Polytechnic University of the Philippines
Engineering Data Analysis
Non Parametric Test
One Sample Sign Test
Non parametric equivalent of tests regarding a single
population mean. It makes inferences regarding the
median, rather than the mean
One Sample Sign Test
Assumptions
Samples must be
independent of each other
Null Hypothesis (Ho)
Alternative Hypothesis (Ha)
M = M0
M ≤ M0
M ≥ M0
M ≠ M0
Non Parametric Test
One Sample Sign Test
Wilcoxon Signed Rank
Mann Whitney U - Test
M > M0
M < M0
Kruskal Wallis H - Test
Alternative
Hypothesis (Ha)
Command
Spearman Rank Correlation
M ≠ M0
signmedian.test(x, mu = 0, alternative = “two.sided”, conf.level = 0.95)
Chi – Square Test
M > M0
signmedian.test(x, mu = 0, alternative = “greater”, conf.level = 0.95)
M < M0
signmedian.test(x, mu = 0, alternative = “less”, conf.level = 0.95)
Non Parametric Statistics
Engineering Data Analysis
One Sample Sign Test
Assumptions
Samples must be
independent of each other
Non Parametric Test
One Sample Sign Test
Wilcoxon Signed Rank
Mann Whitney U - Test
Kruskal Wallis H - Test
Spearman Rank Correlation
A website administrator for a
company claims that the
median number of visitors
per day to the company’s
website is more than 1500.
An employee doubts the
accuracy of this claim. The
number of visitors per day for
20 randomly selected days
are listed below.
Chi – Square Test
At α = 0.05, can the employee
reject the administrators
claim?
Non Parametric Statistics
Engineering Data Analysis
Example
No
No of
Visitors
No
No of
Visitors
1
1469
11
1525
2
1463
12
1568
3
1487
13
1602
4
1579
14
1544
5
1462
15
1548
6
1476
16
1492
7
1523
17
1500
8
1620
18
1452
9
1634
19
1511
10
1570
20
1649
One Sample Sign Test
Assumptions
Samples must be
independent of each other
Step 1:
Non Parametric Test
Ho: M ≤ 1500
Ha: M > 1500
One Sample Sign Test
Step 2
Wilcoxon Signed Rank
α = 0.05
Step 3
Mann Whitney U - Test
Kruskal Wallis H - Test
Spearman Rank Correlation
Chi – Square Test
Non Parametric Statistics
Engineering Data Analysis
Solution
Since we are comparing the median of one sample to a
known standard median, we will use the one sample sign
test
One Sample Sign Test
Assumptions
Samples must be
independent of each other
Non Parametric Test
One Sample Sign Test
Wilcoxon Signed Rank
Step 4
library(signmedian.test)
visitor <- c(1649,1463,1487,1579,1462,1476,1523,1620,1634,1570,1525,1568,
1602,1544,1548,1492,1500,1452,1511,1549)
Step 5
signmedian.test(visitor, mu = 1500, alternative = "greater", conf.level = 0.95)
Mann Whitney U - Test
Kruskal Wallis H - Test
Spearman Rank Correlation
Chi – Square Test
Non Parametric Statistics
Engineering Data Analysis
Step 6
Solution
One Sample Sign Test
Solution
Assumptions
Samples must be
independent of each other
Non Parametric Test
One Sample Sign Test
Step 5
Since the p-value is greater than α = 0.05, then we fail
to reject the null hypothesis
Wilcoxon Signed Rank
Mann Whitney U - Test
Kruskal Wallis H - Test
Spearman Rank Correlation
Chi – Square Test
Non Parametric Statistics
Engineering Data Analysis
Step 6
There is no sufficient evidence to support the claim of
the website administrator