2.1.7.1.1. Language Means Comparison
Means comparison concerning each independent variable was then
made. To start with, this is a description of the comparison made between the
first independent variable means i.e. language means. The T-
test formula entails a series of calculations before the T-value is calculated.
These are each group's scores' mean, the difference between both means, the
standard deviation (SD) of each group's scores and the square value of each
(SD).
N
· A group's mean formula is as follows: X = /x
· Group A's mean (3CA) = 305.75 --
13.90 22
XA= 13.90
230.02
· Group B's mean B) = = 10.46
22
XB= 10.46
· Difference between means =5CA -- 5iB= 13.90 --
10.46 = 3.44 XA--XB=3.44
E ( X- X)2
· Standard deviation is calculated as follows: SD= N
· Standard deviation, then, requires that the mean (X) be
subtracted from each score (X - X). Each of the resulting values is squared (X-
X) 2, then added up (E). After this, the sum (s) should be divided
by the number of scores (N=22). The result's square root gives us the standard
deviation.
63.97
SDA = 22 = N/2.91 = 1.71
74.23
SD B = 22 = 'N/ 3.37 = 1.84
· The square value of SDA = 1.712= 2.92
· The square value of SD B 1.842
3.38
XA--
The T-ratio formula is as follows:
SD A2+ SDB 2 NA
NB
3.44
t = 6.49
..\1
2.92 3.38 22 22
t= 6.49
Consulting a table of critical values of t, provided
us with the value our T-ratio should exceed to be statistically significant.
Our sample size was 44, which made a degree of freedom (df = n-2) of
42. This means that, with this sample size, any T value below the critical
value would have occurred by chance alone. The alpha level we set for this
study was: a < 0.01 directional. Therefore, the t critical value
was 2.423. It is obvious that the observed t-value largely exceeds the critical
t-value.
t obs > t crit ( 6.49 > 2.423)
Thus, the means difference was statistically significant.
This permitted the rejection of the null hypothesis suggesting that GA mean of
language Baccalaureate exams scores is not significantly higher than that
of GB. In addition, at p < 0.01, we could
say that 99% of mean differences are due to factors other than chance.
2.1.7.1.2. Culture Means Comparison
Secondly, the same steps were followed to calculate the
t-test concerning the second independent variable (*) i.e.
Culture means. Following is the list of the values leading to the calculation
of the T- value.
· XA*= 11.03
· X B* = 10.98
· X A* - X B* = 0.05
89.83
· SD A* = 22 = \4.08 = 2.02
SD A* = 2.02
.\1 50.34
· SD B* = 22 = \2.29 = 1.51
0.05
T-ratio* -- -- 0.17
..\/
(2.02)2 + (1.51)2 22
22
t = 0.17
It is clear that the T observed value (0.17) does not exceed the
critical T value (2.423).
t obs < t crit (0.17 < 2.423)
In this case, the null hypothesis, saying that GA cultural mean
is not significantly higher than that of GB , was accepted.
Following is a table summarising all the previous statistical
analyses.
Table 2: Means, Standard Deviations and T-values
Independent
|
Group A
|
Group B
|
T values
|
Variables
|
Mean
|
SD
|
Mean
|
SD
|
t obs
|
t crit
|
Culture
|
11.03
|
2.02
|
11.98
|
1.51
|
0.17*
|
2.423
|
Language
|
13.90
|
1.71
|
10.46
|
1.84
|
6.49*
|
2.423
|
*p < 0.01 ; df = 42
|