Tests and Distributions (Basic Stats)

Question 1

Null Hypothesis

Answer 1

“no effect”

Question 2

Alternative Hypothesis

Answer 2

Some real effect

Question 3

Test Statistic

Answer 3

Standardized difference

Question 4

Obtain p-value from the…

Answer 4

sampling distribution
(If we had lots of samples, and the H_0 were true, what is the [theoretical] distribution of the test statistic?

Question 5

General framework of a test:

Answer 5

1. State null and alternative hypotheses
2. Calculate test statistic
3. Obtain p-value from sampling distribution
4. Make conclusion

Question 6

“Under H_0” means…

Answer 6

“if H_0 is true”

Question 7

p-value is:

Answer 7

probability of observing the data we did (or more extreme), just by chance give that H_0 is true.

Question 8

When is the t-distribution appropriate?

Answer 8

When the model assumptions are met:
- need to check the distribution for normality
(If the underlying distribution isn’t normal, than the distribution from which the p-value comes from will be incorrect, and will give an erroneous value!)

Question 9

What graphical checks can we do to check normality?

Answer 9

• Boxplot
• Histogram
• Normal Probability Plot (Q-Q plot) (compare observed values to expected

Question 10

Boxplots don’t really test for…

Answer 10

outliers

Question 11

What is a Kernel?

Answer 11

Basically a smoothed histogram

Question 12

What shape is a Q-Q plot if the distribution is short-tailed?

Answer 12

S- shaped!

Question 13

What shape is a Q-Q plot if the distribution is long-tailed?

Answer 13

Inverted S (like x^3 graph)

Question 14

What shape is a Q-Q plot if the distribution is right-skewed?

Answer 14

Like e^x function (curves upwards to inf)

Question 15

What shape is a Q-Q plot if the distribution is left skewed?

Answer 15

like sqrt(x) function. (curves to a steady value)

Question 16

What do we do if normality assumptions are violated?

Answer 16

• Transform the response variable
• or try a non-parametric test (aka no distribution is assumed) (these are usually less statistically powerful)
• Generate the sampling distribution by the Permutation Approach

Question 17

What transformations can we try for right-skewed data?

Answer 17

• log

- sqrt

Question 18

What is the permutation approach? (for t-tests)

Answer 18

Since H_0 says the labels don’t matter, if the underlying distribution isn’t normal, then we can rearrange the labels randomly a LOT (or possibly all) of times and find the distribution of all possible t-values.

Then finding the area under the tails from our t-value onwards will give us the p-value!

Question 19

What is resampling?

Answer 19

When we generate the sampling distribution with repeat samples of the data
(ie: bootstrap sampling (with replacement), or permutation (w/o replacement)

Question 20

What are non-parametric tests?

Answer 20

Wilcoxon Rank sum

Mann-Whitney test

Question 21

Hypotheses for numerical normality tests?

Answer 21

H_0: the data are normal
H_A: the data are not normal

Question 22

When to use the Shapiro-Wilk test for normality?

Answer 22

When 10 < n < 2000

Question 23

When to use the Kolmogorov-Smirnov Test for normality?

Answer 23

When n > 2000