Study Questions: Inferential Statistics

  1. In a single figure (single pair of x-y axes) draw two t distributions, one with a large number of degrees of freedom (df) and another with a small df. Label the two axes and the two curves.
  1. In a single figure (single pair of x-y axes) draw two X2 distributions, one with a large df and another with a small df. Label the two axes and the curves.
  1. In a single figure (single pair of x-y axes) draw two F distributions, one with a large df and another with a small df. Label the two axes and the curves.
  1. Explain why the denominators for sample and population variance are different.
  1. Explain what your professor meant when he emphasized that the t test was always based on a comparison of treatment means.
  1. Explain why the X2 is not used to compare treatment means. What does it compare?
  1. Explain why the computations for the t test for independent groups and the t test for matched groups are handled differently (that is, explain the logic of the comparisons – don’t just say that one is for matched groups and one for independent groups).
  1. Does the t test for repeated measures use the same family of t distributions as does the t test for independent groups? Explain.
  1. Explain the differences between parametric versus nonparametric statistical tests. What “parameters” are responsible for the difference?
  1. The X2 test makes fewer assumptions than does the t test. Identify the differences.
  1. Explain how contingency tables are useful for setting up X2 tests.
  1. Explain why the t test requires the use of ratio or interval scales.
  1. Explain why the X2 test does not require the use of ratio or interval scales.
  1. How does the sample size affect the tcv?
  1. What five basic questions must we answer before we can select the appropriate statistical test for an experiment?
  1. Our computed value of t is +3.28. Our critical value of t is +2.048. We have 28 degrees of freedom and we are using a two-tailed test. Draw a simple figure to illustrate the relationship between the critical and computed values of t for this result.

  1. Our computed value of t is –1.07. We have made a directional prediction and our critical value is –1.734. Make a rough illustration of the relationship between the computed and table values of t in this case. Is there a significant difference between the treatment means?
  1. A health magazine recently reported a study in which researchers claimed that iron supplements increased memory and problem-solving abilities in a random sample of college women. All of the women took memory and problem-solving tests at the beginning of the study, then took iron supplements, and then took the same tests again at the end of the study. What is wrong with this design? What confounds could be leading to the results of improved memory and problem-solving skills?
  1. In an experimental study of the effects of exercise on stress, subjects are randomly assigned to either the no exercise or the exercise conditions. Identify what type of study this is—between-, within-, or matched-subjects. In addition, identify the independent and dependent variables and the control and experimental groups.
  1. What are the advantages and disadvantages in the use of a posttest-only control group design versus a pretest-posttest control group design?
  1. What is a confound and how is it related to internal validity?
  1. Briefly explain the confounds of history and maturation.
  1. Briefly explain the confounds of testing and regression to the mean.
  1. Briefly explain the confounds of instrumentation and mortality.
  1. Briefly explain the relationship between participant effects, experimenter effects, single-blind experiments, and double-blind experiments.
  1. What is the relationship between external validity and the college sophomore problem?
  1. Differentiate between an exact replication, a systematic replication, and a conceptual replication.
  1. Identify the two types of correlated-groups designs discussed in the text and explain why each is considered a correlated-groups design.
  1. Explain what counterbalancing is, how it is achieved, and which confound it helps to minimize.
  1. Explain what a Balanced Latin square is and how it helps with counterbalancing.
  1. Imagine I conducted the following experiment: I used gender as a nonmanipulated independent variable and measured performance in my class. I measured performance by ranking everyone in the class, giving the person with the highest grade a 1, the person with the 2nd highest grade a 2, etc. Which statistic would I use to determine any differences in performance between these two groups?
  1. What are the assumptions of the Wilcoxon rank-sum test?

Suppose that your friendly professor carried out a quasi-experiment on the students in his Experimental Methods class. He wanted to determine if females spent more time studying for his course than did males. There were 20 females and 6 males in his class.

So, every day for a period of three weeks, he asked each student to write down the number of hours that he or she spent studying for his course. He totaled the hours for each student. Then he used a statistical test to see if there was a significant difference.

  1. What type of statistical test should he use? Explain why that test is appropriate.
  1. Explain why the other types of statistical tests are not appropriate.
  1. How many degrees of freedom are there?
  1. Should he use a one-tailed or two-tailed test? Explain.
  1. Does it matter that there were many more females than males in the class? Explain.
  1. Is his dependent measure on a ratio, interval, ordinal, or nominal scale? Explain.
  1. Suppose he uses the test you advised (in the question above) and finds a significant difference. In a single well-worded sentence, identify the research hypothesis that was supported.

Suppose that your friendly professor carried out an ex-post facto study using all Wofford students. He was interested in determining whether the 16 categories of the Myers Briggs Type Inventory were predictive of student grades. Assume that all students took the MBTI as entering freshman, and each student was described by a single MBTI type. Accessing student records, the professor counted the number of As, Bs, Cs, Ds, and Fs for each student over all the years at Wofford. Therefore, his dependent measure was the number of As, Bs, etc for each student in each MBTI category. Assume there was exactly the same number of students with each personality type (1440 students divided by the 16 types = 90 students of each type). The professor planned to use inferential statistics to determine whether MBTI type was reliably predictive of grades.

  1. What type of statistical test should he use? Explain why that test is appropriate.
  1. Explain why the other types of statistical tests are not appropriate.
  1. How many degrees of freedom are there?
  1. Should he use a one-tailed or two-tailed test? Explain.
  1. Is his dependent measure on a ratio, interval, ordinal, or nominal scale? Explain.
  1. Suppose he uses the test you recommended (in the question above) and finds a significant difference. In a single well-worded sentence, identify the research hypothesis that was supported.

Answer Questions 40-45(above) for each of the examples below:

  1. A psychologist would like to know how much difference there is between the problem-solving ability of 8-year old children versus 10-year old children. A random sample of 10 children is selected from each age group. The children are given a problem-solving test in which each question contributes the same amount to the overall score.
  1. A researcher is investigating the relation between reaction time and room temperature. A sample of n=16 subjects is obtained and each person’s reaction time is measured in a 70°room and again in a room where the temperature is 95°. On average, this sample showed a reaction time that was 45 milliseconds faster in the 70° room.
  1. A researcher is testing the effectiveness of a blood-pressure medication compared to a placebo using a double-blind procedure. Two samples of subjects are obtained (n=25 each) and divided into the medication group and the placebo group. Each person’s blood pressure is measured before beginning the medication. After 3 weeks, each person’s blood pressure is measured again. The researcher records the amount of change for each individual and compares the two groups.
  1. A common science-fair project involves testing the effects of music on the growth of plants. Of one of these projects, a sample of 24 newly sprouted bean plants is obtained. These plants are randomly assigned to four treatments, with n = 6 in each group. The four conditions are: rock music, heavy metal, country, and classical. The dependent variable is the height of each plant after 2 weeks.
  1. A researcher is examining the effect of sleep deprivation on basic mental processes. A sample of 8 subjects is obtained. These subjects agree to stay awake for a total of 48 hours. Every 12 hours the researcher gives each subject a series of arithmetic problems as a test for mental alertness. The number of problems worked correctly in 10 minutes is recorded for each subject.
  1. The process of interference is assumed to be responsible for much of forgetting in human memory. New information going into memory interferes with the information that already is there. One old, original demonstration of interference examined the process of forgetting while people are asleep versus while they are awake. Because presumably there should be less interference during sleep, there also should be less forgetting. The experiment examined four groups of subjects. All subjects were given a list of words to remember. Then half of the subjects went to sleep, and the others stayed awake. Within both the asleep and awake groups, half of the subjects were tested after 2 hours, and the rest were tested after 8 hours. The dependent variable is the number of words correctly recalled.