This document discusses key concepts related to hypothesis testing. It defines a hypothesis as a proposed explanation made on limited evidence as a starting point for further investigation. It then lists characteristics that a good hypothesis should have such as being clear, testable, and consistent with known facts. The document also discusses null and alternative hypotheses and how they are used in testing. It explains the concept of the level of significance and types of errors that can occur in hypothesis testing. Finally, it provides examples of how hypotheses may be stated and tested for different situations.

1. Associate Professor
Department of PSM
CUSMC

2.  What is hypothesis??
 Characteristics of hypothesis
 Basic concepts concerning testing of hypothesis..

3. A supposition or proposed explanation made on the basis of
limited evidence as a starting point for further investigation..
When a possible correlation or similar relation between
phenomena is investigated, such as whether a proposed remedy
is effective in treating a disease, hypothesis is stated and tested
afterwords..

4. 1. Hypothesis should be clear and precise..
 If the hypothesis is not clear and precise, the inferences drawn
on its basis cannot be taken as reliable.
2. Hypothesis should be capable of being tested..
 In case of untestable hypothesis  Many a times the research
programmes have bogged down.
 Some prior study may be done by researcher in order to make
hypothesis a testable one.

5. 3. Hypothesis should state relationship between variables, if it
happens to be a relational hypothesis..
4. Hypothesis should be limited in scope and must be specific..
 A researcher must remember that narrower hypothesis are
generally more testable and he should develop such
hypothesis.
5. Hypothesis should be stated as far as possible in most simple
terms..
 Easily understandable by all concerned...
 But one must remember that simplicity of hypothesis has
nothing to do with its significance..

6. 6. Hypothesis should be consistent with most known facts..
 It must be consistent with a substantial body of established facts.
 It should be one which judges accept as being the most likely.
7. Hypothesis should be amenable to testing within a reasonable time..
 One should not use even an excellent hypothesis, if the same cannot
be tested in reasonable time for one cannot spend a life time
collecting data to test it.
8. Hypothesis must explain the facts that gave rise to the need for
explanation..
 By using the hypothesis plus other known and accepted
generalizations, one should be able to deduce the original problem
condition.

8.  If we want to compare method A with method B about its
superiority…
 Assumption 1: Both the methods are equally good..
Null hypothesis
 Method A is superior than B or Method B is inferior than A..
Alternate hypothesis
symbolize as =
symbolize as = or
 If we accept (H0) then we are rejecting (Ha) and if we reject (H0)
then indirectly we are accepting (Ha)

9.  Another e.g., we want to compare population mean
with the sample mean (100)…
Population mean = Sample mean = 100
We may consider 3 possible
outcomes
1. Population mean ≠ Sample mean
2. Population mean > Sample mean
3. Population mean < Sample mean

10.  The null hypothesis and alternate hypothesis are
chosen before the sample is drawn..
 In the choice of null hypothesis, the following
consideration are usually kept in mind
a) Alternative hypothesis is usually the one which one wishes to
prove. That means null hypothesis = We are trying to reject
and alternate hypothesis = All other possibilities..
b) If the rejection of certain hypothesis (H0/ Ha), when it is
actually true involves great risk = It is taken as null
hypothesis. Because then the probability of rejecting it when
it is true is α (level of significance) which is chosen very
small.
c) Null hypothesis should always be specific hypothesis i.e., it
should not state about or approximately a certain value.

11.  Very important concept in the context of hypothesis
testing..
 It is some % which should be chosen with great care,
thought and reason.
 Conventional significance levels for testing hypotheses
(acceptable probabilities of wrongly rejecting a true null
hypothesis) are 0.10, 0.05, and 0.01 (10, 5 and 1%)..
 If we take the significant level at , level of significance of
sampling result is <5% (0.05), H0 is rejected if it is true.
 In other words, 5% level of significance means that
researcher is willing to take as much as a 5% risk of
rejecting the null hypothesis when it happens to be true.

12. We make a rule according to which we
accept H0/reject H0.
Certain lot is good (or very few defective items in it)
There are too many defective items in it (or very few items are
good)
We must decide the number of items to be tested
and the criterion for accepting or rejecting the hypothesis (cut off)..
 So if we plan our decision saying that if there are none or only 1
defective item among the 10, we will accept H0 otherwise we will
reject Ha.

13.  In testing of hypothesis: basically two types of error we can
make..
ACTUAL STATUS OF H0
DECISION
ACCEPT H0 REJECT H0
H0 TRUE
H0 FALSE
Type II error
( error)
Correct
decision
Correct
decision
Type I
error
(α error)

14. Determined in advance and it understood as the
level of significance of testing the hypothesis..
Chances of rejecting H0 when it is true is 5 out of 100.
 We can reduce the chances of type I error by fixing it at a lower
level.
 For e.g., if we Maximum probability of committing
type I error would only be 0.01.
 But when we try to reduce type I error, the probability of
committing type II error increases. Both types of error cannot be
reduced simultaneously.
 So, the probability of making one type of error can only be
reduced if we are willing to increase the probability of making the
other type of error.

15.  Result of sample 1 = Result of sample 2 or
 Result of sample 1 ≠ Result of sample 2 (Sample 1 > or < Sample
2)
 Result of sample 1 > or < Result of sample 2.
 If the significance level is 5% and two-tailed test is to be
applied, the probability of the rejection area will be 0.05
(equally splitted on both tails of the curve as 0.025) and
acceptance region will be 0.95.
 If the significance level 5% and one-tailed test is to be
applied, the rejection area of 0.05 will be on one side only.