Sampling & Hypothesis Testing
Define population and sample.
What is the minimum score on Cronbach's alpha needed to infer a Likert-scale is reliable?
a > .70
A dataset contains the scores 4, 6, 8, and 12. What is the mean of this dataset?
7.5
The bare minimum sample size needed for univariate distribution to have a probable chance of being normal.
30
How do you calculate an individual participants mean score on a scaled measure?
Total/sum the individual scores to each question in the scale, then divide by the # of items in the scale.
Describe the difference between the null and alternative hypothesis.
What are the cut-off scores we use to infer there is skewness in your sample distribution?
+/-1
A dataset has a minimum value of 10 and a maximum value of 27. What is the range?
27-10 = 17
Name the two effect sizes we've discussed in the last two weeks.
Pearsons (r) and Shapiro-Wilk (w)
How do you calculate a group mean on a scaled measure?
Total/sum all participants averaged scores, then divide by the # of participants.
Name two types of probability sampling method, and one type of non-probability sampling method.
Simple random, systematic, stratified, cluster; convenience or snowball
A distribution has a skewness score of 2.48, with most numerical values clustered on this end of the scale.
lower end
Two classes have the same mean exam score, but Class A has a much larger standard deviation than Class B. What does the larger standard deviation tell us about Class A’s scores?
The scores are more spread out / have greater variability.
A researcher reports two correlations: r = 0.07 between sleep and exam scores, and r = −0.46 between stress and exam scores. How would you interpret the strength and direction of these correlations?
0.07 = negligible positive correlation; −0.46 = moderate negative correlation
A dataset contains the ordered scores 2, 4, 4, 4, 5, 6, 6, 6, 8. What is the mode?
4 and 6
Hypothesis: Students who study more hours will score higher on the exam than students who study fewer hours.
What direction is this hypothesis?
Positive / directional relationship
A distribution shape has a very sharp peak and heavy tails, meaning many scores are close to the mean but there are also more extreme values than normal.
Leptokurtic
A dataset contains the scores 5, 7, 9, 20. One value is much larger than the others. Which measure of central tendency would be most affected by the extreme value?
Mean
A study reports a 95% confidence interval of −0.12 to 0.35 for the effect of a new teaching method on exam scores. Is this result statistically significant, and why or why not?
No — the interval crosses 0, meaning we cannot rule out no effect.
The class exam mean is 75 and the standard deviation is 5. A student scored 85 on the exam. What is this student’s z-score?
z = (85−75)/5 = 2.0
The sampling method involving selecting every 10th person from a list of students after choosing a random starting point.
Systematic
Name two reasons a survey scale could show low reliability.
Poorly written or inconsistent items that do not measure the same construct, incomplete surveys, small sample size, not culturally responsive.
A distribution of incomes is positively-skewed, with a few extremely high earners pulling the tail to the right. In this distribution, which measure of central tendency will typically be largest?
Mean — the high outlier values pull the mean upward.
How do we calculate degrees of freedom and what does the numerical value tell us?
Degrees of freedom are calculated using the sample size and number of estimated parameters (often n − 1 in bivariate analysis). The value indicates how many scores are free to vary in a statistical calculation
Describe or list out the steps to calculate standard deviation.
Subtract each score from the mean, square the differences, add them up, divide by n−1 (for a sample), and take the square root.