Write a 2-3 page analysis of the results in a Word document that includes a recommendation and a plan of action, and insert the results into this

dataset2

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Getting Started With Assessment #2: Hypothesis Testing for Differences Between Groups

Lecture: Hypothesis Testing In this lecture, we will cover the essential concepts of hypothesis testing, including types of t- tests, the distinction between parametric and non-parametric data, and the rationale behind using the Welch test for this assessment. Hypothesis testing is a fundamental aspect of statistical analysis, allowing researchers to make inferences about populations based on sample data.

Hypothesis Testing

Hypothesis testing involves formulating two hypotheses: The null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis states that there is no effect or difference, while the alternative hypothesis suggests that there is a significant effect or difference. The goal of hypothesis testing is to determine whether the observed data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis. This process helps researchers make informed decisions based on empirical data.

Types of t-Tests

There are several types of t-tests used to compare means between two groups, depending on the data's characteristics:

1. Independent Samples t-Test: Used when comparing the means of two independent groups. It assumes that the data are normally distributed and that the variances of the two groups are equal.

2. Paired Samples t-Test: Used when comparing the means of two related groups, such as measurements taken before and after a treatment on the same subjects.

3. Welch’s t-Test: An adaptation of the independent samples t-test that does not assume equal variances between the two groups. This test is particularly useful when the assumption of equal variances is violated.

Parametric and Non-Parametric Data

Parametric tests, like the t-tests mentioned above, rely on assumptions about the data distribution, such as normality and homogeneity of variances. These tests are appropriate for interval or ratio data that meet these assumptions. When the data do not meet these assumptions, non-parametric tests are used. Non-parametric tests do not assume a specific data distribution and can be applied to ordinal, interval, or ratio data. Examples include the Mann-Whitney U test and the Wilcoxon signed-rank test.

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Why the Assessment Requires the Welch Test

For this assessment, we use Welch’s t-test, which is designed for comparing the means of two samples with unequal variances and possibly different sample sizes. This test is robust against violations of the equal variances assumption, making it suitable for real- world data where equal variances cannot always be assumed. Welch’s t-test provides a more accurate assessment of the differences between groups when the homogeneity of variances is not met. Understanding these key concepts will enable you to effectively conduct hypothesis testing in your assessment. By correctly identifying the appropriate statistical test and understanding the nature of your data, you can draw meaningful conclusions that inform healthcare management decisions.

If you have any questions regarding these notes, please feel free to reach out to me by email or phone. My contact info is located in the announcements. You may also reach out to the course graduate assistants (tutors) by scheduling a meeting or submitting a question to “Ask the Graduate Assistant” as needed.

Assessment Step by Step

Performed in MS Excel ToolPak: Assessment 2 Data Set [XLSX]

• STEP 1. Introduction: Begin by thoroughly reviewing all materials related to Assessment #2. It's important to understand that hypothesis testing is essentially significance testing, which constitutes a form of research. In research, you articulate your inquiry regarding the problem you aim to address, in other words, you ask a question to fill a gap.

• STEP 2. Research Question: After identifying a gap or specific area in the case or dataset, you will formulate a research question. For instance, if the case suggests a potential blood pressure-lowering effect of a new medication, a relevant research question could be, "Does the new medication XYZ-Pak significantly reduce blood pressure in adults with hypertension compared to current gold standard medications?"

• STEP 3. Hypotheses: Translate the research question into a null hypothesis (Ho) and an alternative hypothesis (Ha). The null hypothesis states that there is no significant effect or difference, such as "The new medication does not significantly reduce blood pressure in adults with hypertension compared to the current standard medication." Conversely, the alternative hypothesis proposes the expected effect or difference, is not significant such as "The new medication significantly lowers blood pressure in adults with hypertension compared to the current standard medication." In hypothesis testing, you directly evaluate the null hypothesis to either reject or fail to reject it, thereby providing evidence for the alternative hypothesis. See Figure 1. Generating a hypothesis.

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Figure 1: Generating a Hypothesis—Should Be written out in words for clarity, etc.

Null Hypothesis (Ho) Clinic one and Clinic 2 ____________________visits. Alternative Hypothesis (Ha) Clinic one and Clinic 2 visits.

Note: A Hypothesis may also be written out using

symbols.

Ho can include =, or < or > signs. Ha can include ≠, >, < signs.

• STEP 4. Statistical Test: Choose and run your test. If you chose the t-Test: Paired Two Sample for Equal Means it is not correct; why? Even though the result and interpretation may be close, the correct test is the t-Test: Two-Sample Assuming Unequal Variances; Why? See Table 1:

Table 1. "Comparison of Two-Sample T-Tests: Equal Variance vs. Unequal Variance"

Two-sample T-Test with equal variance (also known as the homoscedastic t-test):

• Normal Distribution (Parametric

Data): Both samples ideally come from normally distributed populations, although this condition can be relaxed for large samples due to the central limit theorem.

• Equal Unknown Standard

Deviations: Assumes that the standard deviations of both populations are equal (central tendency).

• Sufficiently Large Sample Size: Each

sample should ideally have more than 30 observations, ensuring the applicability of the central limit theorem and the t- distribution approximation.

• Interval or Ratio Scale: Parametric tests

are most appropriate for continuous data measured on an interval or ratio scale. This includes data such as height, weight, temperature, and test scores.

Two-sample T-Test with unequal variance (also known as the heteroscedastic or Welch’s t-test):

• Normal Distribution (Parametric

Data): Similar to the equal variance case, both samples should ideally come from normally distributed populations, although this condition can be less stringent for large samples.

• Unequal Unknown Standard

Deviations: Assumes that the standard deviations of the two populations are unequal. Welch's t-test adjusts for differences in variance.

• Sufficiently Large Sample Size: Each

sample should have more than 30 observations. Welch's t-test is particularly reliable when sample sizes and variances are unequal.

• Measurement Scale: Can be used for

ordinal, interval, or ratio data.

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• Note: The central limit theorem states that the distribution of the sample means will approximate a normal distribution as the sample size increases, regardless of the distribution of the population from which the samples are drawn. Therefore, for large sample sizes, the normality assumption for the underlying populations becomes less critical for conducting parametric tests.

In summary, Table 1 tells us that given these assumptions, choosing the right statistical test is going to be based on if the data is parametric or non-parametric. As shown in Table 2. So, when choosing the correct statistics test, we look at statistical assumptions, and data considerations, etc.

1. Parametric tests are statistical analyses designed for data that adhere to specific assumptions, including normality, homogeneity of variance, and the use of interval or ratio scale measurements, ensuring the accuracy of inferences drawn from normally distributed, equally variant, and interval or ratio scaled data.

2. Non-parametric tests, conversely, accommodate data that may not meet the stringent assumptions of parametric tests, including normality and homogeneity of variance, making them suitable for analysis of non-normally distributed or unequally variant data across ordinal, interval, or ratio scales.

Table 2. Parametric vs. Non-parametric Statistical Data and Tests Parametric Tests Non-Parametric Tests

Assumptions Considerations

1. Normality: Data are assumed to be normally distributed within each group or population being compared.

1. Distribution: Data may not follow a normal distribution.

2. Homogeneity of Variance: Variances of populations or groups being compared are assumed to be equal.

2. Variance: Variances of groups may be unequal or unknown.

3. Interval or Ratio Scale: Appropriate for continuous data measured on an interval or ratio scale.

3. Measurement Scale: Can be used for ordinal, interval, or ratio data.

• STEP 5. Identify Your Confounders: In hypothesis testing, confounders are variables that can influence both the dependent and independent variables, potentially leading to a spurious association. The presence of confounders complicates determining the true relationship between variables because they can mask or falsely enhance this relationship. For instance, in a study examining the relationship between exercise (independent variable) and weight loss (dependent variable), diet could be a confounder if it influences both exercise habits and weight loss. This introduces the risk of Type I errors, where a significant relationship is detected between variables when none truly exists, or Type II errors, where a significant relationship is missed due to confounding variables not being adequately controlled. Thus, controlling confounders is essential to minimize bias and ensure accurate interpretation of study findings.

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1. Influence on Both Variables: A confounder is associated with both the independent variable (the cause or predictor) and the dependent variable (the effect or outcome). For instance, in a study examining the relationship between exercise (independent variable) and weight loss (dependent variable), diet could be a confounder if it influences both exercise habits and weight loss.

2. Potential to Cause Bias: The presence of confounders can lead to biased results. Without controlling for these variables, the effect of the independent variable on the dependent variable might be overestimated, underestimated, or wrongly inferred.

• STEP 5. Interpret and explain your results: P-Values The p-value signifies the likelihood of obtaining test results as extreme as, or more extreme than, the observed results under the assumption that the null hypothesis holds true. In standard practice, a p-value of less than 0.05 indicates a less than 5% chance that the observed effect occurred by chance alone, thus meeting the threshold for statistical significance.

o Researchers may choose higher confidence intervals for increased precision. For instance, a 99% confidence interval corresponds to a p-value of less than 0.01, indicating less than a 1% probability of the observed effect being due to chance. In critical scenarios like drug studies, tighter confidence intervals, such as a 99.999% level, reflect an extremely low chance of chance influence, with a corresponding p-value of less than 0.001.

o Conversely, in marketing research focusing on broad perceptions rather than precise measurements, researchers might opt for lower confidence intervals, like 80-90%, accepting higher p-values of 0.2 or 0.1. This approach allows for a broader margin of error in capturing overall sentiment, aligning with the study's objectives and context.

• STEP 5. Create an Action Plan: Finally, write your narrative and management recommendations in the form of an action plan. A good way to write an action plan is to list your findings and recommendations based on your metrics and what you are trying to solve:

The Healthcare System administrators need to decide on whether to implement the new pre-natal program in rural clinics. You have been asked whether there is a significant difference in the total number of visits per month between clinic 1 and clinic 2. Based on your data analysis, which of the clinics is performing better? Recommend an improvement plan for the underperforming clinic.

Write a recommendation for a decision and plan of action based on a data analysis and supported with scholarly literature.

Action Plan Findings 1 Recommendations 1 Findings 2 Recommendations 2 and so on.

Conclusion Support all major concepts, numbers, statistics, and dates borrowed from another author with APA in-text source citations and APA references.