1. The document discusses various statistical tests used for testing hypotheses, including t-tests, ANOVA, non-parametric tests, and tests of correlation and relationships between variables.
2. Key concepts covered include the difference between null and alternative hypotheses, types of errors, p-values, assumptions of different tests, and choosing appropriate tests based on the scale and distribution of the data.
3. Examples are given of common tests like paired t-test, Wilcoxon test, repeated measures ANOVA, independent t-test, and tests for comparing multiple groups like ANOVA and Kruskal-Wallis test. Tests of relationships like correlation, regression, chi-square, and Fisher's exact test are also summarized
Hypothesis Testing is important part of research, based on hypothesis testing we can check the truth of presumes hypothesis (Research Statement or Research Methodology )
A hypothesis is a testable statement about the relationship between two or more variables and errors reveal about the rejection and acceptance of the statement.
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Hypothesis Testing is important part of research, based on hypothesis testing we can check the truth of presumes hypothesis (Research Statement or Research Methodology )
A hypothesis is a testable statement about the relationship between two or more variables and errors reveal about the rejection and acceptance of the statement.
Please like, comment and share
Through this ppt you could learn what is Wilcoxon Signed Ranked Test. This will teach you the condition and criteria where it can be run and the way to use the test.
01 parametric and non parametric statisticsVasant Kothari
Definition of Parametric and Non-parametric Statistics
Assumptions of Parametric and Non-parametric Statistics
Assumptions of Parametric Statistics
Assumptions of Non-parametric Statistics
Advantages of Non-parametric Statistics
Disadvantages of Non-parametric Statistical Tests
Parametric Statistical Tests for Different Samples
Parametric Statistical Measures for Calculating the Difference Between Means
Significance of Difference Between the Means of Two Independent Large and
Small Samples
Significance of the Difference Between the Means of Two Dependent Samples
Significance of the Difference Between the Means of Three or More Samples
Parametric Statistics Measures Related to Pearson’s ‘r’
Non-parametric Tests Used for Inference
This presentation covers statistics, its importance, its applications, branches of statistics, basic concepts used in statistics, data sampling, types of sampling,types of data and collection of data.
Through this ppt you could learn what is Wilcoxon Signed Ranked Test. This will teach you the condition and criteria where it can be run and the way to use the test.
01 parametric and non parametric statisticsVasant Kothari
Definition of Parametric and Non-parametric Statistics
Assumptions of Parametric and Non-parametric Statistics
Assumptions of Parametric Statistics
Assumptions of Non-parametric Statistics
Advantages of Non-parametric Statistics
Disadvantages of Non-parametric Statistical Tests
Parametric Statistical Tests for Different Samples
Parametric Statistical Measures for Calculating the Difference Between Means
Significance of Difference Between the Means of Two Independent Large and
Small Samples
Significance of the Difference Between the Means of Two Dependent Samples
Significance of the Difference Between the Means of Three or More Samples
Parametric Statistics Measures Related to Pearson’s ‘r’
Non-parametric Tests Used for Inference
This presentation covers statistics, its importance, its applications, branches of statistics, basic concepts used in statistics, data sampling, types of sampling,types of data and collection of data.
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2. Hypothesis
• Hypothesis is defined as the statement
regarding parameter (characteristic of a
population)
Dr.Asir John Samuel (PT), Lecturer, ACP 2
3. Test of significance
• A statistical procedure by which one can
conclude, if the observed results from the
sample is due to chance (sampling variation)
or not
Dr.Asir John Samuel (PT), Lecturer, ACP 3
4. A B
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Dr.Asir John Samuel (PT), Lecturer, ACP 4
5. Null hypothesis (H0)
• A hypothesis which states that the observed
result is due to chance
• Researcher anticipate “no difference” or “no
relationship”
Dr.Asir John Samuel (PT), Lecturer, ACP 5
6. Alternate hypothesis (HA)
• A hypothesis which states that the observed
results is not due to chance (research
hypothesis)
• Statement predict that a difference or
relationship b/w groups will be demonstrated
Dr.Asir John Samuel (PT), Lecturer, ACP 6
7. Testing of hypothesis
1. Evaluate data
2. Review assumption
3. State hypothesis
4. Presume null hypothesis
5. Select test statistics
6. Determine distribution of test statistics
7. State decision rule
Dr.Asir John Samuel (PT), Lecturer, ACP 7
8. Testing of hypothesis
8. Calculate test statistics
9. What is the probability that the data conform
10. Make statistical decision
11. If p>0.05, then reject (HA)
12. If p<0.05, then accept (HA)
Dr.Asir John Samuel (PT), Lecturer, ACP 8
9. Testing of Hypothesis
Presume null hypothesis
What is the probability
that data conform to
p>0.05 null hypothesis P<0.05
Retain H0 reject H0
Dr.Asir John Samuel (PT), Lecturer, ACP 9
10. p-value
• Probability of getting a minimal difference of
what has observed is due to chance
• Probability that the difference of at least as
large as those found in the data would have
occurred by chance
Dr.Asir John Samuel (PT), Lecturer, ACP 10
11. p value in decision
• P value very large
- Probability to get the observed result due to
chance
• P value very small
- Small probability to get the observed result
not due to chance
Dr.Asir John Samuel (PT), Lecturer, ACP 11
12. Decision for 5% LOS
• Probability of rejecting true null hypothesis
• If p-value <0.05, then data favours alternate
hypothesis
• If p-value ≥0.05, then data favours null
hypothesis
Dr.Asir John Samuel (PT), Lecturer, ACP 12
13. Type I & II errors
Possible states of Null Hypothesis
Possible True False
actions on Accept Correct Type II
Null Action error
Hypothesis Reject Type I Correct
error Action
Prob (Type I error) – α (LoS)
Prob (Type II error) – β
1-β – power of test
Dr.Asir John Samuel (PT), Lecturer, ACP 13
14. LOS and Power
• Prob (type I error) = α
• Prob (type II error) = β
• α – LOS
• 1- β – power of the study
Dr.Asir John Samuel (PT), Lecturer, ACP 14
15. Test of Hypothesis
• Parametric test
• Non-parametric test
Dr.Asir John Samuel (PT), Lecturer, ACP 15
16. Parametric & non-parametric test
• Paired t-test • Wilcoxon Signed Rank T
• Repeated measure • Friedman test
ANOVA
• Independent t-test • Mann-Whitney U test
• One way ANOVA • Krushal Wallis test
• Pearson correlation • Spearman Rank
coefficient correlation coefficient
Dr.Asir John Samuel (PT), Lecturer, ACP 16
17. Paired t-test
• Two measures taken on the same subject or
naturally occurring pairs of observation or two
individually matched samples
• Variable of interest is quantitative
Dr.Asir John Samuel (PT), Lecturer, ACP 17
18. Assumption
• The difference b/w pairs in the population is
independent and normally or approximately
normally distributed
Dr.Asir John Samuel (PT), Lecturer, ACP 18
19. Wilcoxon Signed Rank test
• Used for paired data
• The sample is random
• The variable of interest is continuous
• The measurement scale is at least interval
• Based on the rank of difference of each paired
values
Dr.Asir John Samuel (PT), Lecturer, ACP 19
20. Repeated measures ANOVA
• Measurements of the same variable are made
on each subject on more than two different
occasion
• The different occasions may be different point
of time or different conditions or different
treatments
Dr.Asir John Samuel (PT), Lecturer, ACP 20
21. Assumptions
• Observations are independent
• Differences should follow normal distribution
• Sphericity-differences have approximately
same variances
Dr.Asir John Samuel (PT), Lecturer, ACP 21
22. Fried Man test
• Data is measured in ordinal scale
• The subjects are repeatedly observed under 3
or more conditions
• The measurement scale is at least ordinal
(qualitative)
• The variable of interest is continuous
Dr.Asir John Samuel (PT), Lecturer, ACP 22
23. Independent t-test
• Compare the means of two independent
random samples from two population
• Variable of interest is quantitative
Dr.Asir John Samuel (PT), Lecturer, ACP 23
24. Assumptions
• The population from which the sample were
obtained must be normally or approximately
normally distributed
• The variances of the population must be equal
Dr.Asir John Samuel (PT), Lecturer, ACP 24
25. Mann Whitney-U test
• Two independent samples have been drawn
from population with equal medians
• Samples are selected independently and at
random
• Population differ only with respect to their
median
• Variable of interval is continuous
Dr.Asir John Samuel (PT), Lecturer, ACP 25
26. Mann Whitney-U test
• Measurement scale is at least ordinal
(qualitative)
• Based on ranks of the observations
Dr.Asir John Samuel (PT), Lecturer, ACP 26
27. ANOVA
• Extension of independent t-test to compare
the means of more than two groups
• F = b/w group variation/within group variation
• F ratio
• Post hoc test (which mean is different)
Dr.Asir John Samuel (PT), Lecturer, ACP 27
28. Assumptions
• Observations are independent and randomly
selected
• Each group data follows normal distribution
• All groups are equally variable (homogeneity
of variance)
Dr.Asir John Samuel (PT), Lecturer, ACP 28
29. Why not t-test?
• Tedious
• Time consuming
• Confusing
• Potentially misleading – Type I error is more
Dr.Asir John Samuel (PT), Lecturer, ACP 29
30. Kruskal Wallis H test
• Used for comparison of more than 2 groups
• Extension of Mann-Whitney U test
• Used for comparing medians of more than 2
groups
Dr.Asir John Samuel (PT), Lecturer, ACP 30
31. Assumptions
• Samples are independent and randomly
selected
• Measurement scale is at least ordinal
• Variable of interest is continuous
• Population differ only with respect to their
medians
Dr.Asir John Samuel (PT), Lecturer, ACP 31
32. Chi-square Test (x2)
• Variables of interest are categorical
(quantitative)
• To determine whether observed difference in
proportion b/w the study groups are
statistically significant
• To test association of 2 variables
Dr.Asir John Samuel (PT), Lecturer, ACP 32
33. Chi-square Test-Assumption
• Randomly drawn sample
• Data must be reported in number
• Observed frequency should not be too small
• When observed frequency is too small and
corresponding expected frequency is less than
5 (<5) – Fischer Exact test
Dr.Asir John Samuel (PT), Lecturer, ACP 33
35. Correlation
• Method of analysis to use when studying the
possible association b/w two continuous
variables
• E.g.
- Birth wt and gestational period
- Anatomical dead space and ht
- Plasma volume and body weight
Dr.Asir John Samuel (PT), Lecturer, ACP 35
37. Properties
• Scatter diagrams are used to demonstrate the
linear relationship b/w two quantitative
variables
• Pearson’s correlation coefficient is denoted by r
• r measures the strength of linear relationship
b/w two continuous variable (say x and y)
Dr.Asir John Samuel (PT), Lecturer, ACP 37
38. Properties
• The sign of the correlation coefficient tells us
the direction of linear relationship
• The size (magnitude) of the correlation
coefficient r tells us the strength of a linear
relationship
Dr.Asir John Samuel (PT), Lecturer, ACP 38
39. Properties
• Better the points on the scatter diagram
approximate a straight line, the greater is the
magnitude r
• Coefficient ranges from -1 ≤ r ≤ 1
Dr.Asir John Samuel (PT), Lecturer, ACP 39
40. Interpretation
• r = 1, two variables have a perfect +ve linear
relationship
• r = -1, two variables have a perfect -ve linear
relationship
• r = 0, there is no linear relationship b/w two
variables
Dr.Asir John Samuel (PT), Lecturer, ACP 40
41. Assumption
• Observations are independent
• Relationship b/w two variables are linear
• Both variables should be normal distributed
Dr.Asir John Samuel (PT), Lecturer, ACP 41
42. Caution
• Correlation coefficient only gives us an
indication about the strength of a linear
relationship
• Two variables may have a strong curvilinear
relationship but they could have a weak value
for r
Dr.Asir John Samuel (PT), Lecturer, ACP 42
43. Judging the strength – Porteney &
Watkins criteria
• 0.00-0.25 – little or no relationship
• 0.26-0.50 – fair degree of relationship
• 0.51-0.75 – moderate to good degree of
relationship
• 0.76-1.00 – good to excellent relationship
Dr.Asir John Samuel (PT), Lecturer, ACP 43
44. Scatter diagram
• Each pair of variables is represented in scatter
diagram by a dot located at the point (x,y)
Dr.Asir John Samuel (PT), Lecturer, ACP 44
45. Scatter diagram - Merits
• Simple method
• Easy to understand
• Uninfluenced
• First step
Dr.Asir John Samuel (PT), Lecturer, ACP 45
46. Scatter diagram - Demerits
• Does not establish exact degree of correlation
• Qualitative method
• Not suitable for large sample
Dr.Asir John Samuel (PT), Lecturer, ACP 46
47. Spearman’s Rank correlation
• Non-parametric measure of correlation
between the two variables (at least ordinal)
• Ranges from -1 to +1
Eg:
- Pain score of age
- IQ and TV watched /wk
- Age and EEG output values
Dr.Asir John Samuel (PT), Lecturer, ACP 47
48. Situation
• Relationship b/w two variables is non-linear
• Variables measured are at least ordinal
• One of the variables not following normal
distribution
• Based on the difference in rank between each
variable
Dr.Asir John Samuel (PT), Lecturer, ACP 48
49. Assumption
• Observation are independent
• Samples are randomly selected
• The measurement scale is at least ordinal
Dr.Asir John Samuel (PT), Lecturer, ACP 49
50. Regression
• Expresses the linear relationship in the form of
an equation
• In other words a prediction equation for
estimating the values of one variable given the
valve of the other,
y = a + bx
Dr.Asir John Samuel (PT), Lecturer, ACP 50
51. Regression - eg
• Wt (y) and ht (x)
• Birth wt (y) and gestation period (x)
• Dead space (y) and height (x)
x and y are continuous
y-dependent variable
x-independent variable
Dr.Asir John Samuel (PT), Lecturer, ACP 51
52. Regression line
• Shows how are variable changes on average
with another
• It can be used to find out what one variable is
likely to be (predict) when we know the other
provided the prediction is within the limits of
data range
Dr.Asir John Samuel (PT), Lecturer, ACP 52
53. Regression analysis
• Derives a prediction equation for estimating
the value of one variable (dependent) given the
value of the second variable (independent)
y = a + bx
Dr.Asir John Samuel (PT), Lecturer, ACP 53
54. Assumption
• Randomly selection
• Linear relationship between variables
• The response variable should have a normal
distribution
• The variability of y should be the same for
each value of the predictor value
Dr.Asir John Samuel (PT), Lecturer, ACP 54
55. Multiple regression
• One dependent variable and multiple
independent variable
• Derives a prediction equation for estimating
the value of one variable (dependent) given
the variable of the other variable
(independent)
Dr.Asir John Samuel (PT), Lecturer, ACP 55
56. Multiple regression
• The dependent variable is continuous and
follows normal distribution
• Independent variable can be quantitative as
well as qualitative
Dr.Asir John Samuel (PT), Lecturer, ACP 56