Lesson test: Comparing two groups

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Comparing two groups

1.[2p]
Why does pairing help when the units come in linked couples?

It removes the variation between pairs, leaving only the within-pair difference to be tested

Correct

It doubles the effective sample size

The answer is: It removes the variation between pairs, leaving only the within-pair difference to be tested

It makes the normality assumption unnecessary

The answer is: It removes the variation between pairs, leaving only the within-pair difference to be tested

It allows a one-sided test to be used

The answer is: It removes the variation between pairs, leaving only the within-pair difference to be tested

2.[3p]
Darwin's 15 paired differences have mean 20.93 and $s = 37.74$ . What is $t$ , to three decimal places?

CorrectNot quite: 2.148

3.[2p]
When two independent sample means are subtracted, their variances subtract as well.

True

The answer is: False

False

Correct

4.[3p]
Group A has $n = 12$ , $s = 3.2$ ; group B has $n = 15$ , $s = 2.8$ . What is the pooled variance $s_{p}^{2}$ , to three decimal places?

CorrectNot quite: 8.896

5.[3p]
Why can the pooled $t$ test disagree with Welch's on the same data?

Pooling assigns one group's variability to the other, which distorts the standard error when variances and sample sizes both differ

Correct

Welch uses a one-sided alternative

The answer is: Pooling assigns one group's variability to the other, which distorts the standard error when variances and sample sizes both differ

Pooling requires equal sample sizes

The answer is: Pooling assigns one group's variability to the other, which distorts the standard error when variances and sample sizes both differ

Welch discards the smaller sample

The answer is: Pooling assigns one group's variability to the other, which distorts the standard error when variances and sample sizes both differ

6.[2p]
In the Salk trial, 33 of 200,745 vaccinated and 115 of 201,229 placebo children developed paralytic polio. What is the placebo rate per 100,000, to one decimal place?

CorrectNot quite: 57.1

7.[3p]
For the same trial, the risk difference is 40.7 per 100,000. What is the number needed to treat, to the nearest hundred?

CorrectNot quite: 2456

8.[3p]
Match each summary of a two-group binary outcome to its definition.

Risk difference
Relative risk
Number needed to treat
Cohen's $d$

one over the risk difference
mean difference over pooled $s$
${\hat{p}}_{1} - {\hat{p}}_{2}$
${\hat{p}}_{1} / {\hat{p}}_{2}$

Show the answer

Risk difference: ${\hat{p}}_{1} - {\hat{p}}_{2}$ Relative risk: ${\hat{p}}_{1} / {\hat{p}}_{2}$ Number needed to treat: one over the risk difference Cohen's $d$ : mean difference over pooled $s$

9.[2p]
Using $15.70 / d^{2}$ per group for 80 per cent power, how many per group are needed to detect $d = 0.5$ ? Round up.

CorrectNot quite: 63

1.[2p] Why does pairing help when the units come in linked couples?

2.[3p] Darwin's 15 paired differences have mean 20.93 and s=37.74. What is t, to three decimal places?

3.[2p] When two independent sample means are subtracted, their variances subtract as well.

4.[3p] Group A has n=12, s=3.2; group B has n=15, s=2.8. What is the pooled variance sp2, to three decimal places?

5.[3p] Why can the pooled t test disagree with Welch's on the same data?

6.[2p] In the Salk trial, 33 of 200,745 vaccinated and 115 of 201,229 placebo children developed paralytic polio. What is the placebo rate per 100,000, to one decimal place?

7.[3p] For the same trial, the risk difference is 40.7 per 100,000. What is the number needed to treat, to the nearest hundred?

8.[3p] Match each summary of a two-group binary outcome to its definition.

9.[2p] Using 15.70/d2 per group for 80 per cent power, how many per group are needed to detect d=0.5? Round up.

1.[2p]
Why does pairing help when the units come in linked couples?

2.[3p]
Darwin's 15 paired differences have mean 20.93 and $s = 37.74$ . What is $t$ , to three decimal places?

3.[2p]
When two independent sample means are subtracted, their variances subtract as well.

4.[3p]
Group A has $n = 12$ , $s = 3.2$ ; group B has $n = 15$ , $s = 2.8$ . What is the pooled variance $s_{p}^{2}$ , to three decimal places?

5.[3p]
Why can the pooled $t$ test disagree with Welch's on the same data?

6.[2p]
In the Salk trial, 33 of 200,745 vaccinated and 115 of 201,229 placebo children developed paralytic polio. What is the placebo rate per 100,000, to one decimal place?

7.[3p]
For the same trial, the risk difference is 40.7 per 100,000. What is the number needed to treat, to the nearest hundred?

8.[3p]
Match each summary of a two-group binary outcome to its definition.

9.[2p]
Using $15.70 / d^{2}$ per group for 80 per cent power, how many per group are needed to detect $d = 0.5$ ? Round up.