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

1. Submitted by,
Pooja. G.
G.F.G.C.W Holenarsipura
P.G Studies.
PARAMETRIC TEST

2. CONTENT
Meaning of parametric.
Types of parametric.
1. Z-test.
2. T-test.
3. ANOVA.
4. F-test.
5. Chi-Square test.

3. Meaning of parametric
Parametric statistic is a branch of
statistic, which assumes that sample data
comes from a population that follows a
probability or normal distribution. When the
assumption are correct, parametric methods
will produce more accurate and precise
estimates.

4. Types of parametric
The types of parametric
are,
1. Z- test.
2. T-test.
3. ANOVA.
4. F-test.
5. Chi-Square test.

5. 1. Z-test.
A Z-test is given by Fisher. A Z-test is a type of
hypothesis test or statistical test.
It is used for testing the mean of a population
versus a standard or comparing the means of two
population with large sample (n>30).
When we can run a Z-test
 Your sample size is greater than 30.
 Data point should be independent from each other.
 Your data should be randomly selected from a
population, where each item has an equal chance of
being selected.

6. Continue….
 Data should follow normal distribution.
 The standard deviation of the populations is known.
There are two ways to calculate z-test
a. one-sample z-test.
b. two-sample z-test.

7. a. one-sample z-test
One-sample z-test we are comparing the mean, calculated
on a single of score (one sample) with known standard deviation.
Ex. The manager of a candy manufacture wants to know
whether the mean weight of batch of candy boxes is equal to the
target value of 10 pounds from historical data.

8. b. Two-sample z-test
When testing for the differences between two groups can imagine
two separate situation. Comparing the proportion of two population.
In two sample z-test both independent populations.
Ex: 1. Comparing the average engineering salaries of men
versus women.
2. Comparing the fraction defectives from two production line.

9. 2. T-tset.
It is derived by W.S Gosset in 1908. It is also
called student t-test. A t-test statistical
significance indicates whether or not the
difference between two groups.
Assumption:
 Samples must be random and independent.
 When samples are small. n<30
 Standard deviation is not known.
 Normal distribution.

10. Continue…
There are two ways to calculate T-test such as,
a. Unpaired t-test.(independent)
b. Paired t-test.
a. Unpaired t-test:
If there is no link between the data then use the unpaired t-test. When two
separate set of independent sample are obtain one from each of the two
population being compared.
Ex:1. Compare the height of girls and boys.
2. Compare the 2 stress reduction intervention.
When one group practiced mindfulness meditation, while other
learned yoga.

11. b. Paired t-test.
Paired t-test consists of a sample of matched pairs of similar
units or one group of units that has been tested twice (a” repeated
measures” t-test). If there is some link between the data then use the
paired t-test.(e.g. Before and after)
Ex: 1. where subject are tested prior to a treatment say for high blood
pressure, and the same subject are tested again after treatment with
a blood pressure lowering medication.
2. Test on person or any group before and after training.

12. 3. ANOVA (Analysis of Variance)
It is developed by Fisher in 1920. ANOVA is a
collection of statistical model used to analyze the
differences between groups. Compare multiple groups at
one time. It is advanced technique for the experimental
treatment of testing differences all of the mean which is
not possible in case of t-test.
Assumptions:
 All population have same standard deviation.
 Individuals in population are selected randomly.
 Independent samples.
 The population must be normal distribution.

13. There are two ways to calculate ANOVA such as.
a. one-way ANOVA.
b. Two-way ANOVA.
a. one-way ANOVA:
One-way anova compare three or more unmatched
groups when data are categorized in one way.
Ex: You might be studying the effect of tea on
weight loss, from three groups, green tea, black tea,
no tea.

14. b. two-way ANOVA
Two way anova technique is used when the data
are classified on the basis of two factors. And two way
anova analyzed a 2 independent variable and 1
dependent variable.
Ex: The agricultural output may be classified on
the basis of different verities of seeds. and also on the
basis of different verities of fertilizer used.

15. 4. F-test
It is derived by Fisher in 1924. The F-test is
designed to test if two population variance are equal.
There are two independent degrees of freedom, one for
numerator another one is denominator.
Numerator: the numerator degrees of freedom will be the
degree of freedom for whichever sample has the larger
variance. s¹
Denominator: the denominator degrees of freedom will be
the degree of freedom for whichever sample has the small
variance. s²
Assumption:
 Samples are drawn at random.
 There is no measurement error.
 F-values are all non negative.

16. Ex:
Two source of raw materials are under consideration by a
company. Both source seem to have similar characteristics but the
company is not sure about their respective uniformity.
A sample of 10 lots source X yields a variance of 225 and a
sample of 11 lots from source Y yield a variance of 200. is it likely
that the variance of source X is significantly greater than the variance
of source Y at ɑ=0.01?
Formula:
F= S²₁(numerator)
S²₂(denominator)

17. 5. Chi-Square test
It is drawn by Karl Pearson. Chi square test is a
statistical test used as a parametric for testing for
comparing variance .
It is denoted as “ x²”.
Formula: