This document discusses parametric statistical tests. It defines parametric tests as those that make assumptions about the population distribution parameters. The key parametric tests covered are: t-tests (paired, unpaired, one sample), ANOVA (one way, two way), Pearson's correlation, and the z-test. Details are provided on the assumptions, calculations, and applications of each test. T-tests are used to compare means, ANOVA compares multiple group means, Pearson's r measures correlation between variables, and the z-test is for large samples when the population standard deviation is known.
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
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
Parametric and non parametric test in biostatistics Mero Eye
ย
This ppt will helpful for optometrist where and when to use biostatistic formula along with different examples
- it contains all test on parametric or non-parametric test
This presentation contains information about Mann Whitney U test, what is it, when to use it and how to use it. I have also put an example so that it may help you to easily understand it.
In Hypothesis testing parametric test is very important. in this ppt you can understand all types of parametric test with assumptions which covers Types of parametric, Z-test, T-test, ANOVA, F-test, Chi-Square test, Meaning of parametric, Fisher, one-sample z-test, Two-sample z-test, Analysis of Variance, two-way ANOVA.
Subscribe to Vision Academy for Video assistance
https://www.youtube.com/channel/UCjzpit_cXjdnzER_165mIiw
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
ย
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 Pearsonโs โrโ
Non-parametric Tests Used for Inference
Parametric and non parametric test in biostatistics Mero Eye
ย
This ppt will helpful for optometrist where and when to use biostatistic formula along with different examples
- it contains all test on parametric or non-parametric test
This presentation contains information about Mann Whitney U test, what is it, when to use it and how to use it. I have also put an example so that it may help you to easily understand it.
In Hypothesis testing parametric test is very important. in this ppt you can understand all types of parametric test with assumptions which covers Types of parametric, Z-test, T-test, ANOVA, F-test, Chi-Square test, Meaning of parametric, Fisher, one-sample z-test, Two-sample z-test, Analysis of Variance, two-way ANOVA.
Subscribe to Vision Academy for Video assistance
https://www.youtube.com/channel/UCjzpit_cXjdnzER_165mIiw
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
ย
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 Pearsonโs โrโ
Non-parametric Tests Used for Inference
Hypothesis is usually considered as the principal instrument in research and quality control. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate object of testing hypothesis. Decision makers often face situations wherein they are interested in testing hypothesis on the basis of available information and then take decisions on the basis of such testing. In Six โSigma methodology, hypothesis testing is a tool of substance and used in analysis phase of the six sigma project so that improvement can be done in right direction
This presentation describes the concept of One Sample t-test, Independent Sample t-test and Paired Sample t-test. This presentation also deals about the procedure to do the t-test through SPSS.
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2. STATISTICAL TEST
โข Statistical tests are intended
to decide whether a
hypothesis about distribution
of one or more populations or
samples should be rejected or
accepted.
Statistical
Tests
Parametric tests
Non โ
Parametric tests
3. PARAMETRIC TESTS
Parametric test is a statistical test that makes assumptions
about the parameters of the population distribution(s) from
which oneโs data is drawn.
4. APPLICATIONS
โข Used for Quantitative data.
โข Used for continuous variables.
โข Used when data are measured on approximate interval or
ratio scales of measurement.
โข Data should follow normal distribution.
7. STUDENTโS T-TEST
โข Developed by Prof.W.S.Gossett
โข A t-test compares the difference between two means of
different groups to determine whether the difference is
statistically significant.
8. One Sample t-test
Assumptions:
โข Population is normally distributed
โข Sample is drawn from the population and it should be
random
โข We should know the population mean
Conditions:
โข Population standard deviation is not known
โข Size of the sample is small (<30)
9. Contd..
โข In one sample t-test , we know the population mean.
โข We draw a random sample from the population and then
compare the sample mean with the population mean and
make a statistical decision as to whether or not the sample
mean is different from the population.
10. Let x1, x2, โฆโฆ.,xn be a random sample of size โnโ has drawn from a
normal population with mean (ยต) and variance ๐2.
Null hypothesis (H0):
Population mean (ฮผ) is equal to a specified value ยต0.
Under H0, the test statistic is ๐ =
๐โยต
๐
๐
11. Two sample t-test
โข Used when the two independent random samples come from the
normal populations having unknown or same variance.
โข We test the null hypothesis that the two population means are same
i.e., ยต1 = ยต2
12. Contdโฆ
Assumptions:
1. Populations are distributed normally
2. Samples are drawn independently and at random
Conditions:
1. Standard deviations in the populations are same and not known
2. Size of the sample is small
13. If two independent samples xi ( i = 1,2,โฆ.,n1) and yj ( j = 1,2, โฆ..,n2) of
sizes n1and n2 have been drawn from two normal populations with
means ยต1 and ยต2 respectively.
Null hypothesis
H0 : ยต1 = ยต2
Under H0, the test statistic is
๐ =
ว ๐ โ ๐ว
๐บ
๐
๐ ๐
+
๐
๐ ๐
14. Paired t-test
Used when measurements are taken from the same subject
before and after some manipulation or treatment.
Ex: To determine the significance of a difference in blood
pressure before and after administration of an experimental
pressure substance.
15. Assumptions:
1. Populations are distributed normally
2. Samples are drawn independently and at random
Conditions:
1. Samples are related with each other
2. Sizes of the samples are small and equal
3. Standard deviations in the populations are equal and not known
16. Null Hypothesis:
H0: ยตd = 0
Under H0, the test statistic
๐ =
ว๐ ฬ ว
๐
๐
Where, d = difference between x1 and x2
dฬ = Average of d
s = Standard deviation
n = Sample size
17. Z-Test
โข Z-test is a statistical test where normal distribution is applied
and is basically used for dealing with problems relating to
large samples when the frequency is greater than or equal to
30.
โข It is used when population standard deviation is known.
18. Contdโฆ
Assumptions:
โข Population is normally distributed
โข The sample is drawn at random
Conditions:
โข Population standard deviation ฯ is known
โข Size of the sample is large (say n > 30)
19. Let x1, x2, โฆโฆโฆx,n be a random sample size of n from a normal
population with mean ยต and variance ฯ2 .
Let xฬ be the sample mean of sample of size โnโ
Null Hypothesis:
Population mean (ยต) is equal to a specified value ยตฮฟ
H0: ยต = ยตฮฟ
20. Under Hฮฟ, the test statistic is
๐ =
ว ๐ โ ยต ๐ว
๐
๐
If the calculated value of Z < table value of Z at 5% level of
significance, H0 is accepted and hence we conclude that there is no
significant difference between the population mean and the one
specified in H0 as ยตฮฟ.
21. Pearsonโs โrโ Correlation
โข Correlation is a technique for investigating the relationship
between two quantitative, continuous variables.
โข Pearsonโs Correlation Coefficient (r) is a measure of the
strength of the association between the two variables
22. Types of correlation
Type of correlation Correlation coefficient
Perfect positive correlation r = +1
Partial positive correlation 0 < r < +1
No correlation r = 0
Partial negative correlation 0 > r > -1
Perfect negative correlation r = -1
23. ANOVA (Analysis of Variance)
โข Analysis of Variance (ANOVA) is a collection of statistical
models used to analyse the differences between group means
or variances.
โข Compares multiple groups at one time
โข Developed by R.A.Fischer
25. One way ANOVA
Compares two or more unmatched groups when data are categorized in
one factor
Ex:
1. Comparing a control group with three different doses of aspirin
2. Comparing the productivity of three or more employees based on
working hours in a company
26. Two way ANOVA
โข Used to determine the effect of two nominal predictor variables on a
continuous outcome variable.
โข It analyses the effect of the independent variables on the expected
outcome along with their relationship to the outcome itself.
Ex: Comparing the employee productivity based on the working hours
and working conditions.
27. Assumptions of ANOVA:
โข The samples are independent and selected randomly.
โข Parent population from which samples are taken is of normal
distribution.
โข Various treatment and environmental effects are additive in
nature.
โข The experimental errors are distributed normally with mean
zero and variance ฯ2.
28. โข ANOVA compares variance by means of F-ratio
F =
๐ฃ๐๐๐๐๐๐๐ ๐๐๐ก๐ค๐๐๐ ๐ ๐๐๐๐๐๐
๐ฃ๐๐๐๐๐๐๐ ๐ค๐๐กโ๐๐ ๐ ๐๐๐๐๐๐
โข It again depends on experimental designs
Null hypothesis:
Hฮฟ = All population means are same
โข If the computed Fc is greater than F critical value, we are likely to reject the null
hypothesis.
โข If the computed Fc is lesser than the F critical value , then the null hypothesis is
accepted.
29. ANOVA Table
Sources of
Variation
Sum of squares
(SS)
Degrees of
freedom (d.f)
Mean squares
(MS)
๐๐๐ ๐๐ ๐๐๐๐๐๐๐
๐ ฬ ๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐ ฬ ๐๐
F - Ratio
Between samples
or groups
(Treatments)
Treatment sum of
squares ( TrSS)
(k-1) ๐๐๐๐
(๐ โ 1)
๐๐๐๐
๐ธ๐๐
Within samples or
groups ( Errors )
Error sum of
squares (ESS)
(n-k) ๐ธ๐๐
(๐ โ ๐)
Total Total sum of
squares (TSS)
(n-1)
30. S.No Type of group Parametric test
1. Comparison of two paired groups Paired t-test
2. Comparison of two unpaired groups Unpaired two sample t-test
3. Comparison of population and sample
drawn from the same population
One sample t-test
4. Comparison of three or more matched
groups but varied in two factors
Two way ANOVA
5. Comparison of three or more matched
groups but varied in one factor
One way ANOVA
6. Correlation between two variables Pearson Correlation
Editor's Notes
One sample t-test is a statistical procedure that is used to know the population
mean and the known value of the population mean. In one sample t-test, we know the
population mean. We draw a random sample from the population and then compare the
sample mean with population mean and make a statistical decision as to whether or not the
sample mean is different from the population mean. In one sample t-test, sample size
should be less than 30.
Now we compare calculated value with table value at certain level of significance ( generally at 5% ). If absolute value of โtโ obtained is greater than table value then reject the null hypothesis and if it is less than table value , the null hypothesis may be accepted.