Single-Sample t-Tests
In this scenario, one key piece of information is missing that prevents us from using the traditional z-test hypothesis testing approach and instead requires us to conduct a t-test.
What is unknown population variance (and standard deviation)
Participant 1 had a pre-intervention score of 35 and a post-intervention score of 45. What is their difference score?
What is 10.
Come up with an independent-samples t-test example/prompt!
What is (depends on example)
Blair is interested in studying the difference between type of ice (cubed, sphere, no ice) and type of tea (sweet, half and half, unsweet) on feelings of refreshment. What are the factors and what are the levels?
Maddie wants to study whether runners have lower stress than non-runners. She samples two groups, one group of runners and one group of non-runners. Then, she matches the groups based on age and gender. She asks each person to report their stress level. What is the study design and sample type?
What is between-subjects dependent samples
What does the t-distribution curve look like? Please draw!
(Drawn on board)
Andy conducts a dependent-samples within-subjects design by asking participants to take an agility test before and after a 10-week training period. What is another name for this type of study?
What is repeated measures
Independent-samples t-tests cannot be which type of sample (within-subjects or between-subjects)? Why?
What is within-subjects. Why -> because within-subjects samples are always dependent on previous scores for comparison.
What does the f-distribution curve look like? Please draw!
(Draw on board)
Max studies whether reaction time predicts the amount of car accidents that students get into. What is the independent variable?
What is reaction time.
You are interested in finding out whether or not people who regularly eat fast food have different IQ than those who don't. You perform a t-test with 15 participants. What is your t-critical score?
What is 2.145.
In single-sample t-tests, we set the mean of the distribution of means to the population mean. In dependent-samples (and independent-samples) t-tests, though, we set the mean of the distribution of means to something different. What is it?
What is 0
For all t-tests, we assume that the population has normal distribution of scores on the dependent variable. For independent-samples t-tests, however, we also have two other assumptions. What are they?
What is homogeneity of variance and independence of scores.
In an ANOVA, we measure between-groups variance and within-groups variance. The between-groups variance tells us real differences between groups, while the within-groups variance tells us what?
What is Error / differences caused by sampling.
Why do we use chi-square tests and what are the two types of chi-square tests?
Chi-square tests allow us to use categorical data instead of quantitative data.
What are 1. Goodness-of-Fit: Does one variable’s distribution match expectations?
2. Test of Independence: Are two categorical variables related?
Do students enrolled in upper-level biology courses differ from the general college population on the question, “How motivated do you feel on a typical school day?” (population mean = 5)?
Fail to reject. T observed (1.06) is not more extreme than (-2.093, 2.093). Students enrolled in upper-level biology courses do not differ from the general college population in motivation at a 95% confidence level.
Jacob measured the quality of children's listening ability before and after story time. Conduct a dependent-samples t-test!
What is reject null hypothesis. T observed (41.18) is more extreme than t-critical (-2.145, 2.145). Children's listening ability was different after story time than it was before story time at a 95% confidence level.
A nutrition researcher, Julia, wants to know whether a new meal-prep program reduces students’ weekly fast-food consumption. She samples one group of students who gets the new meal-prep program, and one that does not. She measures number of fast-food meals in each group over 1 week.
What is fail to reject. T observed (-1.59) is not less than the t-critical value (-1.796). The meal-prep program did not reduce students' weekly fast-food consumption at a 95% confidence level.
Two-way ANOVA interpretation...
What is one significant main effect (education level) and a significant interaction effect (gender and education level) on political interest.
ANOVAs do not tell us which groups are different, but rather that there is a difference between the groups, in general. What type of test tells us which specific groups are different?
What is a Post-hoc test
Enrico suspects that members of the honors program have higher GPAs than the overall college average of 3.10.
After randomly sampling 20 honors students, he finds a mean GPA of 3.35. He wants to determine whether this increase is statistically meaningful or if the 0.25-point difference could simply be the result of sampling unusually high-achieving students by chance.
What is fail to reject. T observed (0.18) is not greater than t critical (1.833). Honors students do not have a significantly higher GPA than students in general at a 95% confidence level.
Jackson measured the quality of studying before and after thanksgiving dinner. Conduct a dependent-samples t-test!
A pharmacist, Stella, wants to know whether a new drug changes students’ weekly fast-food consumption. She samples one group of students who gets the new drug, and one that does not. She measures number of fast-food meals in each group over 1 week.
Fail to reject. T observed (-1.90) is not more extreme than t-critical (-2.262, 2.262). The new drug does not change students' weekly fast-food consumption.
Ayla studies whether employee's desire to quit is different when they have a supportive boss, non-supportive boss, or no boss?
What is the difference between Type 1 and Type 2 Error?
What is that Type 1 error is when you incorrectly reject the null
hypothesis when you should
have failed to reject it.
Type II Error:
Fail to reject the null
hypothesis when you should
have rejected it