# Assessment 2: Hypothesis Testing for Differences Between Groups

## Assessment 2: Hypothesis Testing for Differences Between Groups

### Assessment 2: Hypothesis Testing for Differences Between Groups

Hypothesis testing is often applied in quantitative analysis when making a comparison of two or more groups. In most cases, the t-test is applied when comparing the means to two groups or two variables applied in the study process. On the other hand, ANOVA is often used when there are more than two variables in the research process. Hypothesis testing is important as it can be applied in the decision-making process (Kim et al., 2021). A statistical hypothesis refers to the hypothesis that is testable based on the observed data from the random variables. In quantitative research processes, the hypothesis being tested is always drawn from the possible probability distribution. Before engaging in hypothesis testing, there is always the need to formulate both null and alternative hypotheses (Kelter, 2021). The null hypothesis is always stated in a negative statement, while the alternative hypothesis is tested in a positive statement (Dennis et al., 2019). The purpose of this assignment is to determine if there is significant difference in the total number of visits per month between clinic 1 and clinic 2.

From the above assignment, the variables under consideration are clinic1 (total number of visits per month for clinic 1) and clinic2 Assessment 2 Hypothesis Testing for Differences Between Groups

(total number of visits per month for clinic 2).

Instructions. The research question for the assignment would be: Is there a significant difference in the total number of visits per month between clinic 1 and clinic 2. The hypothesis would be formulated as follows:

H0: There is no significant difference in the total number of visits per month between

clinic 1 and clinic 2.

H1: There is a significant difference in the total number of visits per month between

clinic 1 and clinic 2.

### Data Analysis

The two variables under consideration are continuous and normally distributed. Therefore, two sample t-test can be used to determine if there is difference between the means.

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### Descriptive Statistics

Table 1: Descriptive statistics for clinic1

 clinic1 Mean 124.32 Standard Error 4.678186647 Median 134.5 Mode 150 Standard Deviation 46.78186647 Sample Variance 2188.54303 Kurtosis -0.435747401 Skewness -0.505107701 Range 183 Minimum 24 Maximum 207 Sum 12432 Count 100

#### Table 2: Descriptive statistics for clinic 2

 clinic2 Mean 145.03 Standard Error 3.978082757 Median 149.5 Mode 175 Standard Deviation 39.78082757 Sample Variance 1582.514242 Kurtosis 0.264652849 Skewness -0.062856521 Range 221 Minimum 42 Maximum 263 Sum 14503 Count 100

 Table 3: t-Test: Two-Sample Assuming Equal Variances clinic1 clinic2 Mean 124.32 145.03 Variance 2188.54303 1582.514242 Observations 100 100 Pooled Variance 1885.528636 Hypothesized Mean Difference 0 df 198 t Stat -3.372473414 P(T<=t) one-tail 0.000447968 t Critical one-tail 1.652585784 P(T<=t) two-tail 0.000895937 t Critical two-tail 1.972017478

From table 1, the mean of variable clinic 1 is 124.32 while that of clinic 2 is 145.03. The total sample size used was 100. In other words, there were 100 entries for each of the two variables. The degree of freedom was 198. The two-sample t-test was conducted at a 95% confidence interval. In other words, the t-test was conducted at the 0.05 alpha level. From the result provided, the P (T<=t) two-tail is 0.000895937. 0.000895937 < 0.05, therefore we reject the null hypothesis and use the alternative hypothesis to make a conclusion. This means that there is a significant difference in the total number of visits per month between clinic 1 and clinic 2.

### Conclusion

While undertaking a hypothesis test, a null hypothesis is rejected when the significant value of t is less than 0.05. On the other hand, when the significant value of t is greater than 0.05, we fail to reject the null hypothesis and use it to make a conclusion in the research process. Based on the information provided, the investor can decide on the medical clinic to acquire based on the statistical outcomes.

### References

Dennis, B., Ponciano, J. M., Taper, M. L., & Lele, S. R. (2019). Errors in statistical inference under model misspecification: evidence, hypothesis testing, and AIC. Frontiers in Ecology and Evolution7, 372. https://www.frontiersin.org/articles/10.3389/fevo.2019.00372/full

Kelter, R. (2021). Analysis of type I and II error rates of Bayesian and frequentist parametric and nonparametric two-sample hypothesis tests under preliminary assessment of normality. Computational Statistics36(2), 1263-1288. https://link.springer.com/article/10.1007/s00180-020-01034-7

Kim, I., Ramdas, A., Singh, A., & Wasserman, L. (2021). Classification accuracy as a proxy for two-sample testing. The Annals of Statistics49(1), 411-434. https://projecteuclid.org/journals/annals-of-statistics/volume-49/issue-1/Classification-accuracy-as-a-proxy-for-two-sample-testing/10.1214/20-AOS1962.short