Question

Related T-Test Sample

1. A researcher is interested in testing whether rats learned a maze after daily training sessions. The researcher recorded the number of errors committed by each rat before any training in the maze. Then, the researcher recorded the number of errors made by each rat after training. The scores below summarize the errors by each rat before and after training. Perform a dependent-sample (repeated-measures) t-test on the scores to test whether or not the number of errors was lower after training than before training. Like virtually all real research, please use a two-tailed test. Using two or three sentences, describe the results of the experiment in APA format.

Rat        Before training        After training

A                17                      20

B                22                      14

C                24                      17

D                29                      14

E                20                      13

F                25                      8

G                23                      20

H                18                      11

I                26                      15

Answer 1

This is an example of paired t-test.

Let A and B the averages of errors before and after testing.

H0: B=A

H1: B A ( two tailed test as has been asked in the question)

The first step is to calculate the differences in the errors made by rats.

Rat	Error difference
A	20-17=3
B	14-22= -8
C	17-24= -7
D	14-29 = -15
E	13-20= -7
F	8-25 = -17
G	20-23= -3
H	11-18= -7
I	15-26= -11

Now proceed with calculating the mean and standard deviation of the differences.

Mean X= (3+ - ( 8+7+15+7+17+3+7+11)) / 8 = - 72/8 = -9

variance of differences S^2 (using X as mean) = ((Xi - X)^2 ) / n-1 = 37.125

S= 6.09

As both mean and standard deviation are estimated from the sample, we proceed with t-test.

t-test statistic formula is : (X - U) / (S / n) = ( -9 -0 ) / ( 6.09 /9)

Note : 0 is used in test statistic because we are checking for the difference between averages. Our hypothesis is to check if there is any difference.

t-test value = - 4.433

degree of freedom for the test is = n-1 = 9-1 = 8

Now, level of significane is not mentioned, so let's assume it to be 0.05.

one sided significance is therefore 0.025

critical values using 8 degrees of freedom and 0.05 as two tailed significance is +2.306 and -2.306

our t value -4.433 < -2.306

therefore number of errors was smaller after training.