PSYCH 402 Exam 1
Long Answer (5 points each)
1. You and your research mentor just finished collecting data for a project. Before conducting analyses, your mentor wants to know what indices of central tendency would be most useful for describing the variables of interest.
The variables of interest include Externalizing Behavior. (e.g., aggressive behavior, fighting), Teacher–Child Conflict, Parental Warmth, and the Perceived Stress Scale. Histogram plots are shown below. For each variable, describe which indices of central tendency would best describe a commonly occurring score and why.
2. Let’s pretend that a researcher, Jackie Daytona, has SAT scores from the entire population! Jackie notes that scores from the population are not normally distributed (shown in a histogram below). Let’s also pretend that Jackie Daytona repeatedly drew samples of 40 students from the population data shown in the histogram. Jackie believes that the distribution of sample means from his repeated sampling will not be normally distributed because the population data is not normally distributed. Is Jackie correct or not, and why? According to what theory is Jackie correct or not?
3. You are working in a research lab that examines the development of adolescent risk-taking behavior. In the lab, adolescents complete a simulated driving game to measure risk-taking behavior. A postdoc in the lab wants to know if adolescents engage in more risk-taking behavior. than the general population. He collected data from 28 adolescents and found that the average risk-taking score was 82.3 (alternative mean). The average risk-taking score from the general population is 80.4 (the null mean).
From the example above, how would you decide if 82.3 is statistically different from 80.4 from a null-hypothesis significance testing perspective? Your response should elaborate on the following: the research hypothesis, the statistical hypothesis, the null distribution, the alpha level and its interpretation, the p-value, and Type I error rates. Ultimately, what information do you need to determine statistical significance, and what are the possible outcomes of that decision (e.g., types of errors)?
Short Answer (2 points each)
4. What is a type II error? How is it different from a type I error?
5. Define and describe dispersion. Please also define and describe the average deviation, variance, and standard deviation. Are there any problems with the interpretation of these metrics for dispersion that the others resolve?
6. You have a bag of chips with various colors. The probability of drawing a green is very low (let’s say there is a 2% chance of drawing a green chip). You bet your friend that he will pay for lunch if you draw the green chip. You end up drawing the green chip, and your friend accuses you of cheating because “the green chip has the lowest probability of being drawn.” Is your friend correct in accusing you of cheating? Explain your reasoning.
7. You are helping a graduate student review a paper. In the paper, the researchers report the mean for a categorical variable code as 0 = “Did not attend a charter school” and 1 = “Attended a charter school.” The mean is reported as 0.72. The graduate student says to you “I do not know what they reported a mean for that variable. It is categorical!” Is the graduate student correct? Does the mean for categorical variables have an interpretation? If so, what is the interpretation?
8. Identify and define each component of the boxplot shown in red letters below.
9. What are some key similarities and differences between the standard deviation and the standard error of the mean? How might they apply to the distribution of the observed scores (i.e., data from a sample of participants that you collected) or the distribution of sample means?