# t-statistic before-after

I’m doing an exercise on the Udacity's Intro to Inferential Statistics course (Problem set 10b) where I need to calculate the t-statistic on a before\after treatment situation. My null hypothesis would be that the treatment has no effect and the alternative is that the treatment will reduce the values (so I’ll be doing a one tailed test on the negative direction)

The values before are [8, 7, 6, 9, 10, 5, 7, 11, 8, 7] (mean 7.8) and the after are [5, 6, 4, 6, 5, 3, 2, 9, 4, 4] (mean 4.8)

My t-critical at alpha = 0.05 is -1.83

I thought that I could calculate it by calculating the standard error of the mean (which is the standard deviation of the differences (1.33) divide by sqr(10) -> 0.421637) And then divide the mean difference (-3) by the standard error of the mean, resultin in -7.11

But that is not the value I’m looking for.

Can someone indicate where is the problem please?

Here are the calculations:

Before  After       Difference
8         5           -3
7         6           -1
6         4           -2
9         6           -3
10        5           -5
5         3           -2
7         2           -5
11        9           -2
8         4           -4
7         4           -3

SD ifference    1.333333333

Standard Error of the mean:         0.421637021
Mean differences            -3
t   -7.115124735


Here's the link to the question (https://www.udacity.com/course/viewer#!/c-ud201/l-1905528537)

• Please read the self-study wiki and add the tag if appropriate Jun 3 '15 at 14:31
• Instead of -7.11, what value are you expecting? Jun 3 '15 at 14:33
• But that is not the value I’m looking for. What is then the value you're looking for? Your calculation to get the t-statistics appears to be correct, Jun 3 '15 at 14:33
• Mind to post the website link or the question? Jun 3 '15 at 15:00
• It seems to be -7.14, which is incorrect because it uses the SE that was rounded to two decimal places (from the previous question.) Jun 3 '15 at 15:33

You did the problem correctly; the site did not. It committed a well-known error of not retaining intermediate results to sufficient precision, causing its final answer to be erroneous.

### Forensic Analysis

This site takes the student through a guided sequence of questions to go through the steps of conducting a t-test. After formulating null and alternative hypotheses, the student is asked to compute intermediate results such as the mean difference (-3) and its standard error (approximately 0.421637). However, it insists that the values be entered only to limited precision. The only way to proceed is to round the SE to 0.42. At this point, the system requires the student to replace the correct value of the SE with the rounded value. This causes the correct t-statistic, approximately equal to -7.115125, to be computed as -3/0.42 = -7.14. That (or something very close to it) is the answer one must enter in order to proceed!

### Post-Mortem Rant

The pedagogical errors in this approach are appalling: the practice of statistics is reduced to remembering names for situations and procedures, using them to look up and compute a series of formulas. Correct answers and many near-correct answers are considered wrong. Forcibly incorrect answers have to be propagated through a calculation ultimately to produce an incorrect final answer. Students are reduced to guessing what the site might accept, without having any guidance concerning the errors they might possibly have made. It is difficult to imagine a nastier climate in which to try to learn anything.

• A link or two, or three, to some good books might be in order. Jun 3 '15 at 16:18
• @Scortchi On statistics or on teaching? :-)
– whuber
Jun 3 '15 at 16:49
• +1 This is not the first error I've encountered on Udacity via questions from people trying to do a stats course there. Nov 23 '15 at 2:00