Parametric test such as Z test, T test, ANOVA, F test and Chi Square test is addressed

2. 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.
Assumptions
 The scores must be independent (In other words the selection of any
particular score must not be bias the chance of any other case for
inclusion).
 The observations must be drawn from normally distributed
populations(Follow ND)
 The selected population is representative of general population
 The data is in Interval or Ratio scale
 The populations(If comparing two or more groups) must have the
same variances

3. Types of Parametric test
Types of Parametric test
1. Z- test.
2. T-test.
3. ANOVA.
4. F-test.
5. Chi-Square test.

4. 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.
 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.

5. 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.

6. 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.

7. T-test
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.
 Population is Normal distributed.
There are two ways to calculate T-test such as,
a. Unpaired t-test.(independent)
b. Paired t-test.

8. 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.

9. 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.
Paired t-test.

10. 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.

11. There are two ways to calculate ANOVA such as.
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.
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.

12. Chi-Square test
It is a test that measures how expectations compare
to actual observed data. It is used to investigate
whether distribution of categorical variables differ
from one another
Formula Chi Square= Summation(Oi-Ei)2/Ei
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: