Ch. 12

Question 1

Paired sample vs. 2 independent samples

Answer 1

Paired = both treatment applied to every sampled unit Two-sample design = each treatment group has an independent, random sample of units (see Pg. 329)

Question 2

What is more powerful, paired sample or two-sample and why?

Answer 2

Paired sample, as it the similarities allow for some of the extraneous variation (noise) between plots to be controlled for. In other words, the effects of variation can be reduced and allows you to see a better picture of what really occurs w/ and w/o treatment (i.e. more power). Also increases precision, as less variation.

Question 3

How can we used paired data?

Answer 3

We take the difference between measurements, then can test the effect of treatment using the mean of differences.

Question 4

What is the sample unit in tests with two means?

What is the sample size in a paired test?

Answer 4

The differences in the pairs (NOT the number of measurements). Thus the sample size = # of pairs.

Question 5

How can we narrow a confidence interval?

Answer 5

• Lower the critical value
• Increase sample size

Question 6

Paired t-test

• What is it?
• How is it analyzed?

Answer 6

• Tests a null hypothesis that the mean difference of paired measurements equal a specified value
• Analyzed just like a one sample t-test

Question 7

Assumptions of the paired t-test

Answer 7

Same as a one-sample t-test:

1. sampling units are randomly sampled from the population
2. Paired differences have a normal distribution in the population

Note that there is NO assumption of the distribution of the two measurements of the sampling units; only the DIFFERENCE between the measurements needs to be normally distributed

Question 8

Pooled sample variance definition

Answer 8

The average of the variance of the samples weighted by their degrees of freedom.

Best average of the variance within groups, assuming equal variance.

Question 9

Assumption of the confidence interval formula?

Answer 9

Assmes that the standard deviations (and variances) of the two populations are the same.

Question 10

Degrees of freedom for a two-tailed t-test and two-sample confidence interval?

Answer 10

df = df₁ + df₂ = n₁ + n₂ - 2

Question 11

General procedure for testing two means

Answer 11

• Select appropriate test (two-sample t-test, Paired t-test)
• Do 95% CI
• Make hypotheses
• Do test

Question 12

What test is used to compare the means of a numerical veriable between two independent groups?

Answer 12

Two-sample t-test

Question 13

Common null hypothesis for two-sample t-test?

Answer 13

u₁ = u₂

(population means equal, or alternatively, differences between means = 0)

Question 14

Assumptions of the two-sided t-test and two-sample CI for a difference in means?

Answer 14

• Each of the 2 samples is a random sample from its population
• The numerical variable is normally distributed in each population
• The standard deviation (and variance) of the numerical variable is the same in both populations

Question 15

Limit of differences in deviation of the numerical variable for two-sided t-test?

Answer 15

• Greater than 3x difference in standard deviations
• sample sizes very different between populations
• Sample sizes are less than 30 for both groups

If these are violated, don’t use two-sample t-test

Question 16

Welch’s T-test

• What is it
• When should it be used

Answer 16

• Compares the means of two groups when the variances are not equal
• Use when two-sample t-test is not able to provide a accurate result (ex. more than 3x difference in standard deviation)

Question 17

Fallacy of Indirect comparison

Answer 17

Comparing two grpups seperately against the same null hypothesized value, rather than directly comparing the two means with one another (See sec. 12.5)

Question 18

F-Test

• What is it
• What is it used for
• Test statistic?
• Distriubtion used?

Answer 18

• Tests wheter two population variances are equal
• Test statistic is F, calculated from the ratio of sample variances
• if null is true (equal variance), F should be near 1 (and only deviated by chance)
• Uses the F-distribution

Question 19

F-Test

• Degrees of freedom calculation?
• Problems with the test? (including assumptions)

Answer 19

• Degrees of freedom are paired, (n₁ -1, n₂ - 1) where the first number is the numerator of the F-ratio, and the second for the denominator
• Assumes normal distribution, but is highly sensitive (i.e. not robust) to assumption (ex. falsely reject null if not normally distributed)

Question 20

Levene’s Test

• What is it?
• What advantages does it have over F test?
• Test statistic?
• Distribution used?

Answer 20

• Alternative test to test the null of equal variance between groups
• Advantages
  
  • Less sensitive to non-normal distributions
  • Can be applied to multiple groups (more than 2 at once)
• Test statistic is W, uses a F-distribution