t-tests Flashcards
What is the question we’re trying to answer when comparing two means?
Do people in one group score, perform, react, behave (etc) differently than in another group?
Define the following types of mean:
1. Independent
2. Paired
- Different pts in each group
- Same pts in both groups
What are the three steps of analysis?
- Calculate test statistic (signal-to-noise ratio)
- Compare that test statistic to its distribution under the null hypothesis
- Obtain the probability (p) of encountering a test statistic of the size we have, or larger, assuming the null hypothesis is true
Define ratio
A number that captures the relative size of two quantities, expressed as how many times bigger the first quantity is than the second
How do you calculate the mean?
The first number divided by the second
What is “the signal” when calculating the test statistic?
The relationship of interest (variation in scores explained by group membership)
How do you calculate the signal?
Calculate the mean of each group
Subtract one mean from the other
The size of the difference in means is the signal
What is “the noise” when calculating the test statistic?
The noise is the error, the variation NOT explained by group membership
(the differences in means have a sampling distribution, exactly analogous to the sampling distribution of the mean)
Define test statistic
A number that captures the relationship or comparison of interest
What is the Redux, and how do we calculate it?
Calculate the (standardised) difference between mean scores
Divide the signal (difference in mean) by the noise (standard error of the difference in means)
What can we conclude if p > .05?
Our results are likely to occur under the null hypothesis
We have no evidence that the null hypothesis is not true
Conclusion: RETAIN THE NULL
What can we conclude if p < .05?
Our results are unlikely to occur under the null hypothesis
It may in fact be the case that the null hypothesis is not true
Conclusion: REJECT THE NULL
What does independent samples t-tests test?
Tests the null hypothesis that two samples come from the same population
Calculate test statistic t, which expresses signal-to-noise ratio
Then, evaluate the probability p of obtaining t of this size (or larger) under the null hypothesis
If p < 𝛼, we might conclude that group membership is associated with some difference
In a repeated design, the data are paired. What does this mean?
Both columns (pre and post) contain the same thing (here, reaction time)
Each row contains data from the same person
What does the t-test quantify?
The size of the difference of two means (signal) compared to the error (noise)
