T-tests Flashcards
What is Standard Error of the mean and what is its importance?
Standard Error of the Mean (SEm ) is the measure used to reflect sampling error
SEM is the standard deviation of the sample means
SEM is an acknowledgment that our prediction of the population parameter is an educated guess
- Therefore, it is tied to a statement of the probability that the guess is right/wrong
SEm = SD / Sqr(N)
How does Standard Error of the Mean change when Standard Deviation increases? Why?
Sem would increase, numerator gets bigger but why?
If our sample has a tight cluster of data, then probably we have a lot of people around the population mean,
Why does the Standard Error of the Mean increase as sample size decreases?
If you increase your sample size, your data becomes more reflective of the true population = more confidence
How do we interpret SeM
The standard error tells you how accurate the mean of any given sample from that population is likely to be compared to the true population mean.
What happens to the probability of an error (α) as we increase our estimate of the range that we expect to contain the population mean (i.e. going from the 68% to 95% CI)?
It will decrease as we increase confidence
What is hypothesis testing for a two-tailed test?
An objective method of establishing whether something is NOT true
Null Hypothesis (𝐻𝑜) – Any difference between our samples occurred due to chance (i.e. sampling error)
Alternate Hypothesis (𝐻𝐴) – Difference observed between our samples did not occur due to chance
What is the use of an independent samples t- test? And 3 assumptions made when using it?
Establish the difference between two independent samples drawn from population
Population, and therefore, samples are normally distributed
Groups are mutually exclusive
Homogeneity of variances (e.g. both groups have similar standard deviations)
What is the degrees of freedom for s Independent samples t-test
𝑑f= (𝑁control −1) + (𝑁experimental −1)
What are the problems with a independent t-test?
Assumes no relationship between groups
If there is, then variance gets double-counted.
An effect that may be present in a population may be missed when comparing our two samples
Run paired t-test to combat this
What are the uses from a paired t-test and 3 assumptions?
Establish the difference between two means collected at different time points from the same sample
Assumptions:
Population, and therefore, sample is normally distributed
Same individuals are in both samples
Homogeneity of variances (e.g. both time points have similar standard deviations)
𝑑f = 𝑁 − 1
Why are the df for a paired samples t-test smaller than an independent samples t-test?
You are collecting from the same group in paired as opposed to two in a independent
What are the 3 steps in interpreting a T test
Statement of what type of test was conducted, what the independent and
dependent variables were (typically done in methods section of a paper)
Describe whether the results are significant or not significant, provide relevant statistical information (t, df, p)
Interpret the statistical results relating back to the question of interest (e.g. if significant, go back and look at means to provide specific direction of difference)
If you run a paired samples t-test when you have mutually exclusive groups are you more likely to get a Type I or Type II error? Why?
Think of answer
What is cohens d?
The mean of the control + the mean of the experimental/ SD of control (measured in SD)
Used to measure effect size (How many standard deviations is the experimental group mean from the control group?)
Size
> 0.8 ~0.5 ~0.2
Interpretation
Large effect Moderate effect Small effect