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 Evolution, 7, 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 Statistics, 36(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 Statistics, 49(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