# t tests (psych stats)

#### Kylah

##### New Member
The problem that I'm trying to solve is this:

"Twenty college juniors were randomly selected from a group of volunteers and arbitrarily assigned either to a sleep deprivation group or a control group. The participants in the sleep deprivation group were kept awake for 24 hours; the members of the control group had a normal night's sleep. Participants were then asked to perform a simple mental arithmetic task, and the time it took to complete the task was recorded. The results were as follows:

Deprivation Group
10, 15, 13, 5, 27, 7, 16, 20, 21, 13

Control Group
13, 8, 14, 11, 8, 7, 2, 2, 17, 5

Determine whether or not the groups differ significantly. If you reject the null, tell what it means in the context of the problem."

My calculations were as such:

Deprivation Group:
ΣX = 147
ΣX² = 2563
n = 10
Mean = 14.7
s²=44.68

Control Group:
ΣX = 87
ΣX² = 985
n = 10
Mean = 8.7
s²=25.34

The formula I used:

t = Mean1 - Mean2/√(n1-1)s²1 + (n2-1)s²2/n1 + n2 - 2(1/n1 +1/n2)

t=14.7-8.7/√(10-1)44.68 + (10-1) 24.34/10+10-2(1/10+1/10)

t(18)=7.16, p<.01. There was a significant effect of sleep deprivation on the ability to perform mental arithmetic.

The answer in the back of the text, however, is:

t(18) = 2.26, p<.05. Sleep deprivation resulted in slower cognitive performance.

In either case, the Ho is still rejected, but the t value is different. Where did I go wrong?

#### Gaston

##### New Member
Hi,

You get T = 2.27 for the standard two-sample t-statistic:

T = (m1 - m2) /sqrt(s1^2 / n + s2^2/n).

g.

#### Kylah

##### New Member
I copied the formula right out of the text. I think it's because, for example, n1 should have the n as a sub. It's n for the first set of numbers.

#### JohnM

##### TS Contributor
The file I've attached may help - I get the same answer as your text.