Statistic Research Scenarios
Correlated (paired) t-test
A drug company wants to see if their new pill will improve scores on a really difficult vocabulary test. Participants in each group were matched based on age, gender, and IQ. For each participant in group 1, there's a participant assigned to group 2 with the same age, gender, and IQ, for a total of 20 participants.
Single sample t-test
A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score above 70 on the test. The six students get scores of 62, 92, 75, 68, 83, and 95.
ANOVA
A researcher is interested in whether disturbing people while they dream has an effect on temperament. Groups of normal adults are randomly assigned to one of three conditions.
Independent samples t-test
A researcher is interested in whether there is a greater concentration of acid rain in the northern US than in the southern US. He randomly selects two states (New Jersey and North Carolina) and compares average sulfate levels for July-September, from 1980-1990.
Independent samples T - test
Sally Sleepresearcher hypothesizes that people who are allowed to sleep for only four hours will score significantly lower than people who are allowed to sleep for eight hours on a cognitive skills test. She brings 16 participants into her sleep lab and randomly assigns them to one of two groups. In one group she has participants sleep for eight hours and in the other group she has them sleep for four. The next morning she administers the SCAT to all participants. (Scores range from 1-9)
Z - score
Suppose that some individuals competed in a mini triathlon in which they each had to swim 500 meters, bicycle 10 miles, and run 3 miles. The scores for each of the events are on different scales; however, you want to be able to compare each event on the same scale.
Independent sample T - test
For a group of employees, you measured their level of agreement with their supervisor in regards to policies their supervisor supports. You are interested in examining whether employees with low trust in their leader have a different level of agreement than employees who have a high trust in their leader.
Independent samples T - test
Is there a significant difference between walkers and drivers in their performance on the physical fitness test?
Independent sample T - test
A social psychologist is interested in whether perceptions of likability are based on how often a person makes mistakes. To test this theory, she has one group of subjects watch a quiz show in which a contestant answers each question correctly. A second group of subjects is randomly assigned to watch the same contestant provide the wrong answer for several questions. After watching the show, each group is asked to rate how likable the contestant was on a scale of 1 to 7.
Z-score
A student in your class scored a 75 on the most recent exam and that class average was around 80. You want to calculate the proportion of students who have a score below 75.
Correlated (paired) t-test
A study was conducted to investigate the effectiveness of hypnotism in reducing pain. You want to know if there was a change in a persons pain ratings from before hypnotism to after hypnotism.
Correlated (paired) t-test
An industrial psychologist wants to evaluate the effect of a new profit sharing plan on employee productivity at a computer assembly plant. She randomly selects 10 assembly teams and records the number of units produced for the eight weeks prior and the eight weeks after the implementation of the profit sharing plan.
Correlated (paired) t-test
You are interested in examining how the size of a computer screen influences how quickly people complete tasks. In your experiment, 10 participants complete a set of tasks using a 15 inch monitor and then using a 42 inch monitor. For each participant, you measure how long in seconds it takes them to complete their task on the 15 inch monitor and on the 42 inch monitor. Is there a significant difference in the length of time it takes to complete tasks on a 15 inch monitor compared to a 42 inch monitor?
Regression line
You are interested in seeing if a person's level of extroversion can predict the number of clubs they will join in college.
Single sample t-test
You have a group of students and you think that their IQs are higher than the average IQ of the population (the average IQ score in the population is 100). Determine if your group of students has a significantly different IQ than the population.
Cohens d, independent group
You know there is a difference on the final exam between the students who studied and students who did not study, but you want to know how big that difference is.
Frequency distribution
You want to know what colors your students prefer.
Pearson's r correlation
You want to see if the number of registered automatic weapons (in thousands), is related to the murder rate ( in murders per 100,000) for 8 randomly selected states.