Amrita Kumari from Banaras Hindu University submitted an application discussing parametric tests. Parametric tests were developed by R. Fisher and make assumptions about the population distribution from which a sample is drawn. The key assumptions are that the population is normally distributed, observations are independent, populations have equal variance, and data is on a ratio or interval scale. Parametric tests can be used even when distributions are skewed or variances differ, and they have more statistical power than non-parametric tests. Common parametric tests include t-tests, z-tests, and ANOVA. The document then discusses one-sample, dependent, and independent t-tests in more detail. Both advantages like precision and disadvantages like sensitivity

1.  NAME – AMRITA KUMARI
 AFFILIATION – BANARAS HINDU UNIVERSITY
Application no.-8fff099e67c11e9801339e3a95769ac

2. PARAMETRIC TESTS
 Parametric function were mentioned by R.Fisher.
 It’s a statistical test in which specific assumptions are made
about the population distribution from which the sample is
drawn.
ASSUMPTIONS :
 The population data is normally distributed.
 The observations must be independent.
 The population must have same variance.
 The samples drawn from population must follow
homogenity principle .
 The data should be on ratio or interval scale.

3. WHEN & WHY WE DO PARAMETRIC
TEST?
• It can perform well with skewed and non
normal distributions.
• It can also be done when the spread of each
group is different.
• It has more statistical power.

4. TYPES OF PARAMETRIC TEST
t-test
Two sample
t-test
paired
unpaired
One sample
t-test
Z-test
ANOVA
One-way ANOVA Two-way ANOVA
• t-test
One-sample t-test
Two
sample
Two sample t-test

5. t-test

6. •It’s a method of testing hypothesis about the mean of small
sample drawn from a normally distributed population when
SD(standard deviation) for the sample is unknown.
ASSUMPTIONS
•Observations in the study are independent of each other.
•Homogeneity of variance : distribution of scores around mean
are of 2 or more samples are equal

7. • sample is drawn from a normally distributed
population.
•DVs are on interval or ratio scale.
TYPES OF t-test
Types of t-
test
Two sample
Independent
Paired
One sample

8. ONE SAMPLE t- test
 It’s used to measure whether a sample value significantly
differs from a hypothesized value.
 For eg: a research scholar might hypothesize that on an
average it takes 3 minutes for people to drink a standard
cup of coffee.
 He conducts an experiment & measures how long it takes
his subjects to drink a standard cup of coffee.
 The one sample t-test measures whether the mean amount
of time it took the experimental group to complete the task
varies significantly from the hypothesized 3 min value.

9. Equation for one-sample t-test

10. DEPENDENT t-test
 It compares the means of two related samples to check
whether there is a significant difference between their
means.
 It is an example of within subjects or repeated
measures statistical tests.

11. HYPOTHESIS

12. STEPS TO CALCULATE

13.  After getting the t value calculate the degree of
freedom.
 Now we look at the critical value from the table for the
significance level of 0.05 or 0.01 for the degree of
freedom we got. If our t value obtained is greater than
the critical value, the null hypothesis is rejected and
the alternate hypothesis is accepted.
Hence, this is how correlated t test is calculated.

14. •Independent t-test is used when means of two different samples are
compared.
•The two independent samples are randomly selected and are
completely independent of each other.
•The distribution of dependent variable is normal in the populations
from which samples are drawn and the variances in the population are
roughly equal.
•Data are measured at least at interval level.
TWO SAMPLE :INDEPENDENT
t-test

15. We test the null hypothesis that the two population
means are same against an appropriate one-tailed or
two-tailed alternative hypothesis.
µ1 = µ2
Where µ1 = Mean of population 1 and µ2 = Mean of
population 2
Since null hypothesis assumes that means of both
populations are same, then µ1 - µ2 = 0

16. STEPS TO CALCULATE

20. ADVANTAGES AND
DISADVANTAGES OF
PARAMETRIC STATISTICS

21. 1. Does not require convertable data- biggest advantage.
2. The long calculations provide accuracy and precision to the results.
3. In this specific assumption are made about the population.
4. Based on distribution.
5. There is complete information about the population.
6. Can perform quite well when they have been spread over and each group
happens to be different.
7. It has high statistical power as compared to other tests. Therefore we will be
able to find an effect that is significant when one will exist truly.
ADVANTAGES

22. DISADVANTAGES
1. Influence of sample size- parametric tests are not valid when it comes
to small sample (if < n=10).
2. You have missing values as well as outliers, you just cannot randomly
remove.
3. Susceptibility to violation of assumptions
4. Scope of application
5. Speed of application
6. Ease of application
7. Simplicity of deviation- high level of maths calculations.
8. Parametric test is used for only interval data and ratio data.

23. Acknowledgement
SWAYAM online course - Academic writing

24. Wekipedia.
Winer,,B.J., Brown,D.R. & Michels,K.M.(1991) Statistical
principles in experimental design.NY:McGraw Hill.