Thread: T test.

Hello, I was told by my lecturer that I need to do some T-tests on my data in order to find out if it is significant or not. The data is basically student's grades and I am trying to prove that intrinsic students achieve higher grades in comparison to extrinsic students.


So I used an online calculator to calculate the T test on this data:

Data 1 (extrinsic students):

49.5
52
55
55.5
55.5
59
59.5
60
60.5
63.5
65.75
66
67
69.5
76.5
78
78

Data 2: (Intrinsic students)

55
59.5
60
63.5
64
65
65.5
68
69
72.5
76.5
76.5
77.5
77.5
80
82
83

For this data I set it as of unequal variance and a 2 tail test. I am not too sure If i used the right tail test. The following figure was returned:

Online calculator: = 0.01967
Excel: 0.009833876

I have no idea what either of these numbers mean, can anyone help?

Thanks,
Sean

These numbers will mean nothing to you unless you understand how a T-test works.

Because you have 2 groups of data you will need a 'two sampled T-test' and because you are trying to find if one group is better than the other (not just different) you will need only 1-tail.

Now I suggest you research the type of test I have prescribed.

Based on your data (group 1 vs group 2), I believe that you are testing the alternative hypothesis that the mean for the group 1 is different from the mean of the group 2, or vice-versa - assuming that this difference can be in any direction. In other words, your null hypothesis is that the difference between those means is zero. Running your data in R, I got a two-sided P-value of 0.0196677511603729 (t=-2.4559, with 32 degrees-of-freedom). The value of 0.0098 you mention refers to the one-sided test, in which your alternative hypothesis is that the mean for the group 1 (extrinsic) is smaller (one direction only) than group 2, that is, your alternative is that the difference (mean 1)-(mean 2) < 0. I got these results assuming equal variances. Use of Welch's approximation (unequal variances) gives slightly different results: (P = 0.0193 and P = 0.0097 , t= -2.4559 and 33.9832 degrees-of-freedom)

Thanks for the help so far, I have done further research as suggested. I going to summarize what I have learned and hopefully it is not horribly wrong

My Null Hypothesis is: There is no statistical difference between the intrinsic and extrinsic student grades.

• Two sample test: As there are two sets of data

• unequal variance

• 1 tail: As I am trying to prove Intrinsic students get higher grades than extrinsic students.

Result (using excel): 0.009835258 = 00.1

Based upon this, I can reject the Null hypothesis as it is below the 0.5 figure and say that my data is significant.

Ok so that is my understanding so far, I would really appreciate if someone could advise me if my understanding is correct (or not!).

Thanks

You are on the right track,

The hypothesis formulation here is

the mean of intrinsic students equals the mean of extrinsic students.

the mean of intrinsic students is greater than the mean of extrinsic students.

If the one tailed test returned a p-value of then reject at

(be careful of your rounding, above you have written "Result (using excel): 0.009835258 = 00.1", this is not true)

Originally Posted by pickslides

You are on the right track,

The hypothesis formulation here is

the mean of intrinsic students equals the mean of extrinsic students.

the mean of intrinsic students is greater than the mean of extrinsic students.

If the one tailed test returned a p-value of then reject at

(be careful of your rounding, above you have written "Result (using excel): 0.009835258 = 00.1", this is not true)

Thank you for your help, it is greatly appreciated!