Core concepts
What is the hypothesis test that states "there is no effect or difference"?
The Null Hypothesis
you compare a sample mean to a population mean, and you know the population SD. What test would you use?
Z-test
What is effect size?
Standardized units for comparing mean differences. Tells you how meaningful a result is
what is a point estimate?
one specific number from our data, like the mean. More precise, but less accurate
a psychologist measures stress levels in a class of 25 students and compares them to the national average. They know the mean, but not the standard deviation of the population. What test should they use?
One-sample t-test
what are the general steps of hypothesis tests?
1: set up H(0) and H(A)
2: calculate relevant statistics
3: calculate probability under the null
4: identify cut-off values
5: make your decision
what is the hypothesis that states that there is a difference?
The Alternative Hypothesis
You compare a sample mean to a population mean, but the population SD is unknown. Which test would you use?
One-sample t-test
what is the formula for Cohen's d in a one-sample t-test?
d=M−μ/SD
d = (sample mean) - (population mean)/(standard deviation)
what is an interval estimate?
ranges that include the point estimate, but allows for some error. Less precise, but more accurate
a researcher tests whether caffeine improves memory by comparing a group that drinks coffee to one that doesn't. Which test should they use?
Independent samples t-test
what are the steps for a one-sample t-test
1: set up H(0) and H(A)
2: Calculate M and SD (if not given)
3: calculate SE and DF
4: calculate t
5: look up critical t
6: make a decision
What is the step-by-step process of deciding whether data supports the null or alternative hypothesis?
hypothesis testing
You are comparing two independent groups (treatment vs. placebo, women vs. men, etc). which test would you use?
Independent samples t-test
What is Cohen's d benchmarks for small, medium, and large effect sizes?
~0.2 = small
~0.5 = medium
~0.8 = large
what is the correct interpretation of a 95% confidence interval?
if we were to repeat a study an infinite number of times, 95% of those intervals would contain the true population mean
A therapist measures a clients' anxiety before and after 8 weeks for mindfulness training. Which test should they use?
paired samples t-test
what are the steps for an independent samples t-test?
1: set up H(0) and H(A)
2: calculate M for each group and pooled SD (if not given)
3: calculate SE and DF
4: calculate t
5: look up critical t in the t table
6: make a decision
when results are consistent across multiple studies, what is that called?
replication
you are comparing the same participants at two times or conditions. Which test should you use?
Paired samples t-test (NOTE: this will not be on the test! But it's still important to know)
what is statistical power?
the ability of a study to detect the effect you are interested in. Or, how likely a study is to find a real life effect when one actually exists
if two means' confidence intervals overlap, what does that suggest?
It's likely not statistically significant (fail to reject the null hypothesis)
a cognitive scientist compares average reaction times for gamers to the general population. The population mean is known. Which test should they use?
z-test
what are the steps for a paired samples t-test?
1: set up H(0) and H(A)
2: calculate M(diff) and SD (diff) (if not given)
3: calculate SE and DF
4: calculate t
5: look up critical value in t-table
6: make your decision
What does it mean to ACCEPT the null?
Trick question! There is no such thing as "accepting" the null hypothesis. We can only FAIL TO REJECT the null hypothesis
what is counterbalancing?
When you change the order that participants experience conditions in a study to avoid order effects, such as practice or fatigue
What statistic is NOT affected by sample size?
effect size
as sample size increases, what happens to the confidence interval width?
it becomes narrower, which means a more precise estimate
a social psychologist compares two teaching methods and finds p =0.02 and Cohen's d = 0.15. What can they conclude?
the difference is statistically significant (0.02 < 0.05), but the effect size is really small, meaning it may not be practically meaningful
What are the steps for a z-test?
1: set up H(0) and H(A)
2: calculate mean, if not given
3: calculate z
4: see if it's beyond the critical value in the critical z-table
5: make a decision