologic tests (eg, may have z score of 1.0 [84th percentile] on respiratory function and z score of 0 [50th percentile] on cardiac function A WOC nurse researcher uses the SEM to predict or identify the intervals into which 68%, 95%, or 99% of results would fall. (continues)

J WOCN Volume 35/Number 6 Beitz 563 TABLE 1. Descriptive and Inferential Statistics: Applications (Continued) Term Definition a Real-World Application SE of measurement from the same population. The formula is SD/square root of the size of the sample (larger sample size, the smaller the standard error). Can be used to identify the confidence intervals of the mean) SE of measurement is a measure of the extent to which test takers scores vary over repeated testings with different questions, test conditions, etc. A small SEM is associated with higher test reliability because repeated testing is not affected by error factors. The formula is SD times the square root of 1 minus reliability coefficient of the test. Permits an estimate of error to use when interpreting a person s test score For example, the number of stomal and peristomal complications in a sample vs a population of ostomates A WOC nurse researcher tests knowledge of ostomy complications management in a sample of WOC nurses using a standardized test with an SE of measurement of 2. Researcher knows that students true scores lie between 4 points below (2 SEM below) and 4 points above (2 SEM above) their obtained test scores with 95% assurance Inferential Statistics: Parametric (Interval Ratio Data that are normally distributed) (Must consider P value with interpretation to avoid chance occurrence) test (independent) test (dependent) ANOVA 1-way Two-way ANOVA Multivariate analysis of variance Used to test difference between 2 independent groups mean results. Participants in 1 group are not in the other group Used to test the difference between 2 means of same group tested twice (eg, pretest posttest) May also be used to test 2 dependent groups created when participants are explicitly matched on some relevant characteristics and separated with 1 of each pair assigned to each group. Occasionally, identical twins are used as matched pairs Used to test difference in group means when there are more than 2 groups. Post hoc tests, which control the overall level, are used to determine which group(s) is (are) significantly different if ANOVA F statistic gives statistically significant result Tests the differences between group means when there are more than 1 IV and 1 DV; tests main effects and interactive effects (IV 1; DV 1) Tests the differences in group means (more than 2 groups) when there are more than 1 IV and more than 1 DV. (IV 1; DV 1) A WOC nurse researcher investigates knowledge of deep tissue injury in certified and noncertified registered nurses; compares mean scores on standardized DTI Inventory in 1 group vs another. A WOC nurse institutes an incontinence cessation program with 40 men and women. She tests entire group before and after the intervention. A WOC nurse researcher tests 5 groups of allied health students (nurses, physical therapists, occupational therapists, physician assistants, and clinical psychology students) on knowledge of wound healing. Researcher wants to know whether any group or groups knew significantly more about wound healing A WOC nurse researcher wants to examine the effect of gender (male vs female) and chronic illness presence (yes vs no) on health promotion knowledge; main effects are gender and chronic illness presence; also checking for interaction of both gender and chronic illness presence A WOC nurse researcher wants to test the effect of guided imagery and massage therapy on pain responses of 3 groups of postoperative patients (colostomy, ileostomy, and urostomy). Pain responses are facial grimace, moaning, and muscle tensing. (continues)

564 Beitz J WOCN November/December 2008 TABLE 1. Descriptive and Inferential Statistics: Applications (Continued) Term Definition a Real-World Application Analysis of covariance Repeated measures ANOVA (also called within subjects design or RANOVA) Correlation (bivariate or simple) Regression (bivariate or simple) Regression (multivariate or multiple) Standard Regression (multivariate) Stepwise Regression (multivariate) Hierarchical Logistic regression Canonical correlation Discriminant function analysis Combines regression with ANOVA; allows the researcher to measure groups mean differences when certain variables (covariates) are controlled. May reduce variability and error Examines the effect(s) of individuals particular state when a test or an instrument is administered or some measurement is taken; can be used to test same variable over time on group(s) of subjects or can expose same subjects to various levels of treatments (eg, dosages of drugs) Examines the strength and nature (positive, negative [inverse, none] of relationship between 2 variables that are normally distributed and have a linear relationship Examines the predictive ability of 1 variable for another variable if temporal order can be established between IV and outcome variables. If cross-sectional study, can be used to assess the association Examines the predictive ability of several ( 1) IVs for 1 DV (all IVs entered into computer analysis at the same time) if temporal order can be established between IVs and outcome variable. If cross-sectional study, can be used to assess the association Examines which variable or group of IVs best predicts a measure of the DV. The computer analysis discerns which variables add most to the prediction. If cross-sectional study, can be used to assess the association Examines the predictive ability of several IVs on 1 DV when the researcher controls the order in which variables enter the model. Tests the association of 1 or more IVs when the DV is dichotomous, ordinal, or categorical (polytomous) level data (eg, healed vs not healed) Analysis permits the researcher to assess the association of multiple variables on several other variables (really 2 sets of variables; looks at how they are related as groups of variables) Allows the researcher to discriminate or distinguish among groups based on selected variables; identifies which set of variables will most clearly distinguish among groups with the minimal probability of misclassification A WOC nurse researcher wants to compare the mean scores of patients in 3 different types of ostomy education program formats on a standardized ostomy test; the covariate (possible confounding variable) is amount of knowledge on group entry. A WOC nurse researcher wants to test the effect of 3 forms of counseling over 6 mo in urinary incontinence clients. Data gathered at 1 wk, 1 mo, 3 mos, and 6 mos on same 3 groups of incontinence clients. A WOC nurse wants to know whether anxiety is related to poor self-care in ostomates (and, if related, how strongly and in what manner) A WOC nurse wants to examine the ability of 1 variable, self-esteem, to predict successful ostomy adaptation over time A WOC educator wants to examine the ability of measures of reading level, mathematics scores, and type of basic educational program to predict success on a comprehensive WOC examination A WOC nurse researcher is examining the effect of 7 IVs on wound healing. She wants to know which variables are the best predictors Nurse researcher wants to examine predictive value of sets of IVs including demographic, social, and treatment variables in 3 steps in specific order. A WOC researcher wants to examine the association of grades in WOCNEP and SAE scores on success in WOCN certification (pass-fail) A WOC nurse researcher wants to examine the association of the patient s age, albumin level, and size of pressure ulcer (cm) on psychological adaptation and wound healing A WOC nurse is examining adaptation to chronic illness. The researcher uses discriminant analysis to determine which factors differentiate the following groups: stress UI, urge UI, functional UI (continues)

J WOCN Volume 35/Number 6 Beitz 565 TABLE 1. Descriptive and Inferential Statistics: Applications (Continued) Term Definition a Real-World Application Factor analysis A procedure that allows for data reduction ; a large number of variables are reduced into a smaller number of factors which represent a common underlying domain; is often used in instrument development and theory testing Using Orem s self-care theory, a WOC nurse researcher has developed the stoma quality of life and self-care inventory with 3 underlying themes. The researcher uses factor analysis to determine if 3 underlying factors are identified when the instrument is administered to ostomates Inferential Statistics: Nonparametric (Nominal-Ordinal Data, nonnormally distributed interval data) 2 Mann Whitney U test Kruskal Wallis H-Test Wilcoxon matched pairs rank test Friedman matched samples Spearman rank order correlation Compares expected frequencies in groups ( 1) with the actual frequencies. Expected frequencies are determined by the marginal frequencies under the assumption of no association between groups. If no special influencing factor at work, all groups should have equal proportions of any measure. The nonparametric parallel to the independent test, allows the researcher to compare the ranked scores of 2 mutually exclusive groups using ordinal level data or nonnormally distributed interval data The nonparametric parallel to the ANOVA; compares 3 or more groups ranked scores on some research variable or nonnormally distributed interval data The nonparametric equivalent of the dependent (paired) test; used with ordinal level data or nonnormally distributed interval data The nonparametric equivalent of the repeated-measures ANOVA; used to test same group of people at several different times using ordinal level data or nonnormally distributed interval data The nonparametric equivalent of the Pearson correlation, uses ordinal level data or nonnormally distributed interval data; compares the ranked responses of 2 groups and displays strength and nature of relationship between the 2 variables; relationship is assumed to be linear A nurse epidemiologist is tracing cancer occurrences in the northeast section of a large state. She examines 5 counties proportions of cancer via 2 to see whether there is a cancer zone. The Brace Stress Inventory gives ordinal level data; a nurse researcher gives it to measure differences in ranked stress scores in surgical intensive care unit vs medical intensive care unit nurses The JAC Hypertension Screening Inventory is given to ICU, OR, and labor and delivery nurses to measure risks for high blood pressure. The JAC Inventory gives ordinal data The Brace Stress Inventory is given to neophyte OR nurses at 1 mo and 6 mo; differences in ranked scores are compared In a research study on stress in nurses, the researcher administers the Brace Stress Scale to OR, homecare, and ICU nurses at 1 mo, 3 mo, and 6 mo A WOC nurse researcher asks WOC nurses working in the hospital and WOC nurses in home care to rank the stressors associated with their work; the researcher compares the data Abbreviations: ANOVA, analysis of variance; DTI, deep tissue injury; DV, dependent variable; ICU, intensive care unit; IV, independent variable; OR, operating room; UI, urinary incontinence. a The term measure is used to describe raw data that are not the result of valid and reliable instruments or scales such as height or weight; score is the term reserved for data from valid and reliable tools. of vital importance. When the WOC nurse researcher or research consumer clearly knows the answers to these questions, statistical test selection and/or analytic critique becomes much easier. These crucial questions include the following: 1. What is the research question? Basically, what are differences between groups or associations? 2. What are the independent and dependent variables of the research study in studies that test hypotheses? (It is important to remember that some research

566 Beitz J WOCN November/December 2008 TABLE 2. Golden Reminders for Research and Statistics a When everything else fails, diagram the research design: identify the variables (IV and DV if experimental or quasi-experimental design). Experimental research design requires at least 1 IV and 1 DV for statistical analysis Never forget that quality research designs and rigorous data collection processes really matter ; statistical tests do not make up for poor research processes; in other words, garbage in, garbage out In most instances, a larger sample size makes for a stronger study (increased power). This is called the law of larger numbers. As random observations increase, the closer the sample mean approximates to the population mean In testing the effects of a treatment, the IV must have 2 or more levels (eg, treatment, no treatment) Some research does not test a hypothesis. The researcher just wants to describe what is out there. In other words, you should decide whether hypotheses are confirmatory (testing something) or exploratory (searching) A common statistical mistake in healthcare research is to treat related data as unrelated data. For example, 30 leg ulcers in 20 patients are not 30 independent measures because there are still only 20 patients. Analyses have to be chosen that accommodate related measures Recognize synonyms when you see them. Both IVs and DVs are called by many names including independent: input, cause, antecedent dependent: outcome, effect, consequence When looking at measure of central tendency, the mean is not always the best statistic. For example, depending on the purpose or distribution of the data (eg, nonnormal), the median or mode may be more appropriate. Outlier scores may skew the mean substantially Interpret measures of centrality with measures of dispersion 2 samples with the same mean can have very different distributions of data Clarify early on the nature (level of measurement) of the IV and DV. There are several possibilities: Categorical IV and continuous DV Categorical IV and categorical DV Continuous IV and continuous DV Continuous IV and categorical DV Categorical data are nominal and ordinal level; continuous data are interval or ratio. The levels of data determine which statistical tests you should select If you are familiar with the literature on a research topic and evidence is available that a directional hypothesis is appropriate, use a directional hypothesis. You will be able to use a 1-tail P value for analyses. A 1-tail test permits easier statistical significance with smaller sample size In any inferential statistical test, always check the level of significance (P value) to avoid chance occurrence. For example, a result that is significant at the.05 level means that with 95% assurance the result did not occur by chance alone Correlation does not mean causation Use technology to explore visually properties of research variables and relationships. Graphs, histograms, and scatterplots are extremely helpful in identifying hidden meaning and assessing possible violations of assumptions for statistical tests. These capacities are inherent in common desktop software (eg, Excel) Always accompany tests of significance with confidence intervals. This added step helps you understand the difference between strong evidence of an effect (P value) and strong effect (large difference between means) Effect size and power are critical concepts in statistical utilization. A variable with a stronger effect size will give more powerful results with lesser sample size. A weak effect requires a larger sample for adequate power to detect significant differences between groups Clinical significance and statistical significance are different concepts. Clinical significance refers to meaningful difference or impact based on clinical judgment. For example, an investigational new drug that lowers blood pressure by only 4 mm Hg on average may be statistically significant but not clinically significant. Statistical significance means the findings did not occur by chance Abbreviations: DV, dependent variable; IV, independent variable. a From references 3,7,10,11,13-17. designs [eg, descriptive] do not have independent or dependent variables because they are not experimental or quasi-experimental; clearly defining the variables of interest is sufficient in these cases.) 3. In studies involving comparisons, how many groups are being studied? One, 2, more than 2? Do the groups consist of different people so that the data are independent or unpaired? Or, do the same people comprise the groups so that the data resulting are dependent or paired? 4. What level of data is involved? Levels of data can be nominal or categorical, or dinal or ranked, or interval/ratio? (When possible, use interval/ratio level data, do not categorize, because information is lost and false associations can be created in categorizing). Nonparametric statistical tests are used for nominal and ordinal data and parametric tests (if normally distributed) are used for interval/ratio level data. 5. Are the ratio/interval data normally distributed? 6. What statistical test fits the criteria in 1 to 5? Does it analyze centrality (measures of central tendency) (eg, mean, median, mode)?

J WOCN Volume 35/Number 6 Beitz 567 TABLE 3. Application Exercises for Statistical Test Selection Example A The WOC nurse wants to identify whether 2 inpatient units with very heavy patient loads that are located in 2 different hospitals of a 3-hospital system have the same types (acuity levels) of patients. For the dependent variable or outcome, the WOC nurse researcher categorizes the patients according to diagnosis as orthopedic, integumentary, or vascular. The independent variable and dependent variable are both nominal (categorical) data. Example B A WOC nurse researcher wants to examine the effect of a pelvic floor rehabilitation program on men s stress incontinence status post radical prostatectomy controlling for type of surgical procedure (open vs traditional, laparoscopic vs robotic surgery). Incontinence episode is interval/ratio level data (number of episodes). Examination A WOC nurse researcher wants to know if patient race/ethnicity affects the efficacy of pressure ulcer healing. The WOC nurse randomly assigns patients from 3 groups (Hispanic, African American, Asian) to 1 of 2 different treatment regimens, for example, group I is standard care (hydrogel) vs treatment (silver hydrogel). The outcome is pressure ulcer healing measured by decrease in wound area (size) in centimeters. For each example: Identify (1) The IV(s) and DV(s) of the research scenario (if experimental) or clearly identify the variables of interest. (2) How many groups are being studied? If more than 1, are they independent or dependent groups? (3) What level of data is involved for each variable? What statistical test(s) should be chosen? (Use the metacognitive chart) Abbreviations: DV, dependent variable; IV, independent variable. Does it analyze spread (measures of dispersion) (eg, variance, range, standard deviation)? Test mean differences (eg, t test, ANOVA), Mann- Whitney U, Wilcoxon, Kruskall-Wallis ANOVA for nonparametric data Test relationships (eg, Pearson correlation, Spearman correlation, 2 test of association) Test predictive ability (eg, regression; if a temporal, ie, time sequence) order is clear) 7. How does one know what the statistical output means? A P value is a level of specified assurance that the result did not occur by chance alone. A confidence interval is range of measures that has a known probability of including the individual s true score or the true result; most typically 68%, 95%, 99%? 8. Does the selected statistical test answer the research question or address the hypothesis? Table 1 facilitates the WOC nurse in selecting an appropriate statistical test and discerning among the most common statistics and statistical tests; in addition, realistic examples that are pertinent to WOC nursing practice are offered to enhance understanding. Another aid is a collection of Golden Reminders, what Robinson 10 has insightfully called cautionary checkin points. These are listed to remind WOC nurses that statistical test selection is just 1 component of the entire research planning and enactment process, such as clearly identifying the research question and choosing an appropriate design (Table 2). The best way to learn the process of statistical test selection is to practice selection of statistical tests for different types of research questions. Table 3 presents sample scenarios for practice. Summary Application of abstract statistical concepts and processes to real-world situations can be facilitated by metacognitive perspectives and heuristic devices. By analyzing data and understanding applications of statistical analysis, WOC nurses will develop and nurture the metacognitive skills necessary for critical thinking in research and become avid, enthusiastic consumers of published research, thus promoting improved patient care. References 1. Beitz J. Helping students learn and apply statistical analysis: a metacognitive approach. Nurse Educ. 1998;23(1):49-51. 2. Flavell J, Wellman H. Metamemory. In: Kail RV, Hagen JW, eds. Perspectives on the Development of Memory and Cognition. Hillsdale, NJ: Lawrence Erlbaum Associates Inc; 1977:3-33. 3. Carlson M. Graphic organizers can facilitate selection of statistical tests Part I: analysis of group differences. J Phys Ther Educ. 2005;19(2):57-65. 4. Dinov I. Choosing the right test. http://www.socr.ucla.edu/ applets.dir/choiceoftest.htm. Accessed June 27, 2007. 5. Darvin J. Real-world cognition doesn t end when the bell rings : literacy instruction strategies derived from situated cognition research. J Adolesc Adult Literacy. 2006;49(5):398-407. 6. Gelman A. A course on teaching statistics at the university level. Am Stat. 2005;59(1):4-7. 7. Groth RE. An exploration of students statistical thinking. Teach Stat. 2006;28(1):17-21.

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