T-test
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9. Student's t-Test: Results
A: Pre Test
N=11
DF=10
Mean= 63.53
SD= 22.92
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B: Post Test
N=11
DF=10
Mean=
SD=
t-test: rejection (df=10, one tailed, 95% confidence
[appendix, t-dist.]. =2.28 Region of rejection. Calculated t
(bogus example)=1.52
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1.52 |2.28 _
1.52 (calculated t) is outside rejection (of Ho) region so Null
Hypothesis is not rejected. A=B.
Bogus example:
mean B-Mean A
T= s/
square root of n[11]
T= 85-63=22/ 23/3.31= 22/6.95= 3.17
Calculated T is inside rejection reject so reject Ho.
Ours:
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T tests
T tests can be used to compare two groups or treatments.
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Click on any empty cell.
Hit the = sign in the bar at the top of the spreadsheet.
Hit the down arrow to the left of the = sign. Now some options will appear.
If "TTEST" is not on the list, click "more functions", choose "statistical", then
"TTEST".
A dialog box will appear. Click in the box next to "Array 1".
Drag the dialog box out of the way, then highlight your first column of
numbers.
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Click in the box next to "Array 2" and highlight your second column of
numbers.
To answer the "tails" question, remember your prediction about the direction of the
difference between the groups. If you predicted group A would be lower than group
B, pick 1 tail. If you predicted group B would lower than group A, pick one tail. If
you didn’t predict which would be higher, use 2 tails. You can’t change your mind
after the data are gathered.
There are three types of T test you can use on Excel. Let’s say you wanted to test
whether heart rate increased after drinking a cup of hot sauce (don’t actually try this!)
or whether plant growth would increase after adding fertilizer to pots of soil. In these
cases you would be comparing the heart rate of the same people, or the growth of the
same pot of plants before and after the treatment. This would require a "paired" or
"dependent" T test. Excel calls this a "type 1" test.
Let’s look at another situation. Say you want to know whether nursing students
consume more coffee than do biology students. You would then have two groups of
test subjects rather than taking 2 measurements on each person. Now you would use
an "unpaired" or "independent" T-test. Excel calls these "type 2" or "type 3" tests.
Now the tricky part is to decide which of these to use. Are the standard deviations
about the same for both groups, or are they different? You can test this statistically,
but let’s just work with how they seem. If in doubt, go with "type 3" for unequal
variances.
Now hit "OK" and see what the number is. This is your P-value. Remember that a Pvalue below 0.05 is generally considered statistically significant, while one of 0.05 or
greater indicates no difference between the groups. If your number looks like this:
2.03188E-7, Excel is giving you the number in its version of scientific notation. This
number is actually 2.03 X 10 -7, or 0.000000203.
VassarStats Printable Report
t-Test for Independent Samples
Sat Mar 13 2010 18:58:31 GMT-0500 (Eastern Standard Time)
Values entered:
count
1
2
3
4
5
Xa
Xb
70 100
80 80
90 50
100 70
80 70
6
6
7
8
9
10
11
90
80
80
100
90
90
50
60
40
90
20
70
Summary Values
Values
Xa
Xb
n
11
11
950
700
mean
86.3636
63.6364
sumsq
82900
49800
sum
SS
854.5455 5254.5455
variance
85.4545
525.4545
st. dev.
9.2442
22.9228
Variances and standard deviations are calculated
with denominator = n-1.
MeanA - MeanB
22.7273
P
t
df
+3.05 20
one-tailed 0.0031605
two-tailed 0.006321
Home Click this link only if you did not arrive here via the VassarStats main
page.
Conclusion (bogus example): Calculated T +3.05>theoretical T of 2.28 (from tables).
Null hypothesis is rejected. Alternate Hypothesis (there is a statistically significant
difference in the means of the two samples) is accepted.
Calculator online at: http://faculty.vassar.edu/lowry/t_ind_stats.html
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