Walk me through the steps of answering these question in reference to the word problem.
In fictional study, a pretest-posttest design was used to examine the influence of a television program on children's aggressiveness. The number of aggressive responses was measured during an observation period both before and after the television program.
1. What is/are the independent variable(s)?
2. What is the dependent variable?
3. What type of test is this?
4. Calculate the appropriate test statistic and then interpret the results
DATA:
Participant. Before. After.
1. 6. 9.
2. 4. 3.
3. 12. 11.
4 9 12
Since you have a "before" and "after" condition on the same subjects, how about a dependent groups t-test?
reject
To answer the questions based on the word problem, here are the steps:
1. What is/are the independent variable(s)?
The independent variable(s) is the variable that the researcher manipulates or controls in the study. In this case, the independent variable is the television program, which is being used to examine its influence on children's aggressiveness.
2. What is the dependent variable?
The dependent variable is the variable that is being measured or observed in the study and is expected to be influenced by the independent variable. In this case, the dependent variable is the number of aggressive responses, which is being measured both before and after the television program.
3. What type of test is this?
Based on the given information, this study is using a pretest-posttest design to compare the number of aggressive responses before and after the television program. To analyze the data and compare the means, a paired t-test would be appropriate in this case.
4. Calculate the appropriate test statistic and then interpret the results.
To calculate the appropriate test statistic (paired t-test), follow these steps:
Step 1: Calculate the difference between the before and after scores for each participant.
Participant 1: After - Before = 9 - 6 = 3
Participant 2: After - Before = 3 - 4 = -1
Participant 3: After - Before = 11 - 12 = -1
Participant 4: After - Before = 12 - 9 = 3
Step 2: Calculate the mean difference (sum of differences divided by the number of participants):
Mean Difference = (3 + (-1) + (-1) + 3) / 4 = 1
Step 3: Calculate the standard deviation of the differences:
Standard Deviation of Differences = sqrt(([(3 - 1)^2 + (-1 - 1)^2 + (-1 - 1)^2 + (3 - 1)^2]) / 4) = sqrt(8 / 4) = sqrt(2) ≈ 1.41
Step 4: Calculate the t-value using the formula:
t = (Mean Difference - 0) / (Standard Deviation of Differences / sqrt(Number of Participants))
t = (1 - 0) / (1.41 / sqrt(4)) ≈ 0.71
Step 5: Interpret the results:
With a t-value of 0.71 and 3 degrees of freedom (Number of Participants - 1), you can compare the t-value to the critical value from the t-distribution table. If the t-value is greater than the critical value, then you would reject the null hypothesis that there is no significant difference between the means before and after the television program.
Please note that the critical value depends on the desired level of significance (e.g., 0.05, 0.01) and the degrees of freedom. Additionally, you would need to further interpret the results by considering effect sizes, confidence intervals, and other relevant statistical measures to draw meaningful conclusions from the study.