Question

Previously we discussed Confidence Interval methodology to draw conclusions about the difference in the brain size of the children with and without autism. Discuss a different methodology to conclude if there is any significant difference in the average brain size of the children with and without autism.

Answer 1

We can use two sample t test(Welch's t test) for two samples of children with autism(sample 1) and children without autism(sample 2).

We are to take 2 samples(be of equal or unequal sizes) from 2 populations of brain sizes of children with autism(population 1 with population mean of ) and children without autism (population 2 with mean of ) and compare their means.

Since confidence interval for this case has been calculated, then we can expect the normality assumptions hold here and so we can use parametric test of Welch's Two independent samples t test for the means.

We are to take the sample means(​​​​​​, ) , sample sizes(n1, n2) , sample sd of the 2 samples (s1, s2) for the 2 samples initially.

Then we are to create two hypothesis :

H0:There is no significant difference between the two means or

there is no significant difference in the average brain size of the children with and without autism.

that is

H0:

H1:There is significant difference in the two means or

there is a significant difference in the average brain size of the children with and without autism.

H1:​​​​​​

Thus for a particular chosen level of significance, we test our hypothesis.

Note:There is another way of two sample t test of Fisher's t test statistic but that one needs assumptions of equality of two population variances.Hence we did not use that.