Question

The Graded Naming Test (GNT) asks respondents to name objects in a set of 30 black and white drawings in order to detect brain damage. The GNT population norm for adults in England is 20.4. Researchers wondered whether a sample for Canadian adults had different scores from adults in England (Roberts, 2003). If the scores were different, the English norms would not be valid for use in Canada. The mean for 30 Canadian adults was 17.5. Assume that the standard deviation of the adults in England is 3.2. How can we calculate a 95% Confidence Interval (CI) for these data?

1. Calculate a 95% CI and a 90% CI for this data.
2. Are the English norms valid for use in Canadian use? Explain how you know your answer to be true.
3. How do the two CI’s (95% and 90%) compare to one another?
4. What is the effect size for these data?
5. What does this effect size indicate about the meaningfulness of this test for Canadians?
What would you recommend doing to increase the power of this experiment?

Answer 1

1. The 95% confidence interval for population mean is

where ,

For 95% confidence , zc =1.96

Thus , 95% confidence interval for population mean is

= ( 16.35 , 18.65)

For 90% confidence , zc =1.645

Thus , 90% confidence interval for population mean is

= ( 16.54 , 18.46)

2. No , the English norms are not valid for Canandian use

As we can see that the 95% and 90% confidence interval for Canadian score donot contain the standard norm for English , which is 20.4, there is sufficient evidence to conclude that   English norms are not valid for Canandian use.

3. 95% confidence interval is ( 16.35 , 18.65) and 90% confidence interval is (16.54 , 18.46)

We can say that 95% confidence interval is wider than 90% confidence interval.

4. Effect size

=(17.5-20.4)/3.2

= 0.91 ( we neglect the sign )

5. Effect size is greater than 0.8 , which is large

As effect size is large , there is high possibility of getting significant result in hypothesis testing to test whether Candians need different norms for GNT.

Power of the test is the probability of rejecting the false null hypothesis

Null hypothesis here would be : the Canadians dont have different score than English

Test statistic is

For 5% level of significance , critical value is zc = 1.96

That is reject H0 if I z I > 1.96

As n increases , the denominator of z decreases , thus increases the value of z

Which in turn increases the probability of rejecting the null hypothesis

To increase power , we should increase the sample size