1
Does higher power = better study?
Higher power improves your ability to detect real effects, but a “better” study also depends on good design, valid measures, and lack of bias.
What is a t test/what is it used for?
used to compare the means of two groups to determine if they are significantly different
What is type 1 error?
Saying there is an effect when there isnt
what is the formula for Independent mean t test?
𝑡 = 𝑀1 − 𝑀2/𝑆𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐
What is a within subjects design?
Same participates in all conditions
When should you use a Z test?
Use z when population σ is known
when should you use a t test?
Use t when σ is unknown, and/or sample is <30
If Alpha increases, what happens to type 1 error?
Increases
what is the formula for dependent mean t tets?
𝑡 = 𝑀 − µ/Sm
what is a between subjects design?
Different participants in each condition
what is a z test?
tests a hypothesis about a population mean
A researcher compares test scores between two different classes. What test should they use?
Independent t-test
When does Type 1 error occur?
We conclude that there is an effect in the population when there is not.
What does Cohen’s d tell you?
How big the difference is between two groups (in standard deviation units)
what does standard error tell us?
Standard error tells us how much the sample means vary across samples
A sample of 75 people were given an experimental treatment and had a mean of 16 on a particular measure. The general population of individuals has a mean of 15 on this measure and a standard deviation of 5. Do Z test using the five steps of hypothesis testing with a two-tailed test at the .05 significance level, and make a drawing of the distributions involved.
Answer
Step 1 Restate the question as a research hypothesis and a null hypothesis about the populations. The two populations are:
Population 1: Those given the experimental treatment.
Population 2: People in the general population (who are not given the experimental treatment).
The research hypothesis is that the population given the experimental treatment will have a different mean on the particular measure from the mean of people in the general population (who are not given the experimental treatment): μ1≠μ2. The null hypothesis is that the populations have the same mean score on this measure: μ1=μ2.
Step 2 Determine the characteristics of the comparison distribution.
μM=μ=15;σM=σ2N=5275=.33=.57; shape is normal (sample size is greater than 30).
Step 3 Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. Two-tailed cutoffs, 5% significance level, are +1.96 and −1.96.
Step 4 Determine your sample’s score on the comparison distribution. Using the formula,
Z=(M−μM)/σM,Z=(16−15)/.57=1/.57=1.75.
Step 5 Decide whether to reject the null hypothesis. The sample’s Z score of 1.75 is not more extreme than the cutoffs of ±1.96; do not reject the null hypothesis. Results are inconclusive. The distributions involved are shown in
Find the 99% confidence interval for the sample mean in the study just described.
Step 1 Figure out the standard error. The standard error is the standard deviation of the distribution of means. In the preceding problem, it was .57.
Step 2 For the 95% confidence interval, figure the raw scores for 1.96 standard errors above and below the sample mean; for the 99% confidence interval, figure the raw scores for 2.58 standard errors above and below the sample mean. For the 99% confidence interval, upper limit=M+(2.58)(σM)=16+(2.58)(.57)=16+1.47=17.47; lower limit=M−(2.58)(σM)=16−(2.58)(.57)=16−1.47=14.53. Thus, the 99% confidence interval is from 14.53 to 17.47.
What is type 2 error?
failing to detect a real effect
Which test has more statistical power and why?
The dependent t-test has more statistical power because it reduces variability
What is degrees of freedom and why do we use it?
Represent the number of independent values in a sample that are free to vary when estimating parameters.
We use DF to define the shape of probability distributions and to prevent unbiased accurate estimations.
In a study comparing stress levels between two groups (exercise vs. no exercise), one participant is accidentally included in both groups. Why is this a problem, and what would be the issue if the grouping variable were nominal (e.g., gender categories)?
This is a problem because it violates independence, meaning the data are no longer truly separate, which can bias results and increase the chance of false significance. If the variable were nominal, the issue is worse because a person cannot belong to multiple categories at once, making the data invalid.
Why do z-tests and t-tests require data to be measured on an interval or ratio scale?
Because these tests rely on meaningful differences between values, they assume equal intervals so calculations like means and standard deviations are valid.
What increases the likelihood of a Type II error?
Small sample size
What is the difference between significance and effect size?
Statistical significance tells us the likelihood observing the given data if the null was true (aka likelihood of there being an effect), while effect size tells you how big or meaningful that effect is
Why is it a problem to switch from a two tailed test to a one tailed test?
It inflates your chance of finding significance (Type I error)
It’s a form of “p-hacking”