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S519: Evaluation of
Information Systems
Social Statistics
Inferential Statistics
Chapter 9: t test
Last week
This week



what is t test and when to use
TTEST function
T-test ToolPak
Example

Eating attitudes test on a group of 297
Australian and a group of 249 Indian
university students. Each group is only tested
once.

Sjostedt, J. P.; Shumaker, J. F. & Nathawat, S. S.
(1998). Eating disorders among Indian and
Australian university students. Journal of Social
Psychology, 138(3), 351-357.
Which statistic approach we will use?
T test assumption

The amount of variability in each of the two
groups is equal
T test formula
x1  x2
t
 (n1  1) s12  (n2  1) s22   n1  n2 




n1  n2  2

  n1n2 
x1
x2
n1
n2
s12
s22
: is the mean for Group 1
: is the mean for Group 2
: is the number of participants in Group 1
: is the number of participants in Group 2
: is the variance for Group 1
: is the variance for Group 2
T test steps
Group 1
7
3
3
2
3
8
8
5
8
5
5
4
6
10
10
5
1
1
4
3
Group 2
5
7
1
9
2
5
2
12
15
4
5
4
4
5
5
7
8
8
9
8
3
2
5
4
4
6
7
7
5
6
4
3
2
7
6
2
8
9
7
6
T test steps

Step 1: A statement of the null and research
hypotheses.

Null hypothesis: there is no difference between
two groups
H 0 : 1  2

Research hypothesis: there is a difference
between the two groups
H1 : X 1  X 2
T test steps

Step 2: setting the level of risk (or the level of
significance or Type I error) associated with
the null hypothesis


0.05
It is up to your decision
T test steps

Step 3: Selection of the appropriate test
statistic


Using Figure 9.1 to determine which test statistic
is good for your research
T test
T test steps

Step 4: computation of the test statistic value

Calculate mean and standard deviation
T calculation

t= - 0.14

T test steps

Step 5: determination of the value needed for the
rejection of the null hypothesis


Table B2 in Appendix B (S-p360)
Degrees of freedom (df): approximates the sample size



Two-tailed or one-tailed



Group 1 sample size -1 + group 2 sample size -1
Our test df= 58
Directed research hypothesis  one-tailed
Non-directed research hypothesis  two-tailed
Choose the df close to your sample size

According to Table B2, df=58, two-tailed, Type I error=0.05,  the
value needed to reject the null hypothesis with 58 degrees of freedom
at the 0.05 level of significance is 2.001.
T test steps

Step 6: A comparison of the obtained value
and the critical value



-0.14 and 2.001
If the obtained value > the critical value, reject the
null hypothesis
If the obtained value < the critical value, accept
the null hypothesis
T test steps

Step 7 and 8: make a decision

What is your decision and why?
Interpretation
 t(58)

= -.14, p>0.05
Write down your interpretation and discuss
with your group
Excel: TTEST function

TTEST (array1, array2, tails, type)



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array1 = the cell address for the first set of data
array2 = the cell address for the second set of
data
tails: 1 = one-tailed, 2 = two-tailed
type: 1 = a paired t test; 2 = a two-sample test
(independent with equal variances); 3 = a twosample test with unequal variances
Excel: TTEST function


It does not compute the t value
It returns the likelihood that the resulting t
value is due to chance (the possibility of the
difference of two groups is due to chance)

88% of possibility that two groups are different
caused by chance  without chance, 88%
possibility that the two groups are not different 
there is no different between these two groups
Excel ToolPak
Group 1
Group 2
7
3
3
2
3
8
8
5
8
5
5
4
6
10
10
5
1
1
4
3
5
7
1
9
2
5
2
12
15
4
5
4
4
5
5
7
8
8
9
8
3
2
5
4
4
6
7
7
5
6
4
3
2
7
6
2
8
9
7
6
Excel ToolPak

Select t-test: two sample assuming equal
variances
t-Test: Two-Sample Assuming Equal Variances
Mean
Variance
Observations
Pooled Variance
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Variable 1
5.433333333
11.70229885
30
7.979885057
0
58
-0.137103112
0.44571206
1.671552763
0.891424121
2.001717468
Variable 2
5.533333333
4.257471264
30
Effect size

If two groups are different, how to measure
the difference among them

Effect size
X1  X 2
ES 
SD
ES: effect size
X : the mean for Group 1
X : the mean for Group 2
SD: the standard deviation from either group
1
2
Effect size

A small effect size ranges from 0.0 ~ 0.2


A medium effect size ranges from 0.2 ~ 0.5


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The two groups are different
A large effect size is any value above 0.50


Both groups tend to be very similar and overlap a lot
The two groups are quite different
ES=0the two groups have no difference and overlap entirely
ES=1the two groups overlap about 45%
Exercise
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Chapter Data set 1
1 (s-p209)
2
3
4