# NURS 8201 t-Tests and ANOVA

## NURS 8201 t-Tests and ANOVA

NURS 8201 t-Tests and ANOVA

**Introduction**

The topic in which I focused on as a discussion, highlighted the point that there is an increasing number of nurse prescribers (NIP), however, there is little evidence that exists about their antibiotic prescribing practices (Ness, Currie, Reilly, McAloney-Kocaman, & Price, 2021). The article reports that the objective of the study was to measure nurse independent prescribers, who are managing the care of patients presenting with an upper respiratory tract infection for the first time, without prescribing an antibiotic, and assess what are the determinants for not prescribing antibiotics (2021). The literature shared that the inferential analysis was carried out using Spearman’s correlation to explore the relationship of the direct and indirect measures (independent variables) with intention (dependent variable) (2021). The analysis identified the significant predictors of intention for the multiple linear regression model, which was used due to the ordinal nature of the data and lack of normality. Also, the researchers used the Test-retest reliability to carry out the study by asking participants to complete the questionnaire again two weeks later and Spearman’s ρ correlation coefficient was used to check for stability of indirect measures. In my opinion, this strengthened the research (2021). In my opinion, this standard of practice strengthened.

**Study Findings**

The findings from 184 participants it was found that NIPs intended to manage their patients who presented with a URTI for the first time, without prescribing an antibiotic (2021). Key determinants were perceived norm, perceived behavioral control, and moral norm for this study (2021).

**ANOVA**

Calculating statistical data to obtain the mean is often a long and tedious process (Rosenfeld, 2021). The t-test and the one-way analysis of variance (ANOVA) are the two most common tests used for this purpose (2021). The literature reports that in the first decades of the twentieth century, an Englishman by the name of Ronald Aylmer Fisher radically changed the use of statistics in research (2021). He invented the technique called Analysis of Variance and founded the entire modern field called Design of Experiments (2021). ANOVA is a test that provides a global assessment of a statistical difference in more than two independent means (Sullivan, 2021).

**ANOVA Example**

A clinical trial is run to compare weight loss programs and the participants are randomly assigned to one of the comparison programs and these individuals are counseled on the details of the assigned program (Sullivan, 2021). Partakers in the test followed the assigned program for 8 weeks. The outcome of interest focused on is weight loss, in which is defined for the study as the difference in weight measured at the start of the study (baseline) and weight measured at the end of the study (8 weeks), measured in pounds. The trial included three popular weight loss programs. The first one is a low-calorie diet. The second is a low-fat diet and the third is a low carbohydrate diet. For comparison purposes, the team built in a fourth group as a control lineup (2021). The trial implemented the ANOVA by using the following five-step approach.

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Set up hypotheses and determine the level of significance

Select the appropriate test statistic

Set up decision rule.

Compute the test statistic

Conclusion

**T-Test**

William Sealy Gosset introduced the t-statistic in 1908 (Peckinpaugh, 2018). The t-test is a statistical hypothesis test where it follows a Student’s t – distribution if the null hypothesis is supported (2018). The t-test conveys how significant the differences between groups are; In other words, the t-test identifies if the differences (measured in means) could have happened by chance (2018). With that being said, both the t-test as well as the ANOVA looks at the difference in means and the spread of the distributions (i.e., variance) across groups; however, the ways that they determine the statistical significance are different (Peckinpaugh, 2018). The t-test is used when determining whether two averages or means are the same or different (2018). A t-test has more odds of committing an error when more means are used, which is why ANOVA is used when comparing two or more means (2018).

### **T-Test Example**

T-tests can be used in real life to compare averages (Glen, 2021). For example, a drug company may want to test a new cancer drug to find out if it improves life expectancy. In an experiment, there’s always a control group (Glen, 2021). The control group may show an average life expectancy of +5 years, while the group taking the new drug might have a life expectancy of +6 years (2021). It would seem that the drug might work. But it could be due to a fluke. To test this, researchers would use a t-test to find out if the results are repeatable for an entire population. There are three main types of t-test:

An Independent Samples t-test compares the means for two groups.

A Paired sample t-test compares means from the same group at different times (say, one year apart).

A-One sample t-test tests the mean of a single group against a known mean.

Use the following tools to calculate the t-test:

How to do a T-test in Excel.

T-test in SPSS.

T distribution on the TI 89.

T distribution on the TI 83.

**Reference**

Circulation (2008). Analysis of variance Retrieved From https://doi.org/10.1161/CIRCULATIONAHA.107.654335Circulation. 117:115–121

Glen, S., (2021). T-Test (Student’s T-Test): Definition and Examples From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/probability-and-statistics/t-test/

Franscisco, (2017). Difference Between T-TEST and ANOVA. Difference Between Similar Terms and Objects. http://www.differencebetween.net/miscellaneous/difference-between-t-test-and-anova/.

Ness, V., Currie, K., Reilly, J., McAloney-Kocaman, K., & Price, L. (2021). Factors associated with independent nurse prescribers’ antibiotic prescribing practice: a mixed-methods study using the Reasoned Action Approach. Journal of Hospital Infection, 113, 22–29. https://doi-org.ezp.waldenulibrary.org/10.1016/j.jhin.2021.04.008

Rosenfeld, B., Vermont Mathematics Initiative (2021) https://higherlogicdownload.s3.amazonaws.com/AMSTAT/1484431b-3202-461e-b7e6-ebce10ca8bcd/UploadedImages/Classroom_Activities/HS_8__FISHER_and_Design_of_experiments.pdf

Sullivan, L., (2021). Hypothesis Testing – Analysis of Variance (ANOVA). https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_hypothesistesting-anova/bs704_hypothesistesting-anova_print.html

Inferential statistics facilitates the researcher to analyze data and draw inferences and conclusions from the respective data. They are statistical procedures used to reach conclusions about associations between variables and are explicitly designed to test hypotheses. The selected topic investigates the application of MI (motivational interviewing) and whether it increases referrals and promotes compliance with appointments to treatment programs. It examines the effects of motivational interviewing to determine if patients afflicted with an opioid use disorder accepted referrals to MAT clinics and adherence to scheduled appointments.

### APA Citation

Morgenstern et al. (2017). Dismantling motivational interviewing: Effects on initiation of behavior change among problem drinkers seeking treatment. Psychology of Addictive Behaviors: Journal of the Society of Psychologists in Addictive Behaviors, 31(7), 751–762.

Morgenstern et al. (2017) examined MI’s hypothesized active ingredients using a dismantling design. Problem drinkers (N=139) seeking treatment were randomized to one of three conditions: MI, relational MI without the directional elements labeled spirit-only MI (SOMI), or a non-therapy control (NTC) condition and followed for eight weeks. On average, participants were middle-aged, well-educated (70% college graduates), employed (78%), Caucasian (76%), and female (57%). Those assigned to MI or SOMI received four sessions of treatment over eight weeks. Condition equivalence on demographics, drinking, and other problem severity at baseline were determined using chi-square tests, t-tests, and one-way ANOVAs.

There were no significantly different effects of the average of MI and SOMI compared to NTC on either TLFB drinking outcome (MI + SOMI vs NTC: SSD: B = .11, SE = .10, p = .22; HDD: B = −.04, SE = 0.18, p = .73). In addition, there were no significantly different effects on drinking between MI and SOMI (MI vs SOMI: SSD: B = −.00, SE = .09, p = .97; HDD: B = .13, SE = 0.12, p = .27). The study investigated the mechanism of behavior change associated with motivational interviewing, contrasting MI and SOMI to test whether strategies that selectively identify and reinforce change talk led to improved outcomes relative to a client-centered therapy that did not include directional strategies. In addition, the contrast between SOMI and NTC was designed to test whether client-centered therapy strategies alone improved outcomes relative to a non-therapy condition in which participants were offered normative feedback and encouragement to change on their own. Neither hypothesis was supported.

Inferential statistics used t-tests and one-way ANOVAs, among other statistics. No significant differences were found in attrition across conditions. All participants significantly reduced their drinking by week 8, but reductions were equivalent across conditions. The hypothesis that baseline motivation would significantly moderate condition effects on outcome was generally not supported.

### References

Morgenstern, J., Kuerbis, A., Houser, J., Levak, S., Amrhein, P., Shao, S., & McKay, J. R. (2017). Dismantling motivational interviewing: Effects on initiation of behavior change among problem drinkers seeking treatment. Psychology of Addictive Behaviors: Journal of the Society of Psychologists in Addictive Behaviors, 31(7), 751–762. https://doi.org/10.1037/adb0000317

Polit, D. F., & Beck, C. T. (2020). Essentials of nursing research: Appraising evidence for nursing practice. Lippincott Williams & Wilkins.

This is insightful, inferential statistics facilitate the researcher analyzing data and drawing inferences and conclusions from the respective data. They are statistical procedures used to reach conclusions about associations between variables and are explicitly designed to test hypotheses. Some of the inferential statistics that can be applied in the quantitative study process include ANOVA, t-test, Pearson correlation, chi-square tests, and regression analysis (Franscisco, 2017). The choice of inferential statistics to use depend on the variables in the study. In most cases, the research variables need to have continuous data and sometimes categorical variables, as in the case of an independent sample t-test. Before considering the application of inferential statistics, there is always the need for data analysis to perform descriptive statistics to establish the attributes of each variable (Weissgerber et al., 2018).

The study that you have selected is quantitative; it has all the attributes of quantitative research. The sample size that has been used is appropriate and representative of the population under consideration. However, one of the questions that I would like to ask is: from the study selected, how was the data collected? Did the researcher consider the types of variables during the process of data collection? From the study, there were clear research outcomes. In other words, there were no significantly different effects of the average of MI and SOMI compared to NTC on either TLFB drinking outcome. The ANOVA and t-test were correctly applied given the variables that were under consideration (Kim, 2017). Finally, inferential statistics can be applied to compare the relationship between the variables under consideration. When Pearson correlation is used, the coefficient is normally considered in determining whether there is a correlation between the variables.

**References**

Franscisco, (2017). Difference between T-TEST and ANOVA. Difference between Similar Terms and Objects. http://www.differencebetween.net/miscellaneous/difference-between-t-test-and-anova/

Kim, T. K. (2017). Understanding one-way ANOVA using conceptual figures. *Korean journal of anesthesiology*, *70*(1), 22. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5296382/

Weissgerber, T. L., Garcia-Valencia, O., Garovic, V. D., Milic, N. M., & Winham, S. J. (2018). Meta-Research: Why we need to report more than’Data were Analyzed by t-tests or ANOVA’. *Elife*, *7*, e36163. https://elifesciences.org/articles/36163