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JA5. ANOVA Analysis in JASP

Statement

In your work, assume the 5% significance level. Use the following data WickedWitch.csv to answer the below questions.

Take a screenshot of your output and based on that, answer the following questions.

  • a) Import the data into JASP and provide an explanation on the descriptive statistics for the variable Complaint split across regions.
    1. Which of the regions has the highest average number of complaints, indicate the average?
    2. Which of the regions has the largest standard deviation of complaints, indicate the standard deviation?
    3. Based on the descriptive output from JASP, can we expect the average number of complaints across the four regions to be different? Why?
  • b) Write a hypotheses for evaluating whether the average number of complaints caused varies across the four regions.
  • c) Run the ANOVA analysis in JASP (with Complaints as the dependent variables and Region as the Fixed Factors). Provide a capture of the output and answer the following questions:
    1. What is the F-statistics and the p-value?
    2. What is the conclusion for the hypotheses of question (b)?

Answer

a) Import the data into JASP
descriptive analysis screenshot
Image 1: Descriptive analysis of the Complaints variable split across regions (JASP, 2024)
descriptive analysis only
Image 2: A clearer view of the descriptive analysis of the Complaints variable (JASP, 2024)

1. Which of the regions has the highest average number of complaints, indicate the average?.

The region with the highest average number of complaints is the region 4 with an average of 4.2 complaints (Image 2).

2. Which of the regions has the largest standard deviation of complaints, indicate the standard deviation?.

The region with the largest standard deviation of complaints is the region 1 with a standard deviation of 1.225 (Image 2). This indicates that the complaints in region 1 are more spread out than in the other regions, or in other words, the complaints in region 1 are usually further away from the average number of complaints in that region.

3. Based on the descriptive output from JASP, can we expect the average number of complaints across the four regions to be different? Why?.
total descriptive analysis
Image 3: Descriptive analysis of the Complaints variable without split (JASP, 2024)

From the descriptive output in Image 2, we find:

  • Average number of complaints in region 1: 1.
  • Average number of complaints in region 2: 1.4.
  • Average number of complaints in region 3: 3.6.
  • Average number of complaints in region 4: 4.2.

Notice how the average number of complaints varies significantly across the four regions. From 1 to 4.2, this indicates that the average number of complaints across the four regions is different.

From the descriptive output in Image 3, we find the overall overage of complaints is 2.55 across all regions. We notice the average of each group may be significantly different from the overall average; but we can’t be for sure until we run an ANOVA analysis in the next section.

b) Write a hypotheses

Write a hypotheses for evaluating whether the average number of complaints caused varies across the four regions.

  • H0: Null Hypothesis (No difference): The average number of complaints caused across the four regions is the same, that is, μ1 = μ2 = μ3 = μ4.
  • H1: Alternative Hypothesis (Difference): The average number of complaints varies across the four regions, that is, at least one region has an average number of complaints different from the others.

c) Run the ANOVA analysis in JASP
ANOVA analysis screenshot
Image 4: ANOVA analysis of the Complaints variable split across regions (JASP, 2024)
ANOVA analysis only
Image 5: A clearer view of the ANOVA analysis of the Complaints variable (JASP, 2024)

1. What is the F-statistics and the p-value?.

From the ANOVA analysis in Image 5, we find:

  • F-statistics: 10.486.
  • p-value: <0.001.

2. What is the conclusion for the hypotheses of question (b)?.

Since the p-value = 0.001 < α = 0.05, we reject the null hypothesis. This means that the average number of complaints varies across the four regions. And we are 95% confident that there is statically significant difference between the average number of complaints across the four regions, thus, the number of complaints varies between the regions.

References

  • JASP Team (2024). JASP (Version 0.19) [Computer software].