What Are The Assumptions For A T Test And How Should These B

1 What Are The Assumptions For A T Test How Should These Be Run Do

What are the assumptions for a t-test? How should these be run? Do you want to see a p value of <0.05? Why or why not? (50-80 words).

A t-test assumes that the data are normally distributed, observations are independent, and variances are equal across groups (Welch, 1947). To run the assumptions, perform normality tests such as Shapiro-Wilk, and leverage Levene’s test for homogeneity of variances. A p-value of <0.05 indicates statistical significance, suggesting the null hypothesis may be rejected. However, reliance solely on p-values is cautioned against; effect size and confidence intervals provide essential context (Cohen, 1988).

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The assumptions underlying a t-test are essential to ensure the validity of the statistical inference drawn from the analysis. Primarily, the data should be normally distributed, which can be evaluated using normality tests such as the Shapiro-Wilk test (Shapiro & Wilk, 1965). When samples are independent, the assumption of independence must be satisfied, meaning that the observations in one group are not related to those in another. The assumption of homogeneity of variances, often tested through Levene’s test, requires that the variances across the groups being compared are approximately equal (Levene, 1960).

Prior to conducting a t-test, data should be examined to verify these assumptions. If assumptions are violated, alternative methods such as the Welch's t-test, which adjusts for unequal variances, or non-parametric tests like the Mann-Whitney U test may be appropriate. Running assumption checks ensures the test's reliability and accuracy. Regarding p-values, a significance threshold of 0.05 is commonly used. Nonetheless, focusing solely on whether the p-value falls below this threshold can be misleading. It is more informative to consider the effect size and confidence intervals, which provide insights into the magnitude and precision of the observed effects (Cohen, 1988). Hence, while a p-value less than 0.05 suggests statistical significance, it does not necessarily imply practical importance.

Sample Size Calculation for Paired T-Test

When planning a project comparing pre- and post-intervention survey results with the same participants, a paired t-test is suitable. To determine the sample size, tools like G*Power can be used, setting parameters such as effect size (d), alpha level (0.05), and desired power (typically 0.80). For example, assuming a moderate effect size (d=0.5), a sample size of approximately 34 participants is needed to detect significant differences (Faul et al., 2007). A larger sample reduces the risk of Type II errors and increases the study’s validity; insufficient sample size may lead to underpowered results, compromising the validity and generalizability of findings (Cohen, 1988).

Impact of Sample Size on Validity

A sufficiently large sample size enhances the statistical power of the study, enabling the detection of true differences between pre- and post-intervention measures. Conversely, a small sample size may result in low power, increasing the likelihood of Type II errors and diminishing the validity of the conclusions. Therefore, proper sample size calculation is crucial for ensuring reliable and generalizable results, especially in studies with paired designs where individual differences are accounted for (Cohen, 1988).

Collection of Protected Health Information and Its Effect on Project

Protected health information (PHI) includes any data that can identify an individual, such as medical records, health histories, or biometric data (HHS, 2012). In assessing diabetes self-care management, relevant PHI may include blood glucose levels, medication adherence, and healthcare provider notes. Collecting this data ensures comprehensive assessment accuracy but raises privacy concerns. If such data is collected, strict adherence to privacy regulations like HIPAA is necessary, which could impact data security measures and participant willingness to share information, thereby affecting the project’s scope and validity (Bazzell, 2020).

References

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Routledge.
• Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for social, behavioral, and biomedical sciences. Behavior Research Methods, 39(2), 175-191.
• Health and Human Services (HHS). (2012). Summary of the HIPAA Privacy Rule. Office for Civil Rights.
• Levene, H. (1960). Robust tests for equality of variances. Contributions to Probability and Statistics, 279-292.
• Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality. Biometrika, 52(3-4), 591-611.
• Welch, B.. (1947). The generalization of 'Student's' problem when several different population variances are involved. Biometrika, 34(1-2), 28-35.
• Bazzell, M. (2020). Protecting Patient Privacy: Data Security and HIPAA. Journal of Healthcare Information Management, 34(2), 45-50.