Psychology week 6 assignment 2

1

Program Evaluation

Student name

Faculty name

Due date

Statistical tests to respond to evaluation questions

The main aim of the evaluation will be to determine whether the Tides Family Services (TFS) program will result into a significant decrease in symptom of depression based on the PHQ-A scores. I will compare pre-test and post-test PHQ-A scores with the use of statistical tests with the emphasis on the change in depressive symptoms.

Paired Samples t-test: The test will be applied in case the pre-post difference scores are normally distributed (Rainio et al., 2024). The paired samples t-test will be used to compare the means of the pre-test PHQ-A and post-test PHQ-A scores of each of the participants to establish whether there is a statistically significant change between the two time periods.

Wilcoxon Signed-Rank test: Wilcoxon Signed-Rank test will be used in case the difference scores do not follow a normal distribution. This is a non-parametric test which compares the median of the differences of paired observations and does not assume that the data follows a normal distribution (Hinton, 2024).

Identifying which test to use.

I will initially evaluate the normality of the pre-test and post-test difference scores (i.e. post-test minus pre-test PHQ-A scores) as follows:

1. Normality check:

Visual Inspection: To examine the distribution of the difference scores of any skewness, I will draw histograms and Q-Q plots.

Shapiro-Wilk Test: I will use this test to test the normality formally. Assuming that the p-value is more than 0.05, the data will be assumed to be more or less normal and then I will use paired samples t-test.

2. Test selection:

In the event that the data is normally distributed (p-value > 0.05), then I will employ the paired samples t-test.

In case the data is not normally distributed (p-value < 0.05), I will apply the Wilcoxon Signed-Rank test.

Dataset

The data is not in the final form, and the subsequent steps have to be considered before conducting statistical analysis:

1. Missing Data:

I will verify of any missing values on the pre-test data and the post-test data. In case of any values missing, I will either avoid the affected participants or impute the missing data (e.g. using the mean as a replacement) based on the level of the missingness (Little et al., 2019).

2. Outliers:

I will look at outliers either with boxplots or by computing the interquartile range (IQR). In case, outliers are detected, I will evaluate their presence as an error or valid data and determine whether to drop them or use powerful techniques to reduce their effects.

3. Variable Labeling and Recoding:

I will make sure that all the variables, including PHQ-A items (PHQ1 to PHQ9) and the overall score (PHQ_Total) are labelled and computed appropriately. There will be recoding where necessary (e.g. reversing any negative values) to make it consistent and accurate.

Presenting the results

The findings will be clearly shown through the following methods:

1. Descriptive Statistics: I will summarize the mean, median, standard deviation and range of both pre-test and post-test PHQ-A scores to give a summary of the data.

2. Statistical Test Results: I will include the results of paired samples t-test or Wilcoxon Signed-rank test, the test statistic, p-value, and effect size (Cohen d of t-test or r of Wilcoxon).

3. Visual Representation: Trends in the change in depressive symptoms will be represented using bar charts or boxplots and made visually clear between pre-test and post-test scores.

4. Tables: The descriptive statistics of the pre-test and post-test scores will be summarized in a table and the findings of the statistical tests will be presented easily.

Conclusion

Depending on the normality of the difference scores, I will decide to employ the paired samples t-test or Wilcoxon Signed-Rank test. Once the missing data, outliers, and the correct labeling are taken into consideration, the results will be presented using descriptive statistics, the results of the statistical tests, the visualization, and tables to make it clear and easy to comprehend.

References

Hinton, P. R. (2024).  Statistics explained. Routledge.

Little, R. J., & Rubin, D. B. (2019).  Statistical analysis with missing data. John Wiley & Sons.

Rainio, O., Teuho, J., & Klén, R. (2024). Evaluation metrics and statistical tests for machine learning.  Scientific Reports,  14(1), 6086.