Wilcox on Signed Ranks Test Pre and Post Comparison

RESULT

TABLE OF CONTENTS
DATA of pretest and post test.........................................................................................................1
Normal Distribution....................................................................................................................2
Paired Sample T-test...................................................................................................................4
Wilcoxon matched-pairs test.......................................................................................................5

DATA of pretest and post test
Pre-test
Post
test
Composite
Score
Composite
Score Mean Mean
Composite
Score
Composi
te Score Mean Mean
Name
(i) Y-
balance
(Right)
(i) Y-
balance
(Left)
(ii)
Illinois
Test
(iii) 5-10-
5 agility
test
(i) Y-balance
(Right)
(i) Y-
balance
(Left)
(ii)
Modified
Illinois Test
(iii) 5-10-
5 agility
test
AFZAL
Tanwir 94 92 16.352 5.283 93.6 95 15.828 5.21
HAYAT
Babar 82.9 84.5 15.943 5.215 89.5 87.4 15.224 4.893
KHAN
Waqas
KHAN
Nizakat 85.2 83.3 16.314 5.362
KHAN
Aizaz 100.9 101.8 15.498 5.245 103.7 101.7
NAWAZ
Ehsan 92 90.2 16.428 5.107 89.1 89.8 15.725 4.954
AHMEDE
Tanveer 92.5 89.7 16.061 5.124 91.8 90.6 15.664 4.879
KHAN
Ehsan 102.1 100.8 15.229 5.105 121 116.8 15.154 4.758
Ahsan
Abbasi 96.3 100.2 16.312 5.463 101.8 103.6
WASIF
Shahid 94.5 93 15.454 5.021 100.7 98.8 15.454 5.012
Wajid
Shah 84.8 87.1 15.557 5.018
Mariko
Hill
Hassan
Khan 94.9 95.2 15.803 5.011
1

Hassain
Khan 80.6 78 16.157 5.334
AFZAL
Tanwir 94 92 16.352 5.283 93.6 95 15.828 5.21
HAYAT
Babar 82.9 84.5 15.943 5.215 89.5 87.4 15.224 4.893
NAWAZ
Ehsan 92 90.2 16.428 5.107 89.1 89.8 15.725 4.954
AHMEDE
Tanveer 92.5 89.7 16.061 5.124 91.8 90.6 15.664 4.879
KHAN
Ehsan 102.1 100.8 15.229 5.105
1 ‘Results
Sample’
format . Please
do the good
and correct
analysis in this
work.21 116.8 15.154 4.758
WASIF
Shahid 94.5 93 15.454 5.021 100.7 98.8 15.454 5.012
Left Leg Length Right Leg Length
100 100
99 99
97 97
94 95
93 94
91 91
SD:3.559026084 3.346640106
Mean:95.66666667 96
Normal Distribution
It is symmetric about mean which reflects data is near to mean and frequent in occurrence
compared to data far from the mean. In the above scenario, average of left lag is 95.67 with
2

standard deviation of 3.55. Apart from this, right left lag has average of 96 with standard
deviation of 3.34.
The mean and standard deviation has been replicated along with Shapiro-wilk test of
normality for extracting outcome opf normally distributed and testing the variation of mean
score of pre and post test. The above table is stating descriptive statistics of pretest and post test
of different measures such as Preybaance right and left is 93 and 91.7 respectively. In this aspect,
the highest average is of PCS y balance left along with lowest is of PCS 5105 agility test with
accuracy of 1.741 and 0.845 of Kurtosis and Skeweness significantly.
3

Paired Sample T-test
The outcome of paired sample t test is a process to test that mean of two metric variable
are equal in similar population. In simple words, it is used for analyzing mean difference of
every direction among pre and post test for normally distributed data. The below table is
reflecting paired sample t test.
The above table is reflecting output of paired sample statistics and correlation is extracted
as 0.801 for pair 1 is Preilinois and Postillinois test are strongly correlated and positive
relationship. Furthermore, with context to pair 2 of pre 5105 agility and post 5105 agility test has
0.471 underlies with moderate positive linear relationship.
4

The above table is showing paired sample t test as here for pair 1 p value is less than 0.05
as 0.024 then alternative hypothesis is accepted. It could be elaborated that Prellinois test and
post illinois test are effective at significant level of 5%. In the same series, with application of
this test in pair 2, its p value is 0.018 which is less than 0.05 so could be concluded that
effectiveness about Pre 510 agility and post 105 agility test with acceptance of alternative
hypothesis.
Nutshell
Pair 1 has strong positive relationship and pair 2 has moderate positive relationship with
context to correlation. There is no significant mean difference in both Pair 1 and pair 2 at 95%
confidence interval which is statistically prooved.
Wilcoxon matched-pairs test
The reported measure of Wilcoson Signed-Ranked test result as non parametric test
which is equivalent to dependent t test and does not assume normality in the data. Generally, it
has need of different scores for being normally distributed in population. It is a statistical
comparison of average of two dependent variables and works with metric data which is not
multivariate normal and with ranked and ordinal data. This is non parametric alternative to the
dependent sample t test and it tests that null hypothesis that average signed rank of two
dependent samples is zero.
5

The above table consists of statistics which are necessary for extracting Wilcoxon signed
ranks test's W. These are the size of sample along with aggregate of ranks as it has mean rank
which is not important for reaching W-value but its significance in stating interpretation of this
data set. From pair of right, it is clearly viewed that total of 6 '3 observations were made of pre
and post y balance right. The Wilcox sign test answers about question if the variation is
significant different from 0, however if observed variation in mean ranks(2 vs 5) could also be
extracted in general population. From pair of left, it is clearly viewed that total of 6 '5
observations were made of pre and post y balance left. The Wilcox sign test answers about
question if the variation is significant different from 0, however if observed variation in mean
ranks(1 vs 4) could also be extracted in general population. The answer of both right and left is
replicated with help of second table which comprises test of significance statistics.
6

The SPSS output comprises z value of right pair is -.943 as its p value is 0.345 and for
left, it z value is -1.992 with p value of 0.046. Here alternative hypothesis could be accepted in
right because of lower significant and in left null hypothesis is accepted due to lower p value.
7

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