chapter 13: hypothesis tests for two samples

Question 1

two sample t test

Answer 1

t test statistic can be used to test hypotheses about mean difference between two populations

Question 2

𝛅o (delta sub not) is

Answer 2

the hypothesized difference between the population means

Question 3

usually we test…

Answer 3

the hypothesis that the population means are equal, which means 𝛅o= 0

Question 4

sigma hat x-bar1 minus x-bar2

Answer 4

is an estimator of the standard error of the difference between two population means

Question 5

two-sample t-test assumptions

Answer 5

1. random sampling or assignment (assures independent samples)
2. homogeneity of variances (variances of population 1 and population 2 are equal)
   - if they arent equal, but have equal sample sizes its still okay
3. normal distribution

Question 6

random sampling and random assignment produces independent samples
what are independent samples?

Answer 6

the selection of elements in one sample is not affected by the selection of elements in the other

Question 7

two sample t’ test unequal variances (independent samples)

Answer 7

• we have to use t’ with violations to homogeneity of variance assumption and unequal sample sizes
• if both sample sizes are 5 or more the t critical values in table D.3 are a good approx. to the critical value of t’
• 𝛎’ is truncated to the next smaller whole number
• the degrees of freedom and critical values have an inverse relationship ( as one increases the other decreases, and vice versa)

Question 8

z test for independent samples

Answer 8

can never be computed because we will never know the two population variances

Question 9

practical significance

Answer 9

• interpretation of hedges g is the same as cohens d
• pooled sd is only used if homogeneity of variance is assumed
• if not then the sample sd of the control/baseline should be used

Question 10

to estimate the required sample size?

Answer 10

to estimate the required sample size, specify alpha, power, and cohens d

Question 11

confidence interval for independent samples

Answer 11

pooled sd used for computing confidence interval is the same as previously define d

Question 12

confidence interval for independent samples (unequal variances)

Answer 12

if the samples are unequal and population variances are unequal then construct a confidence interval using the t’ statistic

Question 13

randomization strategies

Answer 13

• you can either randomly sample from 2 populations, or randomly assign elements of one sample to the experimental and control conditions
• you can combine the two if you want
• they both help control for extraneous variables

Question 14

causal relationship

Answer 14

IV x causes changes in DP y, showing x is both necessary and sufficient for the occurrence of y

Question 15

concomitant relationship

Answer 15

x and y seem to be related

- random assignment is usually our focus over random sampling