Sampling & Variability
Dr. Mac wants to know how Kansas college students feel about campus safety. Instead of surveying every student, she randomly selects 200 students. What kind of group has she collected?
A sample — a smaller group representing the population. *Random sample is also accepted.
A teacher reports the average exam score for the class. Which measure of central tendency is being used?
The mean.
Dr. Mac’s analysis shows p = .04 with α = .05. What decision should she make?
Reject H₀ — the result is statistically significant.
A researcher tests if caffeine affects memory and states “Caffeine has no effect.” What hypothesis is that?
The null hypothesis (H₀).
A survey reports that average stress is 6 ± 1 on a 95% CI. What does that mean?
We’re 95% confident the population mean is between 5 and 7.
A researcher posts a survey link only to her own psychology class. What kind of problem might this create?
Sampling bias — the sample isn’t representative of the population.
A histogram of income shows a long right tail. What kind of distribution is that?
Positively skewed distribution.
A researcher changes how outliers are handled until the p-value drops below .05. What questionable practice is that?
p-hacking.
A study finds a difference by chance, leading researchers to believe a false effect exists. What kind of error occurred?
Type I error (false positive).
You run a study with n = 20. You don’t know the population σ. Should you use a z or t test?
A t-test, since σ is unknown and sample is small.
You compute sample variance using n – 1 instead of n. Why?
To correct bias; dividing by n – 1 gives an unbiased estimate of population variance (i.e., degrees of freedom).
A researcher is examining whether or not looking at cats give people an improvement in mood. Is this an example of a one-tailed or two-tailed hypothesis?
One-tailed - improvement in mood implies directionality.
After running analyses, a student writes a “prediction” that matches her results and claims she planned it that way. What is she doing?
HARKing — Hypothesizing After Results are Known.
Dr. Mac predicts that teens in CBT will show lower anxiety than those on a wait-list. Should she use a one- or two-tailed test?
One-tailed, because direction is predicted.
A t-test output shows t(24) = 2.45, p < .05. What does the (24) represent?
Degrees of freedom (df = n – 1).
Two classes have the same mean exam score, but Class A’s scores cluster tightly while Class B’s range widely. Which class has the larger standard deviation?
Class B, because the scores are more spread out.
Two tests use different scales, but you standardize both with z-scores to compare students. Why does this work?
Standardization puts scores on the same metric (mean 0, SD 1).
What is the difference between alpha and the p-value?
Alpha - significance threshold set before research begins.
P-value - the actual significance value of the model.
Two treatments both have significant p-values, but one has d = .80 and the other d = .20. What does that tell you?
The first has a larger effect size — a stronger, more meaningful difference.
Two researchers calculate 95% CIs for mean sleep hours.
Researcher A: n = 25, CI = [6.0 - 8.5]
Researcher B: n = 200, CI = [6.8 - 7.3]
What statistical factor explains why Researcher B’s interval is narrower?
The larger sample reduces the standard error, leading to a narrower (more precise) confidence interval.
A psychology lab collects stress ratings from 25 participants and gets a sample mean of 7.2. Another lab replicates the study with 400 participants and gets a mean of 7.1. Why is the second lab’s result considered more reliable, even though the means are nearly identical?
Because the larger sample reduces sampling error, giving a more stable and precise estimate of the population mean.
A researcher sees that her dataset has a very sharp peak and thin tails compared to a normal curve. What term describes this?
Leptokurtic distribution (high kurtosis).
Why is random sampling so important for calculating probabilities accurately?
It ensures each member has equal chance, keeping probabilities unbiased.
A researcher finds p = .08 when comparing two anxiety treatments, but the effect size is Cohen’s d = .75. What might explain the nonsignificant p-value despite a large effect?
The sample size was too small — the study had low statistical power, so even a large true effect didn’t reach significance.
What confidence level is typically used in psychology?
95% confidence interval