# پایان نامه رایگان درمورد t، group، difference

for each subject in each SI session.

4.3.2 Pretest, t-test
Like in any other experimental study, it was necessary for us to make sure there was no significant difference between the two groups regarding the dependent variable (participants’ SI competence) of the study. To do so, the SI pretest was administered and the results were tabulated. Tables 4.9 and 4.10 present the pretest scores for the subjects in the control group and experimental group respectively. It is worthwhile to mention that for ease of calculation, the average scores were rounded up.

Table 4.9 Control Subjects’ SI Pretest Scores
Subject
Aver. Score

Subject
Aver. Score
S1
10

S19
67
S2
15

S20
7
S3
7

S21
19
S4
7

S22
15
S5
24

S23
7
S6
25

S24
10
S7
15

S25
10
S8
7

S26
10
S9
9

S27
7
S10
7

S28
37
S11
7

S29
40
S12
22

S30
44
S13
7

S31
14
S14
7

S32
10
S15
29

S33
14
S16
25

S34
30
S17
24

S35
10
S18
32

Table 4.10 Experimental Subjects’ SI Pretest Scores
Subject
Aver. Score

Subject
Aver. Score
S1
22

S19
10
S2
9

S20
5
S3
7

S21
54
S4
9

S22
65
S5
10

S23
5
S6
7

S24
5
S7
25

S25
7
S8
7

S26
35
S9
24

S27
19
S10
20

S28
22
S11
14

S29
42
S12
10

S30
7
S13
12

S31
34
S14
25

S32
35
S15
17

S33
34
S16
10

S34
30
S17
32

S35
32
S18
7

The mean for the experimental and control groups were 20 and 18 respectively. It goes without saying that only ‘eyeballing’ the means for the groups cannot be a reliable indication of whether there is a difference or not. What we needed was a statistical procedure to make sure the difference observed was statistically (non-)significant. Given the fact that this was a ‘Between-Groups’ design and we were dealing with a parametric comparison of two groups where “we have means from two groups […]. We want to know whether the means of these two groups truly differ” (Hatch & Lazaraton, 1991, p. 250), the t-test was chosen as the best statistical procedure.
The t value could be calculated using the following formula:

t_obs=(X ̅_e-X ̅_c)/S_((X ̅_e-X ̅_c))

The numerator is easy to calculate: it is the difference between the mean of the experimental group (X ̅_e=20) and that of the control group (X ̅_c=18).
The denominator is calculated using the following formulas:

S_((X ̅_e-X ̅_c))=√((S_e^2)/n_e +(S_c^2)/n_c )
S=√((∑▒x^2 -[(∑▒x)^2÷N])/(N-1))
S_e= √((21730-〖708〗^2÷35)/34)=√(7408/34)=14.7
S_c=√((17644-〖630〗^2÷35)/34)=√(6304/34)=13.6
S_((X ̅_e-X ̅_c))=√((S_e^2)/n_e +(S_c^2)/n_c )=√(216/35+185/35)=√11.45=3.38

Therefore we have the denominator in the formula:

t_obs=(X ̅_e-X ̅_c)/S_((X ̅_e-X ̅_c)) =( 20-18)/3.38= 0.59

Turning to the table for t critical values (Hatch & Lazaraton, 1991, p. 595) we can see that the value of t observed for pretest scores of the two groups (0.59) is much smaller than 2.000 (the t critical value required to be able to claim that there is a statistically significant difference between the two groups with df being 68 and p being 0.05).
As a result, it could be concluded that there was no significant difference between the experimental group and control group regarding their SI competence at the beginning of the experiment. The following table summarizes this information:

Table 4.11 T-Test Results for SI Pretest Scores
Group
n
Mean
sd
t value
df
p
Control
35
18
14.7
0.59
68
n.s.
Exper.
35
20
13.6

4.3.3 Posttest, t-test
Within the course of the experiment, the participants were expected to make improvement in terms of their SI performance. Therefore, upon the completion of the experiment the subjects’ SI performance was tested to measure the improvement they had made. To that end, the SI posttest was administered and the results tabulated. Tables 4.12 and 4.13 present the posttest scores obtained by the subjects in the control group and experimental group respectively. Here, too, the average scores were rounded up for ease of calculation.

Table 4.12 Control Subjects’ SI Posttest Scores
Subject
Aver. Score

Subject
Aver. Score
S1
25

S19
79
S2
34

S20
7
S3
17

S21
15
S4
10

S22
17
S5
34

S23
7
S6
44

S24
7
S7
19

S25
15
S8
7

S26
15
S9
14

S27
10
S10
7

S28
47
S11
7

S29
52
S12
34

S30
64
S13
7

S31
34
S14
7

S32
35
S15
37

S33
42
S16
34

S34
80
S17
34

S35
42
S18
44

Table 4.13 Experimental Subjects’ SI Posttest Scores
Subject
Aver. Score

Subject
Aver. Score
S1
60

S19
52
S2
42

S20
27
S3
42

S21
64
S4
35

S22
70
S5
49

S23
25
S6
42

S24
25
S7
70

S25
25
S8
30

S26
70
S9
44

S27
42
S10
64

S28
62
S11
62

S29
64
S12
54

S30
25
S13
40

S31
70
S14
69

S32
62
S15
37

S33
64
S16
40

S34
60
S17
70

S35
64
S18
27

The same statistical procedure (t-test) was utilized to see whether the subjects’ performance in the two groups differed at the end of the experiment. Below are the calculations for obtaining the t value for the posttest scores:

S_((X ̅_e-X ̅_c))=√((S_e^2)/n_e +(S_c^2)/n_c )
S=√((∑▒x^2 -[(∑▒x)^2÷N])/(N-1))
S_e= √((96138-〖1748〗^2÷35)/34)=√(8837.9/34)=16.12
S_c=√((41607-〖983〗^2÷35)/34)=√(13998.7/34)=20.29
S_((X ̅_e-X ̅_c))=√((S_e^2)/n_e +(S_c^2)/n_c )=√(259.9/35+411.6/35)=√19.18=4.3
t_obs=(X ̅_e-X ̅_c)/S_((X ̅_e-X ̅_c)) =(50 -28)/4.3=5.1

Again we have to turn to the table for t critical values. The t value observed (5.1) is greater than 2.000 (the value required to be able to reject the null hypothesis with df being 68 and p being 0.05).
This allows us to reject our first null hypothesis (H0.1) stated in section 1.7. The t value observed for the posttest statistically proves that there is a significant difference between the two groups and that at the end of the experiment the subjects in the experimental group excelled those in the control g
roup in the task of SI. The following table summarizes this information:

Table 4.14 T-Test Results for SI Posttest Scores
Group
n
mean
sd
t value
df
p
Control
35
28
20.29
5.1
68
s.
Exper.
35
50
16.12

4.3.4 Eta2
A t value equal to or greater than the critical value is all we need in order to be able to reject the null hypothesis and prove that there is a significant difference between the performance of the two groups after the experiment and most research reports stop there. However, there is another fruitful statistical procedure to undertake. As Hatch and Lazaraton (1991, p. 266) state:

When the sample statistic is significant, one rough way of determining how much of the overall variability in the data can be accounted for by the independent variable is to determine its strength of association. For the t-test and matched t-test this measure of strength of association is called eta squared (ƞ^2).

The value of ƞ^2 lets you know how important the independent variable is and to what extent the difference observed between the two groups can be certainly accounted for by your independent variable. Using this measure helps you better interpret the results and broadens your horizon for future research. The ƞ^2 for our data was calculated as follows:

ƞ^2=t^2/(t^2+df)=〖5.1〗^2/(〖5.1〗^2+68) =26/94=0.276

A value of 0.276 for eta2 means that 27% of the variability in our sample can be surely attributed to the independent variable, i.e. application of certain interpreter-training-specific techniques in classroom. This indicates a rather strong association as an eta2 of 50%, for example, means “a very strong association” (Hatch & Lazaraton, 1991, p. 266, my emphasis) and that with it “you can make a big deal about your findings” (Hatch & Lazaraton, 1991, p. 267). However, with an eta2 of less than 10% “you might want to be more conservative and say that there are, of course, other factors that need to be highlighted in future research” (Hatch & Lazaraton, 1991, p. 267).
It should be born in mind that whatever the value of eta2 (even if it is less than 10%), it does not serve to undermine the effect of the independent variable tested (as it is already statistically proved), rather it makes you aware of the possibility of other factors, besides that independent variable, which may affect the dependent variable. Therefore it inspires conducting future research to shed more light on the issue.
In the case of this study, it was by no means the intention of the researcher to claim that this independent variable (application of certain interpreter-training-specific techniques) was the only decisive factor affecting the SI competence in the trainees. On the contrary, the researcher is sure and would like to stress that there are plenty of other variables that can have an effect. Factors like personality types, character traits, psychological specificities, etc. are all tentative factors the effects of which need to be tested in future research projects.
Along the same lines, two other factors that could, at least in the eye of the researcher, have an impact on the trainees’ performance were included in the design of the present study: multiple intelligences and personality type. Such a tentative assumption gave rise to two further questions (and by extension hypotheses) to follow the main question of the study.

4.4 MI and SI Scores Correlation
As already stated in Chapter 3, towards the end of the experiment period, a standard test of multiple intelligences was administered to the experimental subjects in order to test the possible relation between the trainees’ scores on the MI test and the improvement they made in terms of their SI competence in the course of