Lecture 3

Question 1

What is a t distribution?

Answer 1

A distribution for a small sample size.

All t-distributions resemble normal distributions in that they are unimodal with the mean centered.
t-distributions have somewhat “fatter” tails than normal distributions.

Question 2

How do you calculate degrees of freedom?

Answer 2

n-1

where n is the sample size

Question 3

What is the use of t tests?

Answer 3

Providing CI’s around the mean

Question 4

What is the alpha number?

Answer 4

The 1-CI

e.g. 95% CI has an alpha number of 0.05

Question 5

How is this interpreted:

95%CI = 63.36 ± (2.228)(3.41) = 60.36 ± 7.60 = 52.76, 67.96

Answer 5

We are 95% confident that the mean is between 52.76 and 67.96

Question 6

What assumptions must be made to do a t-test?

Answer 6

1. The sample is random or unbiased.
2. All observations are independent
3. We are sampling from a normal population.

Question 7

When can you not use pooled variance?

Answer 7

If the difference in variance (SD) is different by a factor of 2, you should use separate variances rather than pooled variances.

Question 8

Based on CI, how can you tell if two means are significantly different?

Answer 8

If the CI of the difference between the two does not include zero.

Question 9

How do you calculate df for pooled (equal) variance?

Answer 9

n1 + n2 -2

Question 10

What determines df?

Answer 10

ALWAYS SAMPLE SIZE!

Question 11

What is a shortcut for calculating df for unequal variances?

Answer 11

df = n-1

using n of the SMALLER of the two sample sizes

Question 12

What is true of repeated measures on the same individual?

Answer 12

They can never be independent! Must first find the difference between the paired measurements and look at the variance in THAT (basic t test).

Question 13

What test in stata do you use to test for equal variances?

Answer 13

Robust-equal variance test. aka as Levene’s test

Question 14

What is the null hypothesis for Levene’s test?

Answer 14

That the variances are equal

Question 15

Does a p value tell you anything about the magnitude of the difference between values?

Answer 15

Nope

Question 16

What test would you use for a simple hypothesis test?

Answer 16

A one-sample t test. Compares your sample to a theoretical value.

Question 17

What is Ho and Ha?

Answer 17

Ho = null hypothesis
Ha = alternative hypothesis

Question 18

What is the difference between z scores and t scores?

Answer 18

The z-test (resulting in a z-score) can be used to test a hypothesis when researchers know, or can closely estimate, population parameters like μ and σ. The z-score is based on a standard normal distribution.

Question 19

What does it mean for a test to be ‘robust’?

Answer 19

It can withstand significant derivation from normality and still be functional.

Question 20

Is a one-sided or two-sided test more conservative (harder to reject the null).

Answer 20

two-sided

Question 21

Why is a two-sided test more conservative?

Answer 21

Your alpha (usually 0.05) is divided by two. 1/2 below and 1/2 above, leading to a wider acceptance area/narrower rejection area