Assignment 6
NA3C0005-Belle
SPSS exercises
1a.
Valid N
TOEFL 1: LISTENING
TOEFL 2: STRUCT &
TOEFL 3: VOCAB &
STANDARD SCORE
WRITING STANDARD
READING STANDARD
(Tlcstd)
SCORE (Tswstd)
SCORE (Tvrstd)
1448
1448
1448
40
40
40
49.62
51.12
51.49
.175
.181
.176
50.00
51.00
52.00
51
54
54
6.665
6.900
6.696
44.428
47.604
44.839
-.074
-.241
-.503
.064
.064
.064
-.293
-.041
.080
.129
.129
.129
Range
39
43
38
Minimum
29
25
28
Maximum
68
68
66
71848
74019
74556
25
45.00
46.00
47.00
50
50.00
51.00
52.00
75
54.00
56.00
56.00
Missing N
Mean
Std. Error of Mean
Median
Mode
Std. Deviation
Variance
Skewness
Std. Error of Skewness
Kurtosis
Std. Error of Kurtosis
Sum
Percentiles
1b.
Tlcstd:
The value of Skewness is -.074 which refers to negative skewness. The graph skews
to the left. Most scores are distributed over the mean. High score participants are
more than low score ones.
The value of Kurtosis is -.293 which means platykurtic. The Kurtosis of Tlcstd is
flatter than normal kurtosis. Participants in the peak are fewer than normal
distribution. Participants on the both ends are also fewer than normal distribution.
Participants between peak and both ends are more than normal distribution.
In terms of central tendency, when Mean, Median and Mode are equal as well as in
the middle of the figures, it would be the ideal normal distribution. In this case,
Mean is 49.62, Median is 50, Mode is 51. It approaches normal distribution.
Another method to check the degree of normality is to compare the standard deviation
(SD) and the value that the interquartile range divides 1.35 (IQR/1.35). When SD is
higher than IQR/1.35, it would be heavier-than-normal tail. As SD is lower than
IQR/1.35, it would be lighter-than-normal tail. While SD is equal to IQR/1.35, it
would become normal distribution. In this case, SD is 6.665 and IQR/1.35 is 6.667.
It approaches normal distribution.
Tswstd:
The value of Skewness is -.241 which refers to negative skewness. The graph skews
to the left. Most scores are distributed over the mean. High score participants are
more than low score ones. High score participants are more than low score ones.
The value of Kurtosis is -.041 means platykurtic. The Kurtosis of Tswstd is flatter
than normal kurtosis. Participants in the peak are fewer than normal distribution.
Participants on the both ends are also fewer than normal distribution. Participants
between peak and both ends are more than normal distribution.
In terms of central tendency, Mean is 51.12, Median is 51, Mode is 54. It is hard to
decide its degree of normality. Based on interquartile range, SD is 6.9 and IQR/1.35
is 7.407. Tswstd doesn’t approach normal distribution so closely.
Tvrstd:
The value of Skewness is -.503 which refers to negative skewness.
The graph skews
to the left. Most scores are distributed over the mean. High score participants are
more than low score ones. High score participants are more than low score ones.
The value of Kurtosis is .080 means leptokurtic. The Kurtosis of Tvrstd is sharper
than normal kurtosis. Participants in the peak and on the both ends are more than
normal distribution. Participants between peak and both ends are fewer than normal
distribution.
In terms of central tendency, Mean is 51.49, Median is 52, Mode is 54. It is hard to
decide its degree of normality. Based on interquartile range, SD is 6.696 and
IQR/1.35 is 6.667. Tvrstd approaches normal distribution more closely than Tswstd.
2a.
SPEAK:
TOEFL STANDARD SCORE
TOTAL (Tstdtot)
Valid N
SPEAK:
GRAMMAR
RATING (Spgram)
PRONUNCIATION
RATING (Sppron)
1448
1304
1314
40
184
174
Mean
507.43
1.93
2.13
Median
510.00
1.90
2.20
497a
2
2
58.863
.454
.380
3464.867
.206
.145
-.280
.010
-.919
.064
.068
.067
-.233
-.115
1.731
Std. Error of Kurtosis
.129
.135
.135
Range
337
3
3
Minimum
310
0
0
Maximum
647
3
3
734755
2521
2804
25
470.00
1.60
1.90
50
510.00
1.90
2.20
75
550.00
2.20
2.40
Missing N
Mode
Std. Deviation
Variance
Skewness
Std. Error of Skewness
Kurtosis
Sum
Percentiles
2b.
Tstdtot:
The value of Skewness is -.280 which refers to negative skewness. The graph skews
to the left. Most scores are distributed over the mean. High score participants are
more than low score ones. High score participants are more than low score ones.
The value of Kurtosis is -.233 means platykurtic. The Kurtosis of Tstdtot is flatter
than normal kurtosis. Participants in the peak are fewer than normal distribution.
Participants on the both ends are also fewer than normal distribution. Participants
between peak and both ends are more than normal distribution.
In terms of central tendency, Mean is 507.43, Median is 510.00, Mode is 497. It is
hard to decide its degree of normality. Based on interquartile range, SD is 58.863
and IQR/1.35 is 59.259. Tstdtot doesn’t approach normal distribution so closely.
Spgram:
The value of Skewness is .010 which refers to positive skewness.
The graph skews
to the right.
Most scores are distributed lower the mean.
Low score participants
are more than High score ones.
The value of Kurtosis is -.115 means platykurtic. The Kurtosis of Spgram is flatter
than normal kurtosis. Participants in the peak and on the both ends are fewer than
normal distribution. Participants between peak and both ends are more than normal
distribution.
In terms of central tendency, Mean is 1.93, Median is 1.90, Mode is 2. It is hard to
decide its degree of normality. Based on interquartile range, SD is .454 and
IQR/1.35 is .444. Spgram approaches normal distribution.
Sppron:
The value of Skewness is -.919 which refers to negative skewness. The graph skews
to the left. Most scores are distributed over the mean. High score participants are
more than low score ones.
The value of Kurtosis is 1.731 means leptokurtic. The Kurtosis of Sppron is sharper
than normal kurtosis. Participants in the peak and on the both ends are more than
normal distribution. Participants between peak and both ends are fewer than normal
distribution.
In terms of central tendency, Mean is 2.13, Median is 2.20, Mode is 2. It is hard to
decide its degree of normality. Based on interquartile range, SD is .380 and
IQR/1.35 is .370. Sppron approaches normal distribution.
3
(i) FCE Paper 1
The value of Skewness is -.474 which refers to negative skewness. The graph skews
to the left. Most scores are distributed over the mean. High score participants are
more than low score ones.
The value of Kurtosis is .030 means leptokurtic. The Kurtosis of FCE Paper 1 is
sharper than normal kurtosis. Participants in the peak and on the both ends are more
than normal distribution. Participants between peak and both ends are fewer than
normal distribution.
In terms of central tendency, Mean is 25.94, Median is 26.90, Mode is 27. It is hard
to decide its degree of normality. Based on interquartile range, SD is 4.896 and
IQR/1.35 is 4.889. FCE Paper 1 approaches normal distribution.
FCE PAPER 1:
N
CAMB. SCALED SCORE TOTAL
Valid
Missing
1359
129
Mean
25.94
Median
26.90
27a
Mode
Std. Deviation
4.896
Variance
23.976
Skewness
-.474
Std. Error of Skewness
.066
Kurtosis
.030
Std. Error of Kurtosis
.133
Range
31
Minimum
10
Maximum
40
Sum
Percentiles
35259
25
22.50
50
26.90
75
29.10
(ii) FCE Paper 2
The value of Skewness is -.495 which refers to negative skewness. The graph skews
to the left. Most scores are distributed over the mean. High score participants are
more than low score ones.
The value of Kurtosis is .998 means leptokurtic. The Kurtosis of FCE Paper 2 is
sharper than normal kurtosis. Participants in the peak and on the both ends are more
than normal distribution. Participants between peak and both ends are fewer than
normal distribution.
In terms of central tendency, Mean is 24.30, Median is 24.4, Mode is 23. It is hard
to decide its degree of normality. Based on interquartile range, SD is 6.043 and
IQR/1.35 is 5.778. FCE Paper 2 doesn’t approach normal distribution so closely.
Statistics
FCE PAPER 2:
N
CAMB. SCALED SCORE TOTAL
Valid
Missing
1357
131
Mean
24.30
Median
24.40
Mode
23
Std. Deviation
6.043
Variance
36.518
Skewness
-.495
Std. Error of Skewness
.066
Kurtosis
.998
Std. Error of Kurtosis
.133
Range
40
Minimum
0
Maximum
40
Sum
Percentiles
32979
25
20.70
50
24.40
75
28.50
(iii) FCE Paper 4: Grade
The value of Skewness is .561 which refers to positive skewness. The graph skews
to the right. Most scores are distributed lower the mean. Low score participants
are more than High score ones.
The value of Kurtosis is -.935 means platykurtic. The Kurtosis of FCE Paper 4:
Grade is flatter than normal kurtosis. Participants in the peak and on the both ends
are fewer than normal distribution. Participants between peak and both ends are
more than normal distribution.
In terms of central tendency, Mean is 1.96, Median is 2.00, Mode is 1. It is hard to
decide its degree of normality. Based on interquartile range, SD is .996 and
IQR/1.35 is 1.481. FCE Paper 4: Grade doesn’t approach normal distribution so
closely.
Statistics
FCE PAPER 4:
N
GRADE
Valid
Missing
1344
144
Mean
1.96
Median
2.00
Mode
1
Std. Deviation
.996
Variance
.992
Skewness
.561
Std. Error of Skewness
.067
Kurtosis
-.935
Std. Error of Kurtosis
.133
Range
3
Minimum
1
Maximum
4
Sum
Percentiles
2640
25
1.00
50
2.00
75
3.00
(iv) FCE Paper 5: Fluency rating
The value of Skewness is -.399 which refers to negative skewness. The graph skews
to the left. Most scores are distributed over the mean. High score participants are
more than low score ones.
The value of Kurtosis is .106 means leptokurtic. The Kurtosis of FCE Paper 2 is
sharper than normal kurtosis. Participants in the peak and on the both ends are more
than normal distribution. Participants between peak and both ends are fewer than
normal distribution.
In terms of central tendency, Mean is 3.57, Median is 4.00, Mode is 4. It is hard to
decide its degree of normality. Based on interquartile range, SD is .927 and
IQR/1.35 is .741. FCE Paper 5: Fluency rating doesn’t approach normal distribution
so closely.
Statistics
N
Valid
Missing
1379
109
Mean
3.57
Median
4.00
Mode
4
Std. Deviation
.927
Variance
.860
Skewness
-.399
Std. Error of Skewness
.066
Kurtosis
.106
Std. Error of Kurtosis
.132
Range
5
Minimum
0
Maximum
5
Sum
Percentiles
4927
25
3.00
50
4.00
75
4.00