NOTE: Please see the attached file for additional information. Using the Internet or the online library, find a report that includes data collection related to your topic (secondary analysis). Using

Week 8-Assignment, Rubric & Lesson Content

Assignment:

Using the Internet or the online library, find a report that includes data collection related to your topic (secondary analysis). Using Excel or the WolframAlpha website at www.wolframalpha.com, analyze the data provided using one of the inferential statistical techniques (ANOVA, multiple regression, and paired t-test).

Requirement:

Prepare a one-page report that includes the data found, and interpretation of the data (what does it mean), an evaluation of the data (how important the data is to proving or supporting the topic), and presentation of the data in graphical form. Your document should be in Word with an Excel spreadsheet inserted in the document.

APA Format with In-Text citations.

Save your assignment as a Microsoft Word document

Rubric:

Lesson Content:

Inferential Statistics

Inferential statistics allow investigators to detect differences or associations between groups and to generalize those findings from the sample to the entire population of interest. Inferential statistics are based on probability theory (Singleton 179 and Straits 2010, 509) and have two purposes. The first purpose of inferential statistics is to make predictions (inferences) about the population’s characteristics (parameters) from the sample’s characteristics. The second purpose is to test hypotheses—the researcher’s measurable suppositions. This section builds on the information provided in the previous section, explaining some of the commonly encountered inferential statistical tests that were briefly described in table 9.1 and helping readers choose the appropriate inferential statistical test by matching the selection factors to the features of an individual study.

Independent One-Sample t-Test

The independent one-sample t-test is used to detect differences when (1) the dependent variable is continuous (interval or ratio) and normally distributed, and (2) the data are independent observations. There is no independent variable. The independent one-sample t-test detects differences between a group’s mean and a “hypothesized value.” The independent one-sample t-test is also known as the one-sample t-test. Examples of “hypothesized values” include a mean derived from previous research or the literature, a mean based on theory, a benchmark, a historical value, or a known population mean. For example, a health information coding supervisor could compare the coding productivity—minutes per record—of the integrated delivery system’s 32 coding professionals against a benchmark productivity standard—minutes per record— published in the literature.

Independent-Measures t-Test

The independent-measures t-test is used to detect differences in means when (1) the independent variable is dichotomous (for example, gender: male or female; educational level: high school or university) and nominal, (2) the dependent variable is normally distributed and continuous (interval or ratio), and (3) the two samples are independent. The independent-measures t-test is also known as the independent t-test, the independent-samples t-test, the two-sample t-test, the unpaired t-test, and the Student’s t-test. For example, researchers used an independent-measures t-test to compare the e-health literacy among users and nonusers of social media for health information (Tennant et al. 2015, 4). The independent-measures t-test is often used to detect whether outcomes differ between the experimental group and the control group.

Mann-Whitney U Test

The Mann-Whitney U test has the same purpose as the independent measures t-test, except the Mann-Whitney U test detects differences in two groups’ medians and the test is nonparametric. The Mann-Whitney U test is used when (1) the independent variable is dichotomous (male-female) and nominal, (2) the dependent variable is ordinal or nonnormally distributed continuous (interval or ratio), and (3) the two samples are independent. Other names for the Mann-Whitney U test are the Mann–Whitney–Wilcoxon (MWW), the Wilcoxon rank-sum test, or the Wilcoxon–Mann–Whitney test.

A Mann-Whitney U test could be used, for example, to compare opinions of seminar participants at two different professional meetings who attended an expert’s “Big Data” session (which used the same content and slides at both meetings). The two groups of participants ranked their agreement on the value of the session to their work on a Likert scale (strongly agree = 5, agree = 4, neutral = 3, disagree = 2, strongly disagree = 1). The expert could use the Mann-Whitney U test to compare the two sessions’ median rankings by the two groups of seminar participants.

Chi-Square Test

The chi-square test is used to compare results when (1) the dependent variable is nominal or ordinal and there is no independent variable or both the independent and dependent variables are nominal or ordinal, (2) the samples are independent, and (3) the cells contain more than five responses (see the boxes in table 9.6 for examples of cells). Chi stands for the 22nd letter of the Greek alphabet—similar to X in English—and is sometimes shown as χ; thus, chi-square is sometimes designated as χ2 in journal articles. There are two applications of the chi-square: chi-square goodness of fit and the chi-square test of independence. Both are nonparametric tests. The chi-square goodness of fit is used to determine whether the distribution of subjects’ responses is significantly different from the “hypothesized” distribution. The single variable is dichotomous (for example, gender: male chief information officers versus female chief information officers). The researchers could be interested in whether the 180 actual proportion of male and female chief information officers is significantly different from the hypothesized proportions. In the chi-square goodness of fit test, the proportions can be equal or unequal. The chi-square goodness of fit is also called the one-sample goodness-of-fit test and the Pearson’s chi-square goodness-of-fit test. The chi-square test of independence is used to determine whether significant differences exist when (1) there are two nominal or ordinal dependent variables, (2) the independent variable is nominal or ordinal and the dependent variable is ordinal or nominal, and (3) the samples are independent. Other names for the chi-square test of independence are just chi-square, the Pearson chi-square test, and the chi-square test of association. The chi-square test of independence can also be used to as a probe to determine whether an association exists between nominal and ordinal variables. However, the chi-square test does not show the strength of the relationship (association).

For example, researchers conducted a study in which they retrospectively reviewed a convenience sample of EHRs from one home health agency. Using the chi-square test of independence, comparisons were made by age categories, gender, and ethnicity for the frequency of prescribed medication categories and polypharmacy (concurrent prescriptions of more than 4 prescriptions). Statistically significant differences in prescription frequency of cardiovascular agents were found when comparing (1) patients 65 years or older and patients younger than 65 years, and (2) female patients and male patients. Additionally, statistically more white patients than African-American patients met the criterion of polypharmacy (Arena et al. 2015, 98–100).

Fisher Exact Test

The Fisher exact test is used rather than the chi-square test if one of the data cells in the contingency table is 5 or less. For example, in the hypothetical contingency table (table 9.6), the value in the cell for “Rural Hospitals–Adequate access to behavioral health services” is 3, which means the Fisher exact test could be used.

Paired t-Test

The paired t-test is used to detect differences in means when (1) the independent variable is nominal, (2) the dependent variable is continuous, and (3) the samples are dependent, such as the same group with two observations, dyads (supervisor-employer, husband-wife), or matched groups (Cohen 2013, 341–343, 354–355). Several terms are used for this statistical test, depending upon the exact composition of the groups: dependent t-test, paired-samples t-test, related-samples t-test, matched-samples t-test, within-persons t-test, and repeated measures t-test. For example, researchers used the paired t-test to evaluate providers’ knowledge of driving safety for older adults in terms of the providers’ self-assessed preparedness as well as their documentation of assessment and management. Embedded in the EHR was a driving clinical support tool. Providers’ self-assessed preparedness and their documentation were evaluated before and after training on the tool. The post-training evaluation showed significantly increased self-assessed preparedness and improved documentation (Casey et al. 2015, S136).

Wilcoxon Signed-Rank Test

The Wilcoxon signed-rank test is used to detect differences in medians when (1) the independent variable is nominal, (2) the dependent variable is ordinal or continuous, and (3) the samples are dependent, such as two observations on the same subject. As a hypothetical example, leaders of an integrated delivery system asked the Big Data expert to present a two-day seminar on Big Data applications to its supervisory personnel. At the beginning of the first day of the seminar, the expert had the participants rank their agreement on the value of Big Data to their work on a Likert scale (strongly agree = 5, agree = 4, neutral = 3, disagree = 2, strongly disagree = 1). At the end of the seminar’s second day, the expert again had the participants rank the value of Big Data to their work on the same Likert scale. The expert then conducted a Wilcoxon signed-rank test to understand whether the participants’ rating of the value of Big Data to their work changed after they attended the two-day seminar. Note, that while the names are similar, the Wilcoxon signed-rank test and the Wilcoxon rank-sum test are not the same. The former is used when the samples are dependent (paired, matched, same subject, and such); the latter (see Mann-Whitney U test) is used when the samples are independent.

Analysis of Variance

Analysis of variance (ANOVA) is a family of statistical tests to detect differences in means between groups. ANOVAs allow simultaneous comparisons between groups. Types of ANOVAs include one-way ANOVA, two-way ANOVA, repeated-measures ANOVA, multivariate ANOVA (MANOVA), and analysis of covariance (ANCOVA).

One-Way ANOVA

One-way ANOVA is similar to the independent-measures t-test except that ANOVA is used when the independent variable has three or more groups. (Technically, ANOVA could be used for two groups, but typically the independent-measures t-test is used in that situation because it is easier to conduct.) ANOVA is used to detect differences between the means of groups when (1) the one independent variable is nominal with three or more levels, (2) the dependent variable is normally distributed and continuous (interval or ratio), and (3) the samples (groups) are independent. In a one-way ANOVA, one variable is varied. For example, if researchers have three or more levels of a nominal variable (such as level of type of intervention: for example, online module, face-to-face seminar, and none) and are considering running a series of independent-measures t-tests between all the pairs of levels, they can simplify their process by running the one-way ANOVA because the one-way ANOVA analyzes all the data in one calculation. Moreover, one-way ANOVA is desirable because running multiple independent-measures t-tests increases the type I error (false positive) rate (see chapter 12). For example, researchers noted that healthcare insurers have encouraged patients to receive surgical operations at Centers of Excellence. Retrospectively reviewing EHRs, these researchers examined whether, within a regionalized healthcare system, travel distances to receive major cancer surgery varied by sociodemographic factors. Using one-way ANOVA, the researchers made comparisons between age, race, cancer type, and hospital of destination. Significant differences in travel patterns were found by age, race, and cancer surgery type.Younger patients, white patients, or patients receiving esophageal or pancreatic resections were more likely to travel further within the regional system to receive major cancer surgery. In comparison, African-American patients were less likely to travel further than other racial or ethnic groups to receive major cancer surgery (Smith et al. 2015, 99–102). The nonparametric alternative of the one-way ANOVA is the Kruskal-Wallis test, which is used when the dependent variable is ordinal or the dependent variable’s distribution is nonnormal. Other names for the Kruskal-Wallis test are the Kruskal-Wallis H test (H is the test statistic), the Kruskal-Wallis test by ranks, and the one-way ANOVA on ranks.

Two-Way ANOVA

The two-way ANOVA is used to detect differences between the means of groups when (1) the two independent variables are nominal and have two or more levels, (2) the dependent variable is continuous (interval or ratio), and (3) the samples (groups) are independent. For example, a researcher could investigate the effect of level of physical activity (low, moderate, high) and of sex (male, female) on weight loss. Two-way ANOVA helps to show whether there is an interaction between the two independent variables (physical activity and sex in this case) in how they affect the dependent variable (weight loss in this case).

One-Way Repeated Measures ANOVA

One-way repeated measures ANOVA is used to detect differences between the three or more groups means when (1) the two independent variables are nominal and have two or more levels, (2) the dependent variable is continuous (interval or ratio) and normally distributed, and (3) the samples (groups) are dependent. For example, one-way repeated measures ANOVA would be used to understand whether there is a sustained difference in coding speed among coding professionals after a two-day seminar on circulatory anatomy and physiology. Observations of coding speed are made three times: immediately before the seminar, one month after the seminar, and six months after the seminar. Coding speed is the dependent variable. The independent variable is time period: immediately before, post–one month, and post–six months. The measures are dependent (repeated) because the same individuals’ coding speeds are being measured three times.

The Friedman test is the nonparametric alternative to the repeated-measures ANOVA. The two-way repeated-measures ANOVA is used when there are two independent measures (such as time period and on-site versus teleworker).

Multivariate ANOVA (MANOVA)

Multivariate ANOVA (MANOVA) is used when there is more than one dependent variable. For example, in a study of post–hospital discharge Medicare beneficiaries, researchers used MANOVA when examining the differences between beneficiaries who were subsequently re-hospitalized and beneficiaries who were admitted to a skilled nursing facility during the study’s follow-up period. The independent variables in the MANOVA were being readmitted to a hospital and being admitted to a skilled nursing facility, and the dependent variables were age, gender, function, number of diagnoses, number of nursing visits, number of medications, and evidence of depression (Carew and Resnick 2015, 52).

Analysis of Covariance (ANCOVA)

Analysis of covariance (ANCOVA) tests whether means are statistically different and is used when the independent variable is strongly and linearly correlated (covarying) with the dependent variable or when other linearly covarying factors are involved. For example, depression and cardiovascular disease are strongly associated (Renoir et al. 2013, 1), so the two variables are said to covary. ANCOVA accounts for the “noise” (confusion) of the covariance. The two or more independent variables are nominal or normally distributed continuous, and the dependent variable is continuous with a normal distribution. A third variable, the covariate variable, is the control variable (Huck 2012, 347). ANCOVA is a sophisticated test that combines analysis of variance and linear regression analysis (Ritz et al. 2015, 166).

Pearson Product-Moment Correlation Coefficient

The Pearson product-moment correlation coefficient is used detect relationships when (1) both the independent and dependent variables are continuous (interval or ratio), (2) the relationship is linear, and (3) the observations are independent. The Pearson product-moment correlation coefficient is “used to evaluate both the statistical significance of the relationship and the magnitude and direction of the relationship” (Allua and Thompson 2009, 170). The Pearson product-moment correlation coefficient “ranges from −1.0 to +1.0: a +1.0 indicates a perfect direct (positive) relationship, and a –1.0 indicates a perfect inverse (negative) relationship” (Allua and Thompson 2009, 170). Other terms for the Pearson product-moment correlation coefficient are Pearson’s r, correlation coefficient, linear correlation coefficient, and Pearson correlation. Researchers used the Pearson product-moment correlation coefficient in a study to explore the accessibility of Internet mobile health and rehabilitation (iMHere) apps for individuals with spina bifida. The purposes of the iMHere apps are to support self-care and adherence to self-care regimens for individuals who are vulnerable to secondary complications, such as people with spina bifida and other complex conditions. Participants completed 108 multistep tasks using the apps. The Pearson product-moment correlation coefficient revealed a slightly negative statistically significant correlation between the order of tests and the completion time. A significant positive correlation was found between (1) the time to complete a task and the steps to complete tasks, (2) the steps to complete tasks and the mistakes encountered by participants, and (3) the time to complete a task and the mistakes encountered by participants (Yu et al. 2015, 3–4).

Spearman Rank Order Correlation

The Spearman rank order correlation is the nonparametric alternative to the Pearson product-moment correlation coefficient. The independent and dependent variables are ordinal. A Spearman rank order correlation may also be used for continuous data that are not normally distributed, are nonlinear, or have significant outliers (violations of the assumptions for the Pearson product-moment correlation coefficient). The Spearman rank order correlation is also called the Spearman correlation, the Spearman’s correlation, the Spearman rank order r, the Spearman rank r, the Spearman rho, or the Spearman ρ. Rho or ρ is the 17th letter of the Greek alphabet (the same as r in the English alphabet). For example, the Spearman rank order correlation would be performed if either the independent or dependent variables were collected using a Likert scale or other ranking scale. If the sample size is very small, the alternative to the Spearman rank order correlation is the Kendall’s tau-b (τb) correlation coefficient (also known as Kendall’s tau-b).

Simple Regression

The simple regression is used to detect relationships when (1) the one independent (predictor, explanatory) variable is continuous (ratio or interval) with a normal distribution, (2) the one dependent (outcome) variable is continuous with a normal distribution, (3) the samples are independent, and (4) the variables have a linear relationship. Other terms for the simple regression are simple linear regression or linear regression. For example, researchers conducted a study to test the associations between categories of body mass index and other factors among a sample of Mexicans ages 50 years and older. Simple regression revealed that among older adults, body mass index seemed to have a significant relationship with physical activity, age, sex, income, and marital status (Rivas-Marino et al. 2015, 329–330).

Multiple Regression

Multiple regressions are used to detect relationships when (1) two or more independent variables are nominal or continuous (ratio or interval), (2) the dependent variable is continuous (ordinal data require ordinal regression), and (3) the samples are independent. Regression models are used to do the following: Explain causes of outcomes Predict relationships among factors (independent or predictor variables) and outcomes (dependent variables) Adjust for imbalances among predictor variables between groups Make comparisons between and among groups Detect interactions among predictor variables Similar to ANOVA, multiple regression is a family of statistical tests including multiple linear regression, hierarchical regression, logistical regression, and Poisson regression. Multiple regression is commonly used in health-related research. When reading articles, be aware of the specific language that researchers use when describing regressions. Multivariate tests involve multiple dependent (outcome) variables (Hidalgo and Goodman 2013, 39). Multivariable tests involve multiple independent and multiple dependent variables. The use of theory-driven regression models, such as hierarchical regression, should be prioritized over the use of step-wise regression models because step-wise regression models may compound type I (false positive) errors (Norman and Streiner 2014,158–160). In theory-driven regression models, the investigator determines and sets the order of the variables based on theory and information in the literature. In step-wise regression, the computer builds the model by successively adding or removing variables based on their power to explain additional variance. In the study in which the researchers were investigating e-health literacy among users and nonusers of social media, which was previously mentioned in the section on the independent-measures t-test, the investigators also used multiple regression analyses. Multiple regression analyses were used to determine associations between sociodemographics (such as age and gender), social determinants (such as education and income), and electronic device use (such as desktop computer or mobile phone) on self-reported e-health literacy and social media use for seeking and sharing health information (Tennant et al. 2015). Complex variations of multiple regression exist, such as mixed-effects models. Mixed-effects models are sophisticated extensions of regressions used as tools to analyze grouped data. Grouped data result from longitudinal studies, repeated measurements, blocked designs, and multilevel (hierarchical) or clustered structures. Examples of studies that would use mixed-effects models are as follows: Longitudinal studies that analyze change over time, such as survival studies, time-to-event outcomes, and responses to treatments. In these studies, the data are collected multiple times at specific periods. The collected data are called repeated measurement data, longitudinal measurement outcomes, or serial observations (Asar et al. 2015, 334; Johnson 2015, 69). Studies that collect clustered data, such as clinic patients clustered by physician or hospital patients in a multi-hospital integrated delivery system clustered by hospital. These two clustering examples could also be considered multilevel (hierarchical) structures. There are two major categories of mixed-effects models: linear models and nonlinear models. Standardized language for the mixed-effects models has not been established. Variations of the mixed-effects models are also called hierarchical (multilevel) models, mixed models, random effects models, random coefficient models, covariance components models, and variance components models. Variations also occur within the categories, such as hierarchical linear models that are also known as multi-level linear models, nested models, mixed linear models, and covariance components models. The profusion of terms for these models can be confusing; however, readers can determine that the analysis is using a mixed-effects model by focusing on the purpose of the study and the grouping of the data.

Other Tests and Terms

In addition to the commonly used tests in inferential statistics, a general awareness of some other inferential statistical tests and terminology may assist readers in understanding the health literature and determining whether an article’s findings would be applicable to their healthcare organization. Readers may encounter sensitivity analyses, the Cox (proportional hazard regression) model, the hazard rate, the Poisson regression, and the Bonferroni correction in the methods, results, and discussion sections of articles. Sensitivity analyses are analytic techniques to determine whether a study’s results change if assumptions, statistical techniques, inputs, or other elements of a research plan are varied. Sensitivity analyses have many uses, such as the following: To check the impacts of outliers, of cut-off points, or of different ways of handling missing data. To gauge whether a study’s results are the same for all subgroups, such as groups by patient type, gender, age category, race or ethnicity, insurance or socioeconomic status, or other subpopulation characteristic. Sensitivity analyses can answer questions such as, “Does the intervention have the same effects for women and men (or computer-savvy users and computer-illiterate users)?” To check, in meta-analyses, whether one study’s outcomes are unduly influencing the overall measure of effect (Thabane et al. 2013, 2, 3–8) When the results of analyses are consistent or unchanged by testing variations in the plan’s elements, the results are said to be robust (Delaney and Seeger 2013, 145). Decision makers’ confidence in using the conclusions and inferences from robust results is increased. Sensitivity analyses should be a part of the plan for statistical analysis. Clinicians, administrators, policymakers, and other leaders are interested in knowing an intervention’s varying effects on subgroups. Providing this information makes the research meaningful to users. (Note that sensitivity analyses are not the same as sensitivity and specificity that were discussed in chapter 5.) Examples of other inferential statistics tests include: Cox (proportional hazards regression) model: Relates covariates or risk factors to outcome. Often used with hazard rates (death, life expectancy) Hazard (function) rate: Proportion of subjects who die in an increment of time, starting a one point in time, who had survived to that point (in other words, the probability of dying in a specified interval). Outcomes other than death can be studied Poisson regression: Statistical test for data that are discrete counts of independent events occurring in a certain time period and being small in number compared to the entire population (based on Poisson distribution). An example of such data in healthcare would be the number of hospital admissions per day Finally, when reviewing the literature, one might encounter the term Bonferroni correction, which is an adjustment made when multiple hypothesis tests are made on the same set of data; sets likelihood of falsely rejecting a hypothesis at a value (α = value and k = number of tests; Bonferroni correction = α/k).

Misuse of Statistics

Misuse of statistics can be accidental or intentional. For example, statistics are accidentally misused when the wrong statistical test is unintentionally used or some other mistake is made. As a consequence, the study’s reported results and conclusions are untrustworthy. Statistics are intentionally misused when researchers deliberately disguise their actual results by writing in confusing language or glossing over their undesirable or insignificant findings. An undesirable side effect of the misuse of statistics is that some people and policymakers distrust research. Types of accidental and intentional misuse of statistics include invalid statistics, lying with statistics, unit of analysis error, and confusing correlation with causation.

Invalid Statistics for Ordinal Data

Ignorance sometimes leads researchers to treat ordinal data like metric data. Unlike metric data, ordinal data do not have true numerical value. The rankings (scales, ratings) are conceptual, subjective differences; they are not actual differences. As such, means and standard deviations should not be calculated for ordinal data. Although the rankings are presented as numbers, researchers should avoid the temptation of performing these calculations (see also discussion in chapter 2).

Lying with Statistics

In 1954, Huff published his landmark book on how to lie with statistics. Lying with statistics can be achieved by using biased samples, distorting graphics, selecting the wrong statistical test, failing to check whether the test’s assumptions are met, and other methods (De Veaux and Hand 2005, 231). Sometimes, the researchers are not deliberately lying, but they misrepresent data to obscure errors or undesirable results so that their research is published. Sometimes, they overdramatically present research results to get attention, or journalists and advocates of a particular viewpoint take the statistics from a research study out of context. Costs, lengths of stay, mortality rates, and treatment effects are often presented in the most dramatic way possible. Bamboozling the reader is especially easy with percentages, proportions, and ratios because the reader does not have a frame of reference to adequately interpret the numbers. For example, in a study, the risk of error was 2 percent for the experimental group and 1 percent for the control group. The researcher calculated a relative risk: 1 percent divided by 2 percent equals 50 percent. The researcher could have calculated an absolute risk: 2 percent minus 1 percent equals 1 percent. However, 50 percent seems to be a much more notable outcome than 1 percent (example based on ACP 2000). Researchers can provide the greatest clarity by reporting including actual, raw data as well as their statistical manipulations.

Unit of Analysis Error

Researchers can also unintentionally make a procedural error, known as a unit of analysis error. A unit of analysis is the study’s focus that is being examined and for which data have been collected. The unit of randomization reflects the researchers’ focus—individuals, groups, objects, and other phenomenon. A unit of analysis error is a mismatch between the unit of randomization and the data (measurements or observations) that are used for statistical tests (Huck 2012, 249). A unit of analysis error occurs when the unit of randomization and the unit of analysis differ. For example, suppose that the researchers’ question is the effects of an educational module on the functioning of a group practice as a whole; the study is not supposed to investigate the module’s effects on the individual clinicians. Based on their question, the researchers randomize 15 group practices. However, the researchers gather data on the effects of the module on the individual clinicians. Then, to conduct the statistical tests for the unit of analysis, the entire group practice, the researchers must aggregate their data. To do this, they might use the practices’ means, rather than the individuals’ means. A useful tip to avoid this error is that the number of observations (measurements) being analyzed should match the number of units that were randomized (Deeks et al. 2011).

Unit of analysis errors have occurred in health informatics research. Holt and colleagues did a systematic review and meta-analysis of 42 research articles on the influence of EHR reminder systems on clinicians’ processes, such as conducting screenings, and on clinical outcomes, such as blood pressure control, and found that 28 studies were affected by unit of analysis errors. The researchers of the original studies had randomized at the level of the clinician or clinical team, but they had analyzed patient outcome data (Holt et al. 2012, 980).

Confusing Correlation with Causation

Researchers may unintentionally or through ignorance confuse correlation with causation. Correlations cannot prove causation. Correlations only demonstrate associations or relationships among variables. Correlations cannot establish the cause and the effect. (See also discussion of these concepts in chapter 1.) Terms such as prove, cause, and their variants (proves, causes, and so forth) must be avoided when presenting results of correlation studies and any other nonexperimental study.