Hypothesis Testing for Differences between Groups

Hypothesis Testing for Differences between Groups

Hypothesis

We are interested in finding out if there is a significant difference between the total number of visits per month between Clinic 1 and Clinic 2. From the data given for Clinic 1 and Clinic 2, we can calculate the sample standard deviations and sample means of the total number of visits per month. The population standard deviation of the total number of visits per month to clinics is neither known nor given. Therefore, the given data will be of huge importance as it will guide us on how to carry out the hypothesis testing and reach a decision.

 Null and Alternative Hypothesis

On the one hand, the null hypothesis shows that the means of the total number of visits per month of the two clinics are equal. On the other hand, the alternative hypothesis shows that the means of the total number of visits per month of the two clinics are not equal.

 Appropriate Statistical Test

Since there are two samples, one of Clinic 1 and the other of Clinic 2, and the population standard deviation is not known, we will use the t-test of two samples, assuming unequal variances at a significance level of 0.05. Accordingly, two-tailed t-tests will be used by looking at the sign in the alternative hypothesis equation.

Statistical Rationale

The t-test was used because the population standard deviation of the total number of visits per month to the Clinics (Frey, 2018) is unknown. Subsequently, the two-tailed t-test was used because of the “not equal” sign in the alternative hypothesis (Birkett, 2018).

Statistical Test

The statistical test results by the MS Excel data analysis tool pack are given below (Kros & Rosenthal, 2016).

Figure 1: Result Analysis

 Interpreting the Results

The descriptive statistics are given in the first three rows, showing the two clinics’ means, variances, and observations. These are used to arrive at the t statistic, which is used to arrive at the p-value, which is then used to draw a decision about the null hypothesis. The significance level is 0.05, and the two-tailed p-value of the t-test is 0.0009. The null hypothesis is rejected since the p-value is less than the significance level (0.0009<0.05). Therefore, there is sufficient evidence at the significance level of 0.05 to conclude that there is a significant difference in the total number of visits per month between Clinic 1 and Clinic 2.

 Interpreting the P-value and the Statistical Significance

There is stronger evidence against the null hypothesis as the p-value tends to zero, and therefore a smaller p-value means rejecting the null hypothesis. On the other hand, a p-value greater than the significance level means that the null hypothesis should not be rejected. Accordingly, if the p-value is statically significant at the given level of significance (p-value is less than 0.05), then it means that there is less than a 5% probability that the null is correct.

 Narrative Summary of the Results

A significant difference was found after conducting the hypothesis test to determine whether there is a significant difference between the total number of visits per month between the two Clinics (1 and 2). This result, therefore, shows that an investor needs to choose to invest in the Clinic with the highest total number of visits per month. Looking at the sample averages, an investor needs to invest in Clinic 2 because it has a higher total number of visits per month compared to Clinic 1. Investing in Clinic 2 will ensure that the Clinic has sufficient resources to serve many patients.

The main goal of an investment is the generation of returns, with high-return projects attracting more investors in comparison to low-return projects. Additionally, investment returns are highly dependent on the productivity of the investment, with higher productivity translating to bigger market share and higher returns (Chowdhury et al., 2017). Comparing the two investment opportunities, Clinic 2 has a higher number of visits per month, leading to high productivity and thus will generate higher returns for the investor.

 References

Chowdhury, J., Sonaer, G., & Celiker, U. (2017). Market share growth and stock returns. Retrieved 13 March 2022, from.

Frey, B. B. (Ed.). (2018). Hypothesis testing. In The SAGE encyclopedia of educational research, measurement, and evaluation (Vols. 1-4). Thousand Oaks, CA: Sage

Kros, J. F., & Rosenthal, D. A. (2016). Statistics for health care management and administration: working with Excel (3^rd. ed.). San Francisco, CA: Jossey-Bass.

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Perform hypothesis testing on the differences between the two groups and create an Excel document. Write a 2-3 page analysis of the results in a Word document and insert the results into this document.

Hypothesis Testing for Differences between Groups

Hypothesis testing is a foundational statistical technique used to make decisions about a hypothesis. A hypothesis test compares two mutually exclusive statements (null hypothesis, 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 assessment, you will perform hypothesis testing on the differences between the two groups.

Overview & Preparation
Download the Assessment 2 Dataset [XLSX].

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 significance difference in the total number of visits per month between clinic 1 and clinic 2.

For this assessment, perform hypothesis testing on the differences between the two groups in the Assessment 2 Dataset. Create an appropriately labelled 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 Copy From Excel to Another Office Program for instructions.

Submit both the Word document and the Excel file that shows the results.

Grading Criteria
The numbered assessment 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 two groups in a dataset.
State null hypothesis and alternative hypothesis as an explanation and math equation.
Identify the appropriate statistical test in a dataset.
Provide your statistical rationale.
Perform appropriate statistical tests of the difference between two groups in a dataset.
Interpret the 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 of the results that include practical, administration-related implications of the hypothesis test.
Additional Requirements
Your assessment should meet the following requirements:

Written communication: Write clearly, accurately, and professionally, incorporating sources appropriately.
Length: 2–3 pages
Resources: Not required.
APA format: Cite your sources using the current APA format.
Font and font size: Times Roman, 10 points.
Competencies Measured
By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria:

Competency 1: Plan for data collection, measurement, and analysis.
Generate a hypothesis about the difference between two groups in a dataset.
Identify the appropriate statistical test in a dataset.
Competency 2: Analyze data using computer-based programming and software.
Performs appropriate statistical tests of the difference between two groups in a dataset.
Competency 3: Interpret results of data analysis for value-based health care decisions, policy, or practice.
Interpret the results of data analysis and state whether to accept or reject the null hypothesis based on the p-value and an alpha of .05.
Write a narrative summary of the results that include practical, administration-related implications of the hypothesis test.
Competency 5: Communicate audience-appropriate health management content in a logically structured and concise manner, writing clearly with correct use of grammar, punctuation, spelling, and APA style.
Write clearly and concisely, using correct grammar, mechanics, and APA formatting.