Question 1: Define inferential statistics and explain how they differ from descriptive statistics.

Answer: Inferential statistics are methods used to draw conclusions or make predictions about a larger population based on sample data. They differ from descriptive statistics, which simply summarize or describe the characteristics of a dataset without making broader generalizations.

Question 2: A researcher conducts an experiment with two groups: a control group and an experimental group. The experimental group shows a higher average score on a test. Why would the researcher use an inferential statistical test before concluding that the intervention was effective?

Answer: The researcher would use an inferential statistical test to determine whether the difference in scores is statistically significant or could have occurred by chance. This helps to support or refute the hypothesis that the intervention had a real effect.

Question 3: Describe a scenario in psychological research where a t-test would be appropriate, and specify whether it would be an independent or paired t-test.

Answer: A scenario could be comparing the scores of participants on a memory test before and after they undergo a training program. This would require a paired t-test because the same participants are tested twice. Alternatively, comparing two different groups' scores after the training would require an independent t-test.

Question 4: Explain what a p-value indicates in the context of inferential statistics.

Answer: A p-value indicates the probability that the observed results occurred by chance if the null hypothesis is true. A low p-value (typically less than 0.05) suggests that the results are statistically significant and unlikely due to chance.

Question 5: You conduct an ANOVA test to compare the effects of three different teaching methods on student performance. What does a significant ANOVA result tell you?

Answer: A significant ANOVA result indicates that there are statistically significant differences in student performance among at least two of the teaching methods, but it does not specify which ones differ. Further post-hoc tests are needed to identify specific differences.

Question 6: Describe the purpose of a null hypothesis in inferential statistics.

Answer: The null hypothesis states that there is no effect or difference between the groups or variables being studied. It serves as a default assumption that researchers test against to determine if their results are statistically significant.

Question 7: Sketch a simple example of a box plot that could be used to compare the distribution of scores between two groups in a psychological study.

Answer: The sketch should include two boxes representing the interquartile range (IQR) for each group, with lines (whiskers) extending to the minimum and maximum scores, and a line inside each box indicating the median. The boxes should be side by side for comparison.

Question 8: Imagine a scenario where the data from a study do not show a significant difference between groups. What might this imply about the effect being tested?

Answer: It may imply that there is no real effect of the variable being tested, or that the sample size was too small to detect a difference. Alternatively, the effect might exist but was not captured due to variability or measurement issues.

Question 9: Discuss one limitation of using inferential statistics in psychological research.

Answer: One limitation is that inferential statistics rely on assumptions about the data (e.g., normal distribution, equal variances) that, if violated, can lead to inaccurate conclusions. Additionally, they do not prove causation, only suggest associations or differences.

Question 10: Design a simple hypothetical experiment and state which inferential test would be suitable to analyze the results. Briefly justify your choice.

Answer: A study comparing the effectiveness of two different relaxation techniques on reducing stress levels in university students. The stress levels are measured before and after the intervention in two separate groups. An independent samples t-test would be suitable to compare the post-intervention stress scores between the two groups because the groups are separate. Alternatively, a paired t-test could be used if comparing pre- and post-stress levels within each group.