t-tests

Question 1

T-test

Answer 1

A method of comparing two means to determine if there is a significant difference between

Question 2

Dependent sample t-test

Answer 2

Compares two means based on related data.
e.g., The same people measured at different times
Data from “matched” samples

Question 3

Independent t-test

Answer 3

Compares two means based on independent data
e.g., Data from different groups of people

Question 4

Significance testing

Answer 4

Testing the significance of t
Testing the significance of b in a regression

Question 5

Rationale to the t-test
t=

Answer 5

expected difference between population means
(if null hypothesis is true)]
/
estimate of the standard error of the difference between two sample means

Question 6

t-tests are used over z-tests when…

Answer 6

we don’t have the value of the standard deviation a head of time

Question 7

z-test formula vs t-test formula

Answer 7

Denominator difference
Standard error of the mean is now an estimate because we have used the sample SD to estimate the pop SD

Question 8

The standard error of the sampling distribution of the mean (SM)

Answer 8

Question 9

t-distributions are thought of as…

Answer 9

Distorted versions of z-distributions. If the estimate is high quality, then it looks similar to a z-distribution, if not it looks less like a z-distribution. (This depends on sample size, n)

Question 10

For small samples the value of t must be larger than ____ or smaller than ____ to reject the null hypothesis.

Answer 10

1.96, -1.96

Question 11

For n >/= 30 you should treat a t-test like a z-test. That means you…

Answer 11

compare the calculated t-value to +/-1.96 for (a = .05, 2-tailed)

Question 12

For n < 30

Answer 12

t-distribution departs from z distribution (because the s to estimate pop s(Sigma) isn’t accurate) so the old critical points won’t do. You now need t values more extreme then +/-1.96 if you want to end up rejecting the null (for a=.05)

Question 13

Rejection of the null depends on sample size, therefore we…

Answer 13

Keep track of the Degrees of freedom when listing the t-value.
e.g., single sample t-test
n=18
df=n-1=17

t(17)=1.22

Question 14

Central Limit Theorem

Answer 14

guarantees normality if n > 30

Question 15

If sample size is under 30…

Answer 15

we should have to preform preliminary tests to determine if the sample was drawn from a normal population

Question 16

Testing Skew