The document discusses different types of hypothesis testing and statistical tests. It defines what a hypothesis is and characteristics of hypotheses. It explains the difference between the null hypothesis and alternative hypothesis. The key parametric tests discussed are the z-test, t-test, chi-square test, and F-test. These tests can be used to analyze means, variances and frequencies from sample data to determine if hypotheses can be rejected or not. Non-parametric tests are also briefly covered.

1. “ HYPOTHESIS AND ITS IMPORTANT PARAMETRIC
TESTS”
by Mansi Rajendra Gajare

2. What is Hypothesis ?
Hypothesis is a predictive statement, capable of being tested by
scientific methods, that relates an independent variables to some
dependent variable.
A hypothesis states what we are looking for and it is a proportion which
can be put to a test to determine its validity.

3. •Characteristics of Hypothesis
• Clear and precise.
• Capable of being tested.
• Stated relationship between variables
• limited in scope and must be specific.
• Stated as far as possible in most simple terms so that the same is easily
understand by all concerned. But one must remember that simplicity
of hypothesis has nothing to do with its significance.
• Consistent with most known facts.
• Responsive to testing with in a reasonable time.
• .

4. Null Hypothesis and Alternative
Hypothesis
•If we are to compare methodA with method B about its
superiority and if we proceed on the assumption that
both methods are equally good, then this assumption is
termed as the null hypothesis
•As against this , we may think that the methodA is
superior or the method B is inferior we are then we are
then stating what is termed as alternative hypothesis.
The null hypothesis is generally symbolized as H0 and
the alternative hypothesis as Ha

5. • Null hypothesis should always be specific hypothesis i.e., it
should not state about or approximately a certain value.
• Alternative hypothesis is usually the one which one wishes to
prove and the null hypothesis is the one which one wishes to
disprove.Thus, a null hypothesis represents the hypothesis we
are trying to reject, and alternative hypothesis represents all
other possibilities.
• If our sample results do not support this null hypothesis, we
should conclude that something else is true.What we conclude
rejecting the null hypothesis is known as alternative hypothesis.
In other words, the set of alternatives to the null hypothesis is
referred to as the alternative hypothesis

6. TESTS OF HYPOTHESES
Hypothesis testing helps to decide on the basis of a sample
data, whether a hypothesis about the population is likely
to be true or false.
Statisticians have developed several tests of hypotheses
(also known as the tests of significance) for the purpose of
testing of hypotheses which can be classified as:
(a) Parametric tests or standard tests of hypotheses; and
(b) Non-parametric tests or distribution-free test of
hypotheses.

7. Mean of the population can be tested presuming different
situations such as the population may be , normal or other than
normal, it may be finite or infinite, sample size may be large or
small, variance of the population may be known or unknown and
the alternative hypothesis may be two-sided or one-sided.
testing technique will differ in different situations.
We may consider some of the important situations.
Hypothesis testing of means

11. CONCEPT OF STANDARD ERROR
The standard deviation of sampling distribution of a statistic is known
as its standard error (S.E) and is considered the key to sampling
theory.
The utility of the concept of standard error in statistical induction
arises on account of the following reasons:
The standard error helps in testing whether the difference between
observed and expected frequencies could arise due to chance.
The criterion usually adopted is that if a difference is less than 3 times
the S.E., the difference is supposed to exist as a matter of chance and
if the difference is equal to or more than 3 times the S.E., chance fails
to account for it, and we conclude the difference as significant
difference.

12. • We can test the difference at certain other levels of significance as well
depending upon our requirement.
• The following table gives some idea about the criteria at various levels for
judging the significance of the difference between observed and expected
values:

13. The following table gives the percentage of samples having
their mean values within a range of population mean

14. Important formulae for computing the standard errors concerning
various measures based on samples are as under:

15. Two tailed test with
5% significance level

16. Left tailed test with
5% significance level

17. Right tailed test with 5%
significance level

19. SANDLERS A-TEST
Joseph Sandler has developed an alternate approach based on a
simplification of t-test. His approach is described as Sandler’s A-test
that serves the same purpose as is accomplished by t-test relating to
paired data.
Researchers can as well use A-test when correlated samples are
employed and hypothesised mean difference is taken as zero. found
as follows:

20. Hypothesis testing steps
• Null and alternative hypotheses
• Test statistic
• P-value and interpretation
• Significance level (optional)

21. The important parametric tests are:
(1) z-test
(2) t-test
3) χ2-test ( Chi- square )
(4) F-test.
All these tests are based on the assumption of normality.

22. Z - test
• Z test is a statistical procedure used to test an alternative hypothesis against
a null hypothesis.
• Z-test is any statistical hypothesis used to determine whether two samples'
means are different when variances are known and sample is large (n ≥ 30).
• It is Comparison of the means of two independent groups of samples, taken
from one populations with known variance.

26. T test

31. Chi square test
• IMPORTANT CHARACTERISTICS OF A CHI SQUARETEST
• This test (as a non-parametric test) is based on frequencies and
not on the parameters like mean and standard deviation.
• The test is used for testing the hypothesis and is not useful for
estimation.
• This test can also be applied to a complex contingency table with
several classes and as such is a very useful test in research work.
• This test is an important non-parametric test as no rigid
assumptions are necessary in regard to the type of population,
no need of parameter values and relatively less mathematical
details are involved.

35. F test

40. Thank you