SlideShare a Scribd company logo
1 of 51
Download to read offline
NON - PARAMETRIC
TESTS
DR. RAGHAVENDRA HUCHCHANNAVAR
Junior Resident, Deptt. of Community Medicine,
PGIMS, Rohtak
Contents
• Introduction
• Assumptions of parametric and non-parametric tests
• Testing the assumption of normality
• Commonly used non-parametric tests
• Applying tests in SPSS
• Advantages of non-parametric tests
• Limitations
• Summary
Introduction
• Variable: A characteristic that is observed or manipulated.
• Dependent
• Independent
• Data: Measurements or observations of a variable
1. Nominal or Classificatory Scale: Gender, ethnic
background, eye colour, blood group
2. Ordinal or Ranking Scale: School performance, social
economic class
3. Interval Scale: Celsius or Fahrenheit scale
4. Ratio Scale: Kelvin scale, weight, pulse rate,
respiratory rate
Introduction
• Parameter: is any numerical quantity that characterizes a
given population or some aspect of it. Most common statistics
parameters are mean, median, mode, standard deviation.
Assumptions
• The general assumptions of parametric tests are
− The populations are normally distributed (follow normal
distribution curve).
− The selected population is representative of general
population
− The data is in interval or ratio scale
Assumptions
• Non-parametric tests can be applied when:
– Data don’t follow any specific distribution and no
assumptions about the population are made
– Data measured on any scale
Testing normality
• Normality: This assumption is only broken if there are large
and obvious departures from normality
• This can be checked by
 Inspecting a histogram
 Skewness and kurtosis ( Kurtosis describes the peakof the curve
Skewness describes the symmetry of the curve.)
 Kolmogorov-Smirnov (K-S) test (sample size is ≥50 )
 Shapiro-Wilk test (if sample size is <50)
(Sig. value >0.05 indicates normality of the distribution)
Testing normality
Testing normality
Testing normality
Commonly used tests
• Commonly used Non Parametric Tests are:
− Chi Square test
− McNemar test
− The Sign Test
− Wilcoxon Signed-Ranks Test
− Mann–Whitney U or Wilcoxon rank sum test
− The Kruskal Wallis or H test
− Friedman ANOVA
− The Spearman rank correlation test
− Cochran's Q test
Chi Square test
• First used by Karl Pearson
• Simplest & most widely used non-parametric
test in statistical work.
• Calculated using the formula-
χ2 = ∑ ( O – E )2
E
O = observed frequencies
E = expected frequencies
• Greater the discrepancy b/w observed & expected frequencies,
greater shall be the value of χ2.
• Calculated value of χ2 is compared with table value of χ2 for
given degrees of freedom.
Karl Pearson
(1857–1936)
Chi Square test
• Application of chi-square test:
• Test of association (smoking & cancer, treatment &
outcome of disease, vaccination & immunity)
• Test of proportions (compare frequencies of diabetics &
non-diabetics in groups weighing 40-50kg, 50-60kg, 60-
70kg & >70kg.)
• The chi-square for goodness of fit (determine if actual
numbers are similar to the expected/theoretical numbers)
Chi Square test
• Attack rates among vaccinated & unvaccinated children
against measles :
• Prove protective value of vaccination by χ2 test at 5% level of
significance
Group Result Total
Attacked Not-attacked
Vaccinated
(observed)
10 90 100
Unvaccinated
(observed)
26 74 100
Total 36 164 200
Chi Square test
Group Result Total
Attacked Not-attacked
Vaccinated
(Expected)
18 82 100
Unvaccinated
(Expected)
18 82 100
Total 36 164 200
Chi Square test
 χ2 value = ∑ (O-E)2/E
 (10-18)2 + (90-82)2 + (26-18)2 + (74-82)2
18 82 18 82
 64 + 64 + 64 + 64
18 82 18 82
 =8.67
 calculated value (8.67) > 3.84 (expected value
corresponding to P=0.05)
 Null hypothesis is rejected. Vaccination is protective.
Chi Square test
• Yates’ correction: applies when we have two categories (one
degree of freedom)
• Used when sample size is ≥ 40, and expected frequency of
<5 in one cell
• Subtracting 0.5 from the difference between each observed
value and its expected value in a 2 × 2 contingency table
• χ2 = ∑ [O- E-0.5]2
E
Fisher’s Exact Test
• Used when the
• Total number of cases is <20 or
• The expected number of cases in any cell is
≤1 or
• More than 25% of the cells have expected
frequencies <5.
Ronald A.
Fisher
(1890–1962)
McNemar Test
• McNemar Test: used to compare before and
after findings in the same individual or to
compare findings in a matched analysis (for
dichotomous variables)
• Example: comparing the attitudes of medical
students toward confidence in statistics
analysis before and after the intensive
statistics course.
McNemar
Sign Test
• Used for paired data, can be ordinal or continuous
• Simple and easy to interpret
• Makes no assumptions about distribution of the data
• Not very powerful
• To evaluate H0 we only need to know the signs of the
differences
• If half the differences are positive and half are negative, then
the median = 0 (H0 is true).
• If the signs are more unbalanced, then that is evidence against
H0.
– Children in an orthodontia
study were asked to rate how
they felt about their teeth on
a 5 point scale.
– Survey administered before
and after treatment.
How do you feel about your
teeth?
1. Wish I could change them
2. Don’t like, but can put up
with them
3. No particular feelings one
way or the other
4. I am satisfied with them
5. Consider myself fortunate
in this area
Sign Test
child
Rating
before
Rating
after
1 1 5
2 1 4
3 3 1
4 2 3
5 4 4
6 1 4
7 3 5
8 1 5
9 1 4
10 4 4
11 1 1
12 1 4
13 1 4
14 2 4
15 1 4
16 2 5
17 1 4
18 1 5
19 4 4
20 3 5
• Use the sign test to evaluate
whether these data provide
evidence that orthodontic
treatment improves children’s
image of their teeth.
child
Rating
before
Rating
after change
1 1 5 4
2 1 4 3
3 3 1 -2
4 2 3 1
5 4 4 0
6 1 4 3
7 3 5 2
8 1 5 4
9 1 4 3
10 4 4 0
11 1 1 0
12 1 4 3
13 1 4 3
14 2 4 2
15 1 4 3
16 2 5 3
17 1 4 3
18 1 5 4
19 4 4 0
20 3 5 2
• First, for each child, compute
the difference between the
two ratings
child
Rating
before
Rating
after change sign
1 1 5 4 +
2 1 4 3 +
3 3 1 -2 -
4 2 3 1 +
5 4 4 0 0
6 1 4 3 +
7 3 5 2 +
8 1 5 4 +
9 1 4 3 +
10 4 4 0 0
11 1 1 0 0
12 1 4 3 +
13 1 4 3 +
14 2 4 2 +
15 1 4 3 +
16 2 5 3 +
17 1 4 3 +
18 1 5 4 +
19 4 4 0 0
20 3 5 2 +
• The sign test looks at the signs
of the differences
– 15 children felt better
about their teeth (+
difference in ratings)
– 1 child felt worse (- diff.)
– 4 children felt the same
(difference = 0)
• If H0 were true we’d expect an
equal number of positive and
negative differences.
(P value from table 0.004)
25
Wilcoxon signed-rank test
• Nonparametric equivalent of the paired
t-test.
• Similar to sign test, but take into
consideration the magnitude of difference
among the pairs of values. (Sign test only
considers the direction of difference but
not the magnitude of differences.)
WILCOXON
Wilcoxon signed-rank test
• The 14 difference scores in BP among hypertensive patients
after giving drug A were:
-20, -8, -14, -12, -26, +6, -18, -10, -12, -10, -8, +4, +2, -18
• The statistic T is found by calculating the sum of the positive
ranks, and the sum of the negative ranks.
• The smaller of the two values is considered.
Wilcoxon signed-rank test
Score Rank
• +2 1
• +4 2
• +6 3
• -8 4.5 Sum of positive ranks = 6
• -8 4.5
• -10 6.5 Sum of negative ranks = 99
• -10 6.5
• -12 8
• -14 9 T= 6
• -16 10
• -18 11.5
• -18 11.5
• -20 13
• -26 14
For N = 14, and α = .05, the critical
value of T = 21.
If T is equal to or less than T
critical, then null hypothesis is
rejected i.e., drug A decreases the
BP among hypertensive patients.
Mann-Whitney U test
• Mann-Whitney U – similar to Wilcoxon signed-ranks test
except that the samples are independent and not paired.
• Null hypothesis: the population means are the same for the
two groups.
• Rank the combined data values for the two groups. Then find
the average rank in each group.
Mann-Whitney U test
• Then the U value is calculated using formula
• U= N1*N2+ Nx(Nx+1) _ Rx (where Rx is larger rank
2 total)
• To be statistically significant, obtained U has to be equal to or
LESS than this critical value.
Mann-Whitney U test
• 10 dieters following Atkin’s diet vs. 10 dieters following
Jenny Craig diet
• Hypothetical RESULTS:
• Atkin’s group loses an average of 34.5 lbs.
• J. Craig group loses an average of 18.5 lbs.
• Conclusion: Atkin’s is better?
Mann-Whitney U test
• When individual data is seen
• Atkin’s, change in weight (lbs):
+4, +3, 0, -3, -4, -5, -11, -14, -15, -300
• J. Craig, change in weight (lbs)
-8, -10, -12, -16, -18, -20, -21, -24, -26, -30
Jenny Craig diet
-30 -25 -20 -15 -10 -5 0 5 10 15 20
0
5
10
15
20
25
30
P
e
r
c
e
n
t
Weight Change
Atkin’s diet
-300 -280 -260 -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20
0
5
10
15
20
25
30
P
e
r
c
e
n
t
Weight Change
Mann-Whitney U test
• RANK the values, 1 being the least weight loss and 20 being
the most weight loss.
• Atkin’s
– +4, +3, 0, -3, -4, -5, -11, -14, -15, -300
– 1, 2, 3, 4, 5, 6, 9, 11, 12, 20
• J. Craig
− -8, -10, -12, -16, -18, -20, -21, -24, -26, -30
− 7, 8, 10, 13, 14, 15, 16, 17, 18, 19
Mann-Whitney U test
• Sum of Atkin’s ranks:
1+ 2 + 3 + 4 + 5 + 6 + 9 + 11+ 12 + 20=73
• Sum of Jenny Craig’s ranks:
7 + 8 +10+ 13+ 14+ 15+16+ 17+ 18+19=137
• Jenny Craig clearly ranked higher.
• Calculated U value (18) < table value (27), Null hypothesis is
rejected.
Kruskal-Wallis One-way ANOVA
• It’s more powerful than Chi-square test.
• It is computed exactly like the Mann-Whitney test, except that
there are more groups (>2 groups).
• Applied on independent samples with the same shape (but not
necessarily normal).
Friedman ANOVA
• Friedman ANOVA: When either a matched-subjects or
repeated-measure design is used and the hypothesis of a
difference among three or more (k) treatments is to be tested,
the Friedman ANOVA by ranks test can be used.
Spearman rank-order
correlation
• Use to assess the relationship between
two ordinal variables or two skewed
continuous variables.
• Nonparametric equivalent of the
Pearson correlation.
• It is a relative measure which varies
from -1 (perfect negative relationship)
to +1 (perfect positive relationship).
Charles Spearman
(1863–1945)
Cochran's Q test
• Cochran's Q test is a non-parametric statistical test to verify if
k treatments have identical effects where the response
variable can take only two possible outcomes (coded as 0 and
1)
Applying the tests in SPSS
software
Normality tests
42
Chi-square tests
The Sign, Wilcoxon and McNemar
test
Mann Whitney U test
• Mann whitney U
Kruskal Wallis H test
Friendman’s ANOVA and Cochran’s
Spearman’s rho correlation test
Advantages of non-parametric
tests
• These tests are distribution free.
• Easier to calculate & less time consuming than parametric
tests when sample size is small.
• Can be used with any type of data.
• Many non-parametric methods make it possible to work with
very small samples, particularly helpful in collecting pilot
study data or medical researcher working with a rare disease.
Limitations of non-parametric
methods
• Statistical methods which require no assumptions about
populations are usually less efficient .
• As the sample size get larger , data manipulations required for
non-parametric tests becomes laborious
• A collection of tabulated critical values for a variety of non-
parametric tests under situations dealing with various sample
sizes is not readily available.
Summary Table of Statistical Tests
Level of
Measureme
nt
Sample Characteristics Correlation
1
Sample
2 Sample K Sample (i.e., >2)
Independent Dependent Independent Dependent
Categorical
or Nominal
Χ2 Χ2 MacNemar
test
Χ2 Cochran’s
Q
Rank or
Ordinal
Mann
Whitney U
Wilcoxon
Signed
Rank
Kruskal
Wallis H
Friedman’s
ANOVA
Spearman’s
rho
Parametric
(Interval &
Ratio)
z test
or t
test
t test
between
groups
t test
within
groups
1 way
ANOVA
between
groups
Repeated
measure
ANOVA
Pearson’s
test
Factorial (2 way) ANOVA
Χ2
Non parametric tests

More Related Content

What's hot

PPT on Sample Size, Importance of Sample Size,
PPT on Sample Size, Importance of Sample Size,PPT on Sample Size, Importance of Sample Size,
PPT on Sample Size, Importance of Sample Size,Naveen K L
 
01 parametric and non parametric statistics
01 parametric and non parametric statistics01 parametric and non parametric statistics
01 parametric and non parametric statisticsVasant Kothari
 
Test of significance in Statistics
Test of significance in StatisticsTest of significance in Statistics
Test of significance in StatisticsVikash Keshri
 
Analysis of variance (anova)
Analysis of variance (anova)Analysis of variance (anova)
Analysis of variance (anova)Sadhana Singh
 
Null hypothesis AND ALTERNAT HYPOTHESIS
Null hypothesis AND ALTERNAT HYPOTHESISNull hypothesis AND ALTERNAT HYPOTHESIS
Null hypothesis AND ALTERNAT HYPOTHESISADESH MEDICAL COLLEGE
 
Type i and type ii errors
Type i and type ii errorsType i and type ii errors
Type i and type ii errorsp24ssp
 
wilcoxon signed rank test
wilcoxon signed rank testwilcoxon signed rank test
wilcoxon signed rank testraj shekar
 
Analysis of variance (ANOVA)
Analysis of variance (ANOVA)Analysis of variance (ANOVA)
Analysis of variance (ANOVA)Sneh Kumari
 
Statistical tests of significance and Student`s T-Test
Statistical tests of significance and Student`s T-TestStatistical tests of significance and Student`s T-Test
Statistical tests of significance and Student`s T-TestVasundhraKakkar
 
Parametric and non parametric test
Parametric and non parametric testParametric and non parametric test
Parametric and non parametric testAjay Malpani
 
LEVEL OF SIGNIFICANCE.pptx
LEVEL OF SIGNIFICANCE.pptxLEVEL OF SIGNIFICANCE.pptx
LEVEL OF SIGNIFICANCE.pptxRingoNavarro3
 
Parametric vs Nonparametric Tests: When to use which
Parametric vs Nonparametric Tests: When to use whichParametric vs Nonparametric Tests: When to use which
Parametric vs Nonparametric Tests: When to use whichGönenç Dalgıç
 
One way anova final ppt.
One way anova final ppt.One way anova final ppt.
One way anova final ppt.Aadab Mushrib
 
Parametric Statistical tests
Parametric Statistical testsParametric Statistical tests
Parametric Statistical testsSundar B N
 

What's hot (20)

PPT on Sample Size, Importance of Sample Size,
PPT on Sample Size, Importance of Sample Size,PPT on Sample Size, Importance of Sample Size,
PPT on Sample Size, Importance of Sample Size,
 
Parametric Test
Parametric TestParametric Test
Parametric Test
 
The mann whitney u test
The mann whitney u testThe mann whitney u test
The mann whitney u test
 
01 parametric and non parametric statistics
01 parametric and non parametric statistics01 parametric and non parametric statistics
01 parametric and non parametric statistics
 
T test statistics
T test statisticsT test statistics
T test statistics
 
Test of significance in Statistics
Test of significance in StatisticsTest of significance in Statistics
Test of significance in Statistics
 
Analysis of variance (anova)
Analysis of variance (anova)Analysis of variance (anova)
Analysis of variance (anova)
 
Null hypothesis AND ALTERNAT HYPOTHESIS
Null hypothesis AND ALTERNAT HYPOTHESISNull hypothesis AND ALTERNAT HYPOTHESIS
Null hypothesis AND ALTERNAT HYPOTHESIS
 
Type i and type ii errors
Type i and type ii errorsType i and type ii errors
Type i and type ii errors
 
wilcoxon signed rank test
wilcoxon signed rank testwilcoxon signed rank test
wilcoxon signed rank test
 
Analysis of variance (ANOVA)
Analysis of variance (ANOVA)Analysis of variance (ANOVA)
Analysis of variance (ANOVA)
 
Statistical tests of significance and Student`s T-Test
Statistical tests of significance and Student`s T-TestStatistical tests of significance and Student`s T-Test
Statistical tests of significance and Student`s T-Test
 
Parametric and non parametric test
Parametric and non parametric testParametric and non parametric test
Parametric and non parametric test
 
LEVEL OF SIGNIFICANCE.pptx
LEVEL OF SIGNIFICANCE.pptxLEVEL OF SIGNIFICANCE.pptx
LEVEL OF SIGNIFICANCE.pptx
 
{ANOVA} PPT-1.pptx
{ANOVA} PPT-1.pptx{ANOVA} PPT-1.pptx
{ANOVA} PPT-1.pptx
 
Parametric vs Nonparametric Tests: When to use which
Parametric vs Nonparametric Tests: When to use whichParametric vs Nonparametric Tests: When to use which
Parametric vs Nonparametric Tests: When to use which
 
Anova ppt
Anova pptAnova ppt
Anova ppt
 
Chi squared test
Chi squared testChi squared test
Chi squared test
 
One way anova final ppt.
One way anova final ppt.One way anova final ppt.
One way anova final ppt.
 
Parametric Statistical tests
Parametric Statistical testsParametric Statistical tests
Parametric Statistical tests
 

Viewers also liked

Nonparametric tests
Nonparametric testsNonparametric tests
Nonparametric testsArun Kumar
 
DIstinguish between Parametric vs nonparametric test
 DIstinguish between Parametric vs nonparametric test DIstinguish between Parametric vs nonparametric test
DIstinguish between Parametric vs nonparametric testsai prakash
 
Statistical tests /certified fixed orthodontic courses by Indian dental academy
Statistical tests /certified fixed orthodontic courses by Indian dental academy Statistical tests /certified fixed orthodontic courses by Indian dental academy
Statistical tests /certified fixed orthodontic courses by Indian dental academy Indian dental academy
 
Advance Statistics - Wilcoxon Signed Rank Test
Advance Statistics - Wilcoxon Signed Rank TestAdvance Statistics - Wilcoxon Signed Rank Test
Advance Statistics - Wilcoxon Signed Rank TestJoshua Batalla
 
Estimation and confidence interval
Estimation and confidence intervalEstimation and confidence interval
Estimation and confidence intervalHomework Guru
 
Statistical Estimation
Statistical Estimation Statistical Estimation
Statistical Estimation Remyagharishs
 
Hermite spline english_20161201_jintaeks
Hermite spline english_20161201_jintaeksHermite spline english_20161201_jintaeks
Hermite spline english_20161201_jintaeksJinTaek Seo
 
Analytical chemistry_Instrumentation_Introduction
Analytical chemistry_Instrumentation_IntroductionAnalytical chemistry_Instrumentation_Introduction
Analytical chemistry_Instrumentation_IntroductionBivek Timalsina
 
Presentation non parametric
Presentation non parametricPresentation non parametric
Presentation non parametricIrfan Hussain
 
Parametric equations
Parametric equationsParametric equations
Parametric equationsTarun Gehlot
 
Presentation on bezier curve
Presentation on bezier curvePresentation on bezier curve
Presentation on bezier curveSatyendra Rajput
 
Nonparametric statistics
Nonparametric statisticsNonparametric statistics
Nonparametric statisticsTarun Gehlot
 

Viewers also liked (20)

Nonparametric tests
Nonparametric testsNonparametric tests
Nonparametric tests
 
DIstinguish between Parametric vs nonparametric test
 DIstinguish between Parametric vs nonparametric test DIstinguish between Parametric vs nonparametric test
DIstinguish between Parametric vs nonparametric test
 
Statistical tests /certified fixed orthodontic courses by Indian dental academy
Statistical tests /certified fixed orthodontic courses by Indian dental academy Statistical tests /certified fixed orthodontic courses by Indian dental academy
Statistical tests /certified fixed orthodontic courses by Indian dental academy
 
Advance Statistics - Wilcoxon Signed Rank Test
Advance Statistics - Wilcoxon Signed Rank TestAdvance Statistics - Wilcoxon Signed Rank Test
Advance Statistics - Wilcoxon Signed Rank Test
 
Chi square
Chi squareChi square
Chi square
 
Standard error
Standard error Standard error
Standard error
 
Estimation and confidence interval
Estimation and confidence intervalEstimation and confidence interval
Estimation and confidence interval
 
Estimation
EstimationEstimation
Estimation
 
Statistical Estimation
Statistical Estimation Statistical Estimation
Statistical Estimation
 
Parametric vs Non-Parametric
Parametric vs Non-ParametricParametric vs Non-Parametric
Parametric vs Non-Parametric
 
Hermite spline english_20161201_jintaeks
Hermite spline english_20161201_jintaeksHermite spline english_20161201_jintaeks
Hermite spline english_20161201_jintaeks
 
Analytical chemistry_Instrumentation_Introduction
Analytical chemistry_Instrumentation_IntroductionAnalytical chemistry_Instrumentation_Introduction
Analytical chemistry_Instrumentation_Introduction
 
hermite cubic spline curve
hermite cubic spline curvehermite cubic spline curve
hermite cubic spline curve
 
Presentation non parametric
Presentation non parametricPresentation non parametric
Presentation non parametric
 
[Download] rev chapter-5-june26th
[Download] rev chapter-5-june26th[Download] rev chapter-5-june26th
[Download] rev chapter-5-june26th
 
Perspective projection
Perspective projectionPerspective projection
Perspective projection
 
Parametric equations
Parametric equationsParametric equations
Parametric equations
 
Dda line-algorithm
Dda line-algorithmDda line-algorithm
Dda line-algorithm
 
Presentation on bezier curve
Presentation on bezier curvePresentation on bezier curve
Presentation on bezier curve
 
Nonparametric statistics
Nonparametric statisticsNonparametric statistics
Nonparametric statistics
 

Similar to Non parametric tests

Statistics of Non-Parametric test Biostat.ppt
Statistics of Non-Parametric test Biostat.pptStatistics of Non-Parametric test Biostat.ppt
Statistics of Non-Parametric test Biostat.pptDrDeveshPandey1
 
Non parametric study; Statistical approach for med student
Non parametric study; Statistical approach for med student Non parametric study; Statistical approach for med student
Non parametric study; Statistical approach for med student Dr. Rupendra Bharti
 
NON-PARAMETRIC TESTS.pptx
NON-PARAMETRIC TESTS.pptxNON-PARAMETRIC TESTS.pptx
NON-PARAMETRIC TESTS.pptxDrLasya
 
Hypothesis testing for nonparametric data
Hypothesis testing for nonparametric data Hypothesis testing for nonparametric data
Hypothesis testing for nonparametric data KwambokaLeonidah
 
3.1 non parametric test
3.1 non parametric test3.1 non parametric test
3.1 non parametric testShital Patil
 
INFERENTIAL STATISTICS.pdf
INFERENTIAL STATISTICS.pdfINFERENTIAL STATISTICS.pdf
INFERENTIAL STATISTICS.pdfMandar Baviskar
 
Test of significance
Test of significanceTest of significance
Test of significancemigom doley
 
Intro to tests of significance qualitative
Intro to tests of significance qualitativeIntro to tests of significance qualitative
Intro to tests of significance qualitativePandurangi Raghavendra
 
ANOVA_PDF.pdf biostatistics course material
ANOVA_PDF.pdf biostatistics course materialANOVA_PDF.pdf biostatistics course material
ANOVA_PDF.pdf biostatistics course materialAmanuelIbrahim
 
Test of-significance : Z test , Chi square test
Test of-significance : Z test , Chi square testTest of-significance : Z test , Chi square test
Test of-significance : Z test , Chi square testdr.balan shaikh
 
T12 non-parametric tests
T12 non-parametric testsT12 non-parametric tests
T12 non-parametric testskompellark
 
Statistics basics for oncologist kiran
Statistics basics for oncologist kiranStatistics basics for oncologist kiran
Statistics basics for oncologist kiranKiran Ramakrishna
 
Malimu statistical significance testing.
Malimu statistical significance testing.Malimu statistical significance testing.
Malimu statistical significance testing.Miharbi Ignasm
 
tests of significance
tests of significancetests of significance
tests of significancebenita regi
 
univariate and bivariate analysis in spss
univariate and bivariate analysis in spss univariate and bivariate analysis in spss
univariate and bivariate analysis in spss Subodh Khanal
 

Similar to Non parametric tests (20)

Statistics of Non-Parametric test Biostat.ppt
Statistics of Non-Parametric test Biostat.pptStatistics of Non-Parametric test Biostat.ppt
Statistics of Non-Parametric test Biostat.ppt
 
Non parametric study; Statistical approach for med student
Non parametric study; Statistical approach for med student Non parametric study; Statistical approach for med student
Non parametric study; Statistical approach for med student
 
Statistics
StatisticsStatistics
Statistics
 
sta
stasta
sta
 
NON-PARAMETRIC TESTS.pptx
NON-PARAMETRIC TESTS.pptxNON-PARAMETRIC TESTS.pptx
NON-PARAMETRIC TESTS.pptx
 
Test of significance
Test of significanceTest of significance
Test of significance
 
Non parametric-tests
Non parametric-testsNon parametric-tests
Non parametric-tests
 
Hypothesis testing for nonparametric data
Hypothesis testing for nonparametric data Hypothesis testing for nonparametric data
Hypothesis testing for nonparametric data
 
3.1 non parametric test
3.1 non parametric test3.1 non parametric test
3.1 non parametric test
 
INFERENTIAL STATISTICS.pdf
INFERENTIAL STATISTICS.pdfINFERENTIAL STATISTICS.pdf
INFERENTIAL STATISTICS.pdf
 
Test of significance
Test of significanceTest of significance
Test of significance
 
Intro to tests of significance qualitative
Intro to tests of significance qualitativeIntro to tests of significance qualitative
Intro to tests of significance qualitative
 
ANOVA_PDF.pdf biostatistics course material
ANOVA_PDF.pdf biostatistics course materialANOVA_PDF.pdf biostatistics course material
ANOVA_PDF.pdf biostatistics course material
 
Test of-significance : Z test , Chi square test
Test of-significance : Z test , Chi square testTest of-significance : Z test , Chi square test
Test of-significance : Z test , Chi square test
 
T12 non-parametric tests
T12 non-parametric testsT12 non-parametric tests
T12 non-parametric tests
 
Statistics basics for oncologist kiran
Statistics basics for oncologist kiranStatistics basics for oncologist kiran
Statistics basics for oncologist kiran
 
Malimu statistical significance testing.
Malimu statistical significance testing.Malimu statistical significance testing.
Malimu statistical significance testing.
 
Fragility Index
Fragility IndexFragility Index
Fragility Index
 
tests of significance
tests of significancetests of significance
tests of significance
 
univariate and bivariate analysis in spss
univariate and bivariate analysis in spss univariate and bivariate analysis in spss
univariate and bivariate analysis in spss
 

More from Raghavendra Huchchannavar (8)

Pneumoconiosis
Pneumoconiosis Pneumoconiosis
Pneumoconiosis
 
NFHS 3
NFHS 3NFHS 3
NFHS 3
 
Deaddiction programme in india
Deaddiction programme in indiaDeaddiction programme in india
Deaddiction programme in india
 
E waste
E waste E waste
E waste
 
Women empowerment
Women empowermentWomen empowerment
Women empowerment
 
Measles catch up campaign
Measles catch up campaignMeasles catch up campaign
Measles catch up campaign
 
Lay reporting
Lay reportingLay reporting
Lay reporting
 
Genetics and health
Genetics and healthGenetics and health
Genetics and health
 

Recently uploaded

SGK NĂNG LƯỢNG SINH HỌC MỚI 2019 RẤT HAY NHÉ.pdf
SGK NĂNG LƯỢNG SINH HỌC MỚI 2019 RẤT HAY NHÉ.pdfSGK NĂNG LƯỢNG SINH HỌC MỚI 2019 RẤT HAY NHÉ.pdf
SGK NĂNG LƯỢNG SINH HỌC MỚI 2019 RẤT HAY NHÉ.pdfHongBiThi1
 
Aditi Jagtap (Daughter of Ranjit Jagtap).pdf
Aditi Jagtap (Daughter of Ranjit Jagtap).pdfAditi Jagtap (Daughter of Ranjit Jagtap).pdf
Aditi Jagtap (Daughter of Ranjit Jagtap).pdfAditi Jagtap Pune
 
Introduction to Sports Injuries by- Dr. Anjali Rai
Introduction to Sports Injuries by- Dr. Anjali RaiIntroduction to Sports Injuries by- Dr. Anjali Rai
Introduction to Sports Injuries by- Dr. Anjali RaiGoogle
 
Exploring the Variety of Private Blood Tests in the UK
Exploring the Variety of Private Blood Tests in the UKExploring the Variety of Private Blood Tests in the UK
Exploring the Variety of Private Blood Tests in the UKPrivate GP London
 
SYNDESMOTIC INJURY- ANATOMICAL REPAIR.pptx
SYNDESMOTIC INJURY- ANATOMICAL REPAIR.pptxSYNDESMOTIC INJURY- ANATOMICAL REPAIR.pptx
SYNDESMOTIC INJURY- ANATOMICAL REPAIR.pptxdrashraf369
 
SCHOOL HEALTH SERVICES.pptx made by Sapna Thakur
SCHOOL HEALTH SERVICES.pptx made by Sapna ThakurSCHOOL HEALTH SERVICES.pptx made by Sapna Thakur
SCHOOL HEALTH SERVICES.pptx made by Sapna ThakurSapna Thakur
 
SHOCK (Medical SURGICAL BASED EDITION)).pptx
SHOCK (Medical SURGICAL BASED EDITION)).pptxSHOCK (Medical SURGICAL BASED EDITION)).pptx
SHOCK (Medical SURGICAL BASED EDITION)).pptxAbhishek943418
 
CCSC6142 Week 3 Research ethics - Long Hoang.pdf
CCSC6142 Week 3 Research ethics - Long Hoang.pdfCCSC6142 Week 3 Research ethics - Long Hoang.pdf
CCSC6142 Week 3 Research ethics - Long Hoang.pdfMyThaoAiDoan
 
Units of Radiation Measurements, Quality Specification, Half-Value Thickness,...
Units of Radiation Measurements, Quality Specification, Half-Value Thickness,...Units of Radiation Measurements, Quality Specification, Half-Value Thickness,...
Units of Radiation Measurements, Quality Specification, Half-Value Thickness,...Dr. Dheeraj Kumar
 
L1.INTRODUCTION to ENDOCRINOLOGY MEDICINE.pptx
L1.INTRODUCTION to ENDOCRINOLOGY MEDICINE.pptxL1.INTRODUCTION to ENDOCRINOLOGY MEDICINE.pptx
L1.INTRODUCTION to ENDOCRINOLOGY MEDICINE.pptxDr Bilal Natiq
 
Screening for colorectal cancer AAU.pptx
Screening for colorectal cancer AAU.pptxScreening for colorectal cancer AAU.pptx
Screening for colorectal cancer AAU.pptxtadehabte
 
Giftedness: Understanding Everyday Neurobiology for Self-Knowledge
Giftedness: Understanding Everyday Neurobiology for Self-KnowledgeGiftedness: Understanding Everyday Neurobiology for Self-Knowledge
Giftedness: Understanding Everyday Neurobiology for Self-Knowledgeassessoriafabianodea
 
Valproic Acid. (VPA). Antiseizure medication
Valproic Acid.  (VPA). Antiseizure medicationValproic Acid.  (VPA). Antiseizure medication
Valproic Acid. (VPA). Antiseizure medicationMohamadAlhes
 
Systemic Lupus Erythematosus -SLE PT2.ppt
Systemic  Lupus  Erythematosus -SLE PT2.pptSystemic  Lupus  Erythematosus -SLE PT2.ppt
Systemic Lupus Erythematosus -SLE PT2.pptraviapr7
 
PHYSIOTHERAPY IN HEART TRANSPLANTATION..
PHYSIOTHERAPY IN HEART TRANSPLANTATION..PHYSIOTHERAPY IN HEART TRANSPLANTATION..
PHYSIOTHERAPY IN HEART TRANSPLANTATION..AneriPatwari
 
Culture and Health Disorders Social change.pptx
Culture and Health Disorders Social change.pptxCulture and Health Disorders Social change.pptx
Culture and Health Disorders Social change.pptxDr. Dheeraj Kumar
 
COVID-19 (NOVEL CORONA VIRUS DISEASE PANDEMIC ).pptx
COVID-19  (NOVEL CORONA  VIRUS DISEASE PANDEMIC ).pptxCOVID-19  (NOVEL CORONA  VIRUS DISEASE PANDEMIC ).pptx
COVID-19 (NOVEL CORONA VIRUS DISEASE PANDEMIC ).pptxBibekananda shah
 
ANEMIA IN PREGNANCY by Dr. Akebom Kidanemariam
ANEMIA IN PREGNANCY by Dr. Akebom KidanemariamANEMIA IN PREGNANCY by Dr. Akebom Kidanemariam
ANEMIA IN PREGNANCY by Dr. Akebom KidanemariamAkebom Gebremichael
 
Hypersensitivity and its classification .pptx
Hypersensitivity and its classification .pptxHypersensitivity and its classification .pptx
Hypersensitivity and its classification .pptxAkshay Shetty
 
Music Therapy's Impact in Palliative Care| IAPCON2024| Dr. Tara Rajendran
Music Therapy's Impact in Palliative Care| IAPCON2024| Dr. Tara RajendranMusic Therapy's Impact in Palliative Care| IAPCON2024| Dr. Tara Rajendran
Music Therapy's Impact in Palliative Care| IAPCON2024| Dr. Tara RajendranTara Rajendran
 

Recently uploaded (20)

SGK NĂNG LƯỢNG SINH HỌC MỚI 2019 RẤT HAY NHÉ.pdf
SGK NĂNG LƯỢNG SINH HỌC MỚI 2019 RẤT HAY NHÉ.pdfSGK NĂNG LƯỢNG SINH HỌC MỚI 2019 RẤT HAY NHÉ.pdf
SGK NĂNG LƯỢNG SINH HỌC MỚI 2019 RẤT HAY NHÉ.pdf
 
Aditi Jagtap (Daughter of Ranjit Jagtap).pdf
Aditi Jagtap (Daughter of Ranjit Jagtap).pdfAditi Jagtap (Daughter of Ranjit Jagtap).pdf
Aditi Jagtap (Daughter of Ranjit Jagtap).pdf
 
Introduction to Sports Injuries by- Dr. Anjali Rai
Introduction to Sports Injuries by- Dr. Anjali RaiIntroduction to Sports Injuries by- Dr. Anjali Rai
Introduction to Sports Injuries by- Dr. Anjali Rai
 
Exploring the Variety of Private Blood Tests in the UK
Exploring the Variety of Private Blood Tests in the UKExploring the Variety of Private Blood Tests in the UK
Exploring the Variety of Private Blood Tests in the UK
 
SYNDESMOTIC INJURY- ANATOMICAL REPAIR.pptx
SYNDESMOTIC INJURY- ANATOMICAL REPAIR.pptxSYNDESMOTIC INJURY- ANATOMICAL REPAIR.pptx
SYNDESMOTIC INJURY- ANATOMICAL REPAIR.pptx
 
SCHOOL HEALTH SERVICES.pptx made by Sapna Thakur
SCHOOL HEALTH SERVICES.pptx made by Sapna ThakurSCHOOL HEALTH SERVICES.pptx made by Sapna Thakur
SCHOOL HEALTH SERVICES.pptx made by Sapna Thakur
 
SHOCK (Medical SURGICAL BASED EDITION)).pptx
SHOCK (Medical SURGICAL BASED EDITION)).pptxSHOCK (Medical SURGICAL BASED EDITION)).pptx
SHOCK (Medical SURGICAL BASED EDITION)).pptx
 
CCSC6142 Week 3 Research ethics - Long Hoang.pdf
CCSC6142 Week 3 Research ethics - Long Hoang.pdfCCSC6142 Week 3 Research ethics - Long Hoang.pdf
CCSC6142 Week 3 Research ethics - Long Hoang.pdf
 
Units of Radiation Measurements, Quality Specification, Half-Value Thickness,...
Units of Radiation Measurements, Quality Specification, Half-Value Thickness,...Units of Radiation Measurements, Quality Specification, Half-Value Thickness,...
Units of Radiation Measurements, Quality Specification, Half-Value Thickness,...
 
L1.INTRODUCTION to ENDOCRINOLOGY MEDICINE.pptx
L1.INTRODUCTION to ENDOCRINOLOGY MEDICINE.pptxL1.INTRODUCTION to ENDOCRINOLOGY MEDICINE.pptx
L1.INTRODUCTION to ENDOCRINOLOGY MEDICINE.pptx
 
Screening for colorectal cancer AAU.pptx
Screening for colorectal cancer AAU.pptxScreening for colorectal cancer AAU.pptx
Screening for colorectal cancer AAU.pptx
 
Giftedness: Understanding Everyday Neurobiology for Self-Knowledge
Giftedness: Understanding Everyday Neurobiology for Self-KnowledgeGiftedness: Understanding Everyday Neurobiology for Self-Knowledge
Giftedness: Understanding Everyday Neurobiology for Self-Knowledge
 
Valproic Acid. (VPA). Antiseizure medication
Valproic Acid.  (VPA). Antiseizure medicationValproic Acid.  (VPA). Antiseizure medication
Valproic Acid. (VPA). Antiseizure medication
 
Systemic Lupus Erythematosus -SLE PT2.ppt
Systemic  Lupus  Erythematosus -SLE PT2.pptSystemic  Lupus  Erythematosus -SLE PT2.ppt
Systemic Lupus Erythematosus -SLE PT2.ppt
 
PHYSIOTHERAPY IN HEART TRANSPLANTATION..
PHYSIOTHERAPY IN HEART TRANSPLANTATION..PHYSIOTHERAPY IN HEART TRANSPLANTATION..
PHYSIOTHERAPY IN HEART TRANSPLANTATION..
 
Culture and Health Disorders Social change.pptx
Culture and Health Disorders Social change.pptxCulture and Health Disorders Social change.pptx
Culture and Health Disorders Social change.pptx
 
COVID-19 (NOVEL CORONA VIRUS DISEASE PANDEMIC ).pptx
COVID-19  (NOVEL CORONA  VIRUS DISEASE PANDEMIC ).pptxCOVID-19  (NOVEL CORONA  VIRUS DISEASE PANDEMIC ).pptx
COVID-19 (NOVEL CORONA VIRUS DISEASE PANDEMIC ).pptx
 
ANEMIA IN PREGNANCY by Dr. Akebom Kidanemariam
ANEMIA IN PREGNANCY by Dr. Akebom KidanemariamANEMIA IN PREGNANCY by Dr. Akebom Kidanemariam
ANEMIA IN PREGNANCY by Dr. Akebom Kidanemariam
 
Hypersensitivity and its classification .pptx
Hypersensitivity and its classification .pptxHypersensitivity and its classification .pptx
Hypersensitivity and its classification .pptx
 
Music Therapy's Impact in Palliative Care| IAPCON2024| Dr. Tara Rajendran
Music Therapy's Impact in Palliative Care| IAPCON2024| Dr. Tara RajendranMusic Therapy's Impact in Palliative Care| IAPCON2024| Dr. Tara Rajendran
Music Therapy's Impact in Palliative Care| IAPCON2024| Dr. Tara Rajendran
 

Non parametric tests

  • 1. NON - PARAMETRIC TESTS DR. RAGHAVENDRA HUCHCHANNAVAR Junior Resident, Deptt. of Community Medicine, PGIMS, Rohtak
  • 2. Contents • Introduction • Assumptions of parametric and non-parametric tests • Testing the assumption of normality • Commonly used non-parametric tests • Applying tests in SPSS • Advantages of non-parametric tests • Limitations • Summary
  • 3. Introduction • Variable: A characteristic that is observed or manipulated. • Dependent • Independent • Data: Measurements or observations of a variable 1. Nominal or Classificatory Scale: Gender, ethnic background, eye colour, blood group 2. Ordinal or Ranking Scale: School performance, social economic class 3. Interval Scale: Celsius or Fahrenheit scale 4. Ratio Scale: Kelvin scale, weight, pulse rate, respiratory rate
  • 4. Introduction • Parameter: is any numerical quantity that characterizes a given population or some aspect of it. Most common statistics parameters are mean, median, mode, standard deviation.
  • 5. Assumptions • The general assumptions of parametric tests are − The populations are normally distributed (follow normal distribution curve). − The selected population is representative of general population − The data is in interval or ratio scale
  • 6. Assumptions • Non-parametric tests can be applied when: – Data don’t follow any specific distribution and no assumptions about the population are made – Data measured on any scale
  • 7. Testing normality • Normality: This assumption is only broken if there are large and obvious departures from normality • This can be checked by  Inspecting a histogram  Skewness and kurtosis ( Kurtosis describes the peakof the curve Skewness describes the symmetry of the curve.)  Kolmogorov-Smirnov (K-S) test (sample size is ≥50 )  Shapiro-Wilk test (if sample size is <50) (Sig. value >0.05 indicates normality of the distribution)
  • 11. Commonly used tests • Commonly used Non Parametric Tests are: − Chi Square test − McNemar test − The Sign Test − Wilcoxon Signed-Ranks Test − Mann–Whitney U or Wilcoxon rank sum test − The Kruskal Wallis or H test − Friedman ANOVA − The Spearman rank correlation test − Cochran's Q test
  • 12. Chi Square test • First used by Karl Pearson • Simplest & most widely used non-parametric test in statistical work. • Calculated using the formula- χ2 = ∑ ( O – E )2 E O = observed frequencies E = expected frequencies • Greater the discrepancy b/w observed & expected frequencies, greater shall be the value of χ2. • Calculated value of χ2 is compared with table value of χ2 for given degrees of freedom. Karl Pearson (1857–1936)
  • 13. Chi Square test • Application of chi-square test: • Test of association (smoking & cancer, treatment & outcome of disease, vaccination & immunity) • Test of proportions (compare frequencies of diabetics & non-diabetics in groups weighing 40-50kg, 50-60kg, 60- 70kg & >70kg.) • The chi-square for goodness of fit (determine if actual numbers are similar to the expected/theoretical numbers)
  • 14. Chi Square test • Attack rates among vaccinated & unvaccinated children against measles : • Prove protective value of vaccination by χ2 test at 5% level of significance Group Result Total Attacked Not-attacked Vaccinated (observed) 10 90 100 Unvaccinated (observed) 26 74 100 Total 36 164 200
  • 15. Chi Square test Group Result Total Attacked Not-attacked Vaccinated (Expected) 18 82 100 Unvaccinated (Expected) 18 82 100 Total 36 164 200
  • 16. Chi Square test  χ2 value = ∑ (O-E)2/E  (10-18)2 + (90-82)2 + (26-18)2 + (74-82)2 18 82 18 82  64 + 64 + 64 + 64 18 82 18 82  =8.67  calculated value (8.67) > 3.84 (expected value corresponding to P=0.05)  Null hypothesis is rejected. Vaccination is protective.
  • 17. Chi Square test • Yates’ correction: applies when we have two categories (one degree of freedom) • Used when sample size is ≥ 40, and expected frequency of <5 in one cell • Subtracting 0.5 from the difference between each observed value and its expected value in a 2 × 2 contingency table • χ2 = ∑ [O- E-0.5]2 E
  • 18. Fisher’s Exact Test • Used when the • Total number of cases is <20 or • The expected number of cases in any cell is ≤1 or • More than 25% of the cells have expected frequencies <5. Ronald A. Fisher (1890–1962)
  • 19. McNemar Test • McNemar Test: used to compare before and after findings in the same individual or to compare findings in a matched analysis (for dichotomous variables) • Example: comparing the attitudes of medical students toward confidence in statistics analysis before and after the intensive statistics course. McNemar
  • 20. Sign Test • Used for paired data, can be ordinal or continuous • Simple and easy to interpret • Makes no assumptions about distribution of the data • Not very powerful • To evaluate H0 we only need to know the signs of the differences • If half the differences are positive and half are negative, then the median = 0 (H0 is true). • If the signs are more unbalanced, then that is evidence against H0.
  • 21. – Children in an orthodontia study were asked to rate how they felt about their teeth on a 5 point scale. – Survey administered before and after treatment. How do you feel about your teeth? 1. Wish I could change them 2. Don’t like, but can put up with them 3. No particular feelings one way or the other 4. I am satisfied with them 5. Consider myself fortunate in this area Sign Test
  • 22. child Rating before Rating after 1 1 5 2 1 4 3 3 1 4 2 3 5 4 4 6 1 4 7 3 5 8 1 5 9 1 4 10 4 4 11 1 1 12 1 4 13 1 4 14 2 4 15 1 4 16 2 5 17 1 4 18 1 5 19 4 4 20 3 5 • Use the sign test to evaluate whether these data provide evidence that orthodontic treatment improves children’s image of their teeth.
  • 23. child Rating before Rating after change 1 1 5 4 2 1 4 3 3 3 1 -2 4 2 3 1 5 4 4 0 6 1 4 3 7 3 5 2 8 1 5 4 9 1 4 3 10 4 4 0 11 1 1 0 12 1 4 3 13 1 4 3 14 2 4 2 15 1 4 3 16 2 5 3 17 1 4 3 18 1 5 4 19 4 4 0 20 3 5 2 • First, for each child, compute the difference between the two ratings
  • 24. child Rating before Rating after change sign 1 1 5 4 + 2 1 4 3 + 3 3 1 -2 - 4 2 3 1 + 5 4 4 0 0 6 1 4 3 + 7 3 5 2 + 8 1 5 4 + 9 1 4 3 + 10 4 4 0 0 11 1 1 0 0 12 1 4 3 + 13 1 4 3 + 14 2 4 2 + 15 1 4 3 + 16 2 5 3 + 17 1 4 3 + 18 1 5 4 + 19 4 4 0 0 20 3 5 2 + • The sign test looks at the signs of the differences – 15 children felt better about their teeth (+ difference in ratings) – 1 child felt worse (- diff.) – 4 children felt the same (difference = 0) • If H0 were true we’d expect an equal number of positive and negative differences. (P value from table 0.004)
  • 25. 25 Wilcoxon signed-rank test • Nonparametric equivalent of the paired t-test. • Similar to sign test, but take into consideration the magnitude of difference among the pairs of values. (Sign test only considers the direction of difference but not the magnitude of differences.) WILCOXON
  • 26. Wilcoxon signed-rank test • The 14 difference scores in BP among hypertensive patients after giving drug A were: -20, -8, -14, -12, -26, +6, -18, -10, -12, -10, -8, +4, +2, -18 • The statistic T is found by calculating the sum of the positive ranks, and the sum of the negative ranks. • The smaller of the two values is considered.
  • 27. Wilcoxon signed-rank test Score Rank • +2 1 • +4 2 • +6 3 • -8 4.5 Sum of positive ranks = 6 • -8 4.5 • -10 6.5 Sum of negative ranks = 99 • -10 6.5 • -12 8 • -14 9 T= 6 • -16 10 • -18 11.5 • -18 11.5 • -20 13 • -26 14 For N = 14, and α = .05, the critical value of T = 21. If T is equal to or less than T critical, then null hypothesis is rejected i.e., drug A decreases the BP among hypertensive patients.
  • 28. Mann-Whitney U test • Mann-Whitney U – similar to Wilcoxon signed-ranks test except that the samples are independent and not paired. • Null hypothesis: the population means are the same for the two groups. • Rank the combined data values for the two groups. Then find the average rank in each group.
  • 29. Mann-Whitney U test • Then the U value is calculated using formula • U= N1*N2+ Nx(Nx+1) _ Rx (where Rx is larger rank 2 total) • To be statistically significant, obtained U has to be equal to or LESS than this critical value.
  • 30. Mann-Whitney U test • 10 dieters following Atkin’s diet vs. 10 dieters following Jenny Craig diet • Hypothetical RESULTS: • Atkin’s group loses an average of 34.5 lbs. • J. Craig group loses an average of 18.5 lbs. • Conclusion: Atkin’s is better?
  • 31. Mann-Whitney U test • When individual data is seen • Atkin’s, change in weight (lbs): +4, +3, 0, -3, -4, -5, -11, -14, -15, -300 • J. Craig, change in weight (lbs) -8, -10, -12, -16, -18, -20, -21, -24, -26, -30
  • 32. Jenny Craig diet -30 -25 -20 -15 -10 -5 0 5 10 15 20 0 5 10 15 20 25 30 P e r c e n t Weight Change
  • 33. Atkin’s diet -300 -280 -260 -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 0 5 10 15 20 25 30 P e r c e n t Weight Change
  • 34. Mann-Whitney U test • RANK the values, 1 being the least weight loss and 20 being the most weight loss. • Atkin’s – +4, +3, 0, -3, -4, -5, -11, -14, -15, -300 – 1, 2, 3, 4, 5, 6, 9, 11, 12, 20 • J. Craig − -8, -10, -12, -16, -18, -20, -21, -24, -26, -30 − 7, 8, 10, 13, 14, 15, 16, 17, 18, 19
  • 35. Mann-Whitney U test • Sum of Atkin’s ranks: 1+ 2 + 3 + 4 + 5 + 6 + 9 + 11+ 12 + 20=73 • Sum of Jenny Craig’s ranks: 7 + 8 +10+ 13+ 14+ 15+16+ 17+ 18+19=137 • Jenny Craig clearly ranked higher. • Calculated U value (18) < table value (27), Null hypothesis is rejected.
  • 36. Kruskal-Wallis One-way ANOVA • It’s more powerful than Chi-square test. • It is computed exactly like the Mann-Whitney test, except that there are more groups (>2 groups). • Applied on independent samples with the same shape (but not necessarily normal).
  • 37. Friedman ANOVA • Friedman ANOVA: When either a matched-subjects or repeated-measure design is used and the hypothesis of a difference among three or more (k) treatments is to be tested, the Friedman ANOVA by ranks test can be used.
  • 38. Spearman rank-order correlation • Use to assess the relationship between two ordinal variables or two skewed continuous variables. • Nonparametric equivalent of the Pearson correlation. • It is a relative measure which varies from -1 (perfect negative relationship) to +1 (perfect positive relationship). Charles Spearman (1863–1945)
  • 39. Cochran's Q test • Cochran's Q test is a non-parametric statistical test to verify if k treatments have identical effects where the response variable can take only two possible outcomes (coded as 0 and 1)
  • 40. Applying the tests in SPSS software
  • 43. The Sign, Wilcoxon and McNemar test
  • 44. Mann Whitney U test • Mann whitney U
  • 46. Friendman’s ANOVA and Cochran’s
  • 48. Advantages of non-parametric tests • These tests are distribution free. • Easier to calculate & less time consuming than parametric tests when sample size is small. • Can be used with any type of data. • Many non-parametric methods make it possible to work with very small samples, particularly helpful in collecting pilot study data or medical researcher working with a rare disease.
  • 49. Limitations of non-parametric methods • Statistical methods which require no assumptions about populations are usually less efficient . • As the sample size get larger , data manipulations required for non-parametric tests becomes laborious • A collection of tabulated critical values for a variety of non- parametric tests under situations dealing with various sample sizes is not readily available.
  • 50. Summary Table of Statistical Tests Level of Measureme nt Sample Characteristics Correlation 1 Sample 2 Sample K Sample (i.e., >2) Independent Dependent Independent Dependent Categorical or Nominal Χ2 Χ2 MacNemar test Χ2 Cochran’s Q Rank or Ordinal Mann Whitney U Wilcoxon Signed Rank Kruskal Wallis H Friedman’s ANOVA Spearman’s rho Parametric (Interval & Ratio) z test or t test t test between groups t test within groups 1 way ANOVA between groups Repeated measure ANOVA Pearson’s test Factorial (2 way) ANOVA Χ2