An investor needs to make a decision on whether to acquire one of two medical clinics
Hypothesis Testing for Differences Between Groups
Introduction
Hypothesis testing is a foundational statistical technique used to make decisions about a hypothesis. A hypothesis test compares two mutually exclusive statements (null hypothesis and alternative hypothesis) where only one is true. Hypothesis testing can determine statistical significance by examining the probability that a given result would occur under the null hypothesis. For this assignment, you will perform hypothesis testing on the differences between the two groups.
Preparation
Download Assignment 2 Dataset.
The dataset contains the following variables:
Clinic1 (total number of visits per month for clinic 1).
Clinic2 (total number of visits per month for clinic 2).
Instructions
An investor needs to make a decision on whether to acquire one of two medical clinics based on their productivity, as measured by the total number of visits per month. You have been asked whether there is a significant difference in the total number of visits per month between clinic 1 and clinic 2.
For this assignment, perform hypothesis testing on the differences between two groups in the Assignment 2 Dataset. Create an appropriately labeled Excel document with your results. Also, write an analysis of the results in a Word document. Insert the test results into this document (copied from the output file and pasted into a Word document). Refer to the “Copy From Excel to Another Office Program” resource for instructions.
Grading Criteria
The numbered assignment instructions outlined below correspond to the grading criteria in the Hypothesis Testing for Differences Between Groups Scoring Guide, so be sure to address each point. You may also want to review the performance-level descriptions for each criterion to see how your work will be assessed:
Generate a hypothesis about the difference between the two groups in a dataset.
State null hypothesis and alternative hypothesis as an explanation and math equation.
Identify the appropriate statistical test of the difference between the two groups in a dataset.
Provide your statistical rationale.
Perform an appropriate statistical test of the difference between two groups in a dataset.
Interpret statistical results of data analysis and state whether to accept or reject the null hypothesis based on the p-value and an alpha of .05.
Interpret p-value and statistical significance.
Write a narrative summary that includes practical, administration-related implications of the hypothesis test.
Additional Requirements
Your assignment should also meet the following requirements:
Written communication: Write clearly, accurately, and professionally, incorporating sources appropriately.
Length: 2–3 pages.
APA format: Cite your sources using the current APA format.
Font and font size: Times Roman, 12 point.
Solution :
An investor needs to make a decision on whether to acquire one of two medical clinics
In this era characterized by big data, we must use advanced methods of data analysis (Emmert-Streib & Dehmer, 2019) for decision making. An important method of data analysis which we’ll focus on in this paper will be statistical hypothesis testing whose principle idea is finding out whether a data sample is typical or atypical compared to the actual population assuming the hypothesis we have about the population is true. According to Emmert-Sreib & Dehmer (2019), a hypothesis is a quantitative statement that is formulated about the population value of the test static. In this case, our hypothesis is set on the number of visits between two clinics per month. Statistically, there are two hypotheses, a null hypothesis connoted as H_{o} and an alternative hypothesis connoted as H_{1}. A null hypothesis means that the hypothesis we are testing is true while the alternative hypothesis implies that the hypothesis statement is not true.
In our case, the null hypothesis is that there is no significant difference in the number of visits between the two clinics while the alternative hypothesis is that there is a significant difference between the clinics in the number of visits. We measure this difference using the means of the two populations given such that the null hypothesis is true if the two population means are equal while the alternative hypothesis is true if the two means are not equal. Stating the hypothesis statistically, we reject the null hypothesis, H_{0} if
H_{o}: µ_{1}=µ_{2}
Otherwise, we fail to reject H_{0 }if:
H_{1}: µ_{1}≠µ_{2}
Whereby µ_{1}is the mean for the visits in the first clinic and µ_{2}is the mean for the visits in the second clinic.
After stating the hypothesis, we now want to test the hypothesis. Since we have data from the visits of two different clinics, the best method of analysis to use is a 2-sample unpaired t-test. This is because this data is continuous, observations are independent of each other, approximates a normal distribution in each group and we also assume that the variances are approximately equal in both groups (Schober & Vetter, 2019). Also, the t-test is useful since both our sample sizes, n, ≥30. The 2-sample t-test makes use of the p-value which is a numerical value that is obtained from the comparison of the hypotheses. It quantifies the level of significant differences between the two variables given the null hypothesis is true. It is measured against the level of significance α which in this case is set at 0.05. We reject H_{0 }if p-value < 0.05, otherwise we fail to reject it.
Using excel to perform the t-test on the 2-sample unpaired data set provides, the results are as below:
t-Test: Two-Sample Assuming Equal Variances | ||
Clinic 1 | Clinic 2 | |
Mean | 124.1616 | 144.7879 |
Variance | 2208.341 | 1592.74 |
Observations | 99 | 99 |
Pooled Variance | 1900.541 | |
Hypothesized Mean Difference | 0 | |
df | 196 | |
t Stat | -3.32878 | |
P(T<=t) one-tail | 0.000521 | |
t Critical one-tail | 1.652665 | |
P(T<=t) two-tail | 0.001042 | |
t Critical two-tail | 1.972141 |
From the results above, we can see that the variances are approximately equal. Excel provides p-value for both one-tailed and two-tailed t-tests. One-tailed tests can only detect the difference in one direction, for instance, whether Clinic 2 had more visits than Clinic 1. However, the 2-tailed t-test detects differences in both directions; greater than or less than. Using the p=value from the two-tail, we find it is approximately 0.001 which is less than the α=0.05. This thus means we have to reject the null hypothesis H_{0} that there is a significant difference in visits between the two clinics and conclude that there is a significant difference in the number of visits between clinic 1 and clinic 2; with clinic 2 having more visits than clinic 1.
As earlier, the p-value helps in determining the significance of the outcomes of the hypothesis testing in relation to the null hypothesis H_{0}. It is the level of statistical significance, which is the level of evidence that the null hypothesis is true. If the p-value is less than 0.05, we say that it is statistically significant, that is, it shows a lot of evidence against the null hypothesis; that is there’s a less than 5% probability that H_{0} is true (Emmert-Streib & Dehmer, 2019). Hence, from our p-value of 0.001, we’d say it is statistically significant.
From the hypothesis test, we can conclude there is a significant difference in the visits between the two clinics, with clinic 2 having more visits than clinic 1. If the investor was to use these results, then they would opt to invest in clinic 2 as it has significantly more patients visits than clinic one. This implies that it’s slightly more accessible than Clinic 1. Easy and timely access to primary is important to integrated healthcare systems aa primary care offers the first-line of care and preventative measures while being at the junction between patients and meaningful use of the wider available health services (Rubenstein et al., 2020). Therefore, the investor should acquire clinic 2 as it is more productive as measured by the more visits per month than clinic 1.
References
Emmert-Streib, F., & Dehmer, M. (2019). Understanding statistical hypothesis testing: The logic of statistical inference. Machine Learning and Knowledge Extraction, 1(3), 945-961.
Rubenstein, L., Hempel, S., Danz, M., Rose, D., Stockdale, S., Curtis, I., & Kirsh, S. (2020). Eight priorities for improving primary care access management in healthcare organizations: results of a modified Delphi stakeholder panel. Journal of general internal medicine, 35(2), 523-530.
Schober, P., & Vetter, T. R. (2019). Two-sample unpaired t tests in medical research. Anesthesia & Analgesia, 129(4), 911.
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