The Advanced Significance Test Discussion

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If there is statistical significance between the means of more than two independent variables ANOVA can help determine it. It depends on the ratio of the mean of squares and degrees of freedom and employs the F-test to determine whether the means of the samples are different by statistically calculating equality of means. F = variation between sample means/variation within the samples is the formula for the F-statistic ratio.

The two sample t-test examines if the means of two populations are comparable by following the t-distribution under the null hypothesis (Hess & Hess, 2017). The equal sample means represent the null hypothesis. As a result, it enables mean comparison using the derived t-value.

Matched pair test is employed when the data from two sets of the population can be able to be presented in pairs. For this reason, it is also called dependent t-test or paired t-test. It, therefore, depicts to be different from two sample t-test which indicates how separate two sets of measurements are and thus allow one to find out if a factor has changed in sets of distribution by comparing means.

The pooled t-test is used to determine equality of means of the independent or dependent samples when the mean of every sample is different, and the variances are similar. Pooled variance is calculated and used to provide a higher precision estimate of the entire population compared to the variances of the individual samples. This increases the level of statistical power when comparing populations in a t-test.

Two-way ANOVA is an extension of the one-way ANOVA, and here, every variable is classified in two ways contrary to one-way ANOVA. Every classification in a two-way ANOVA is termed as a factor, and row factor and column factor combination are called a treatment.

Chi-square test is a statistical measure of independence and determines if the is a significant relationship between two nominal categorical variables (Lemeshko, 2015). Data of this test is displayed in a contingency table of R rows and C columns.

Application to Health Administration

One way ANOVA could be used to determine patient satisfaction with the quality of primary health care. The two variables are independent, and their means could be used to find out if they are statistically significant. T-value in a two-sample test statistic is applicable in determining the effectiveness of quality of patient satisfaction, primary health care, and the job satisfaction variables.

Job satisfaction and healthcare or patient satisfaction and job satisfaction could be the test variables under two-sample t-test.

Matched pair test is applicable in the analysis of dependence between drug abuse, mental health and post-traumatic stress disorder which could be paired as one.

The matched pair test will be used to detect discrimination as it focuses on investigating the presence of disparate treatments of the test variables. Wassermann (2012) mentions that this can be used in the matched molecular analysis.

The pooled test could be applicable in health education planning. Here the aims of the health education planning such as stakeholder participation and provision of quality healthcare variances are pooled together to find out the impact on the healthcare delivery (Tebbs & Bilder, 2006).

In a two-way ANOVA, factors affecting health administration such as quality of medical services and patient satisfaction are grouped. These treatments are significant in enabling the management to enact measures to enhance patient safety (Kim, 2017).

Chi-square test is applicable in determining if the level of education is dependent on the quality of healthcare delivery. Frequencies of an individual variable are compared to the frequencies of the other variable (Lemeshko, 2015). The null hypothesis is rejected when the calculated chi-square test is greater than the critical value. However, you fail to reject the null hypothesis if the chi-square critical value is greater than the calculated value.

Application to my Research Agenda

My research agenda is to examine the relationship between job satisfaction and the nurse's job retention who work in a nursing home setting in Mississippi. Chi-square test will be used to determine if job satisfaction and nurses' job retention are independent. Here, the critical values will be compared with the calculated valued to determine the independence.

The null and alternative hypothesis will be:

H0: Job satisfaction and nurses' job retention are independent

H1: Job satisfaction and job retention are dependent.

The null hypothesis is that the two samples are independent. The test statistic χ2 is calculated as follows χ2 = Σ ((Observed frequency-Expected frequency) / (Expected frequency))^2 (Lemeshko, 2015). The chi-square test will follow a chi-square distribution, and the underlining assumption is that the data is normally distributed and attest to the central limit theorem. I will fail to reject the null hypothesis if the chi-square critical value is greater than the calculated value. Otherwise, I will reject the null hypothesis.

For a two-sample t-test, the means of organization's policies and nurses' pay could be determined if they are equal and the calculated t-value allow for comparison. Matched paired test will be used to match organizational policies and the nurses' pay as dependent factors that affect job retention for the nurses (Vivia, 2008). These test will be used to find if there is a correlation is between job satisfaction and the retention of nurses who work at nursing homes in Mississippi. This relationship will help improve job satisfaction for nurses and increase their retention at nursing homes to care for a growing population of elderly residents. The analysis of the independent variables which are organizational policies and the nurses pay will be significant in finding the statistical significance of the study.


Hess, A., & Hess, J. (2017). One- and two-sample t tests. Transfusion.

Kim, T. (2017). Understanding one-way ANOVA using conceptual figures. Korean Journal Of Anesthesiology, 70(1), 22.

Lemeshko, B. (2015). Chi-Square-Type Tests for Verification of Normality. Measurement Techniques, 58(6), 581-591.

Tebbs, J., & Bilder, C. (2006). Hypothesis Tests for and against a Simple Order among Proportions Estimated by Pooled Testing. Biometrical Journal, 48(5), 792-804.

Vivian, S. (2008). Statistics in Administration. Public Administration, 1(2), 108-116.

Wassermann, A., Dimova, D., Iyer, P., & Bajorath, J. (2012). Advances in Computational Medicinal Chemistry: Matched Molecular Pair Analysis. Drug Development Research, 73(8), 518-527.

April 06, 2023


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