Lesson test: Errors, power and sample size

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Errors, power and sample size

1.[3p]
Match each quantity to what it is.

Type I error
Type II error
Power
Noncentrality

the chance of detecting a real effect
the true effect in standard errors
failing to reject a null that is false
rejecting a null that is true

Show the answer

Type I error: rejecting a null that is true Type II error: failing to reject a null that is false Power: the chance of detecting a real effect Noncentrality: the true effect in standard errors

2.[1p]
A study of 100 observations tests two-sided at $α = 0.05$ with true standardised effect $d = 0.3$ . What is $λ = d \sqrt{n}$ ?

CorrectNot quite: 3

3.[3p]
For that study, power is $Φ (λ - 1.96)$ . What is it, to two decimal places?

CorrectNot quite: 0.85

4.[3p]
Using $n = 7.849 / d^{2}$ for 80 per cent power, how many observations are needed to detect $d = 0.2$ ? Round up.

CorrectNot quite: 197

5.[2p]
Power can be quoted as a single number for a study, without reference to any particular effect size.

True

The answer is: False

False

Correct

6.[3p]
Why do underpowered studies exaggerate the effects they report?

Only unusually large estimates cross the significance threshold, so the published ones are a biased selection

Correct

Small samples have larger population variance

The answer is: Only unusually large estimates cross the significance threshold, so the published ones are a biased selection

The $p$ -value is computed incorrectly at small $n$

The answer is: Only unusually large estimates cross the significance threshold, so the published ones are a biased selection

Researchers with small samples measure less carefully

The answer is: Only unusually large estimates cross the significance threshold, so the published ones are a biased selection

7.[2p]
A study with 20 per cent power has an exaggeration ratio of 2.26 and reports $d = 0.60$ . What is the implied true effect, to two decimal places?

CorrectNot quite: 0.27

8.[3p]
One hypothesis in ten is true, power is 0.80 and $α = 0.05$ . What fraction of significant findings are true, to two decimal places?

CorrectNot quite: 0.64

9.[3p]
Which changes raise the fraction of significant findings that are true?

Select all that apply

Increasing the power of the studies

Correct

Lowering the significance threshold

Correct

Investigating hypotheses with a higher prior chance of being true

Correct

Increasing the number of hypotheses tested per study

The answer is: Increasing the power of the studies, Lowering the significance threshold, Investigating hypotheses with a higher prior chance of being true

1.[3p] Match each quantity to what it is.

2.[1p] A study of 100 observations tests two-sided at α=0.05 with true standardised effect d=0.3. What is λ=dn?

3.[3p] For that study, power is Φ(λ-1.96). What is it, to two decimal places?

4.[3p] Using n=7.849/d2 for 80 per cent power, how many observations are needed to detect d=0.2? Round up.

5.[2p] Power can be quoted as a single number for a study, without reference to any particular effect size.

6.[3p] Why do underpowered studies exaggerate the effects they report?

7.[2p] A study with 20 per cent power has an exaggeration ratio of 2.26 and reports d=0.60. What is the implied true effect, to two decimal places?

8.[3p] One hypothesis in ten is true, power is 0.80 and α=0.05. What fraction of significant findings are true, to two decimal places?

9.[3p] Which changes raise the fraction of significant findings that are true?

1.[3p]
Match each quantity to what it is.

2.[1p]
A study of 100 observations tests two-sided at $α = 0.05$ with true standardised effect $d = 0.3$ . What is $λ = d \sqrt{n}$ ?

3.[3p]
For that study, power is $Φ (λ - 1.96)$ . What is it, to two decimal places?

4.[3p]
Using $n = 7.849 / d^{2}$ for 80 per cent power, how many observations are needed to detect $d = 0.2$ ? Round up.

5.[2p]
Power can be quoted as a single number for a study, without reference to any particular effect size.

6.[3p]
Why do underpowered studies exaggerate the effects they report?

7.[2p]
A study with 20 per cent power has an exaggeration ratio of 2.26 and reports $d = 0.60$ . What is the implied true effect, to two decimal places?

8.[3p]
One hypothesis in ten is true, power is 0.80 and $α = 0.05$ . What fraction of significant findings are true, to two decimal places?

9.[3p]
Which changes raise the fraction of significant findings that are true?