Hypothesis and Hypothesis Testing

Hypothesis Testing
NABIN KUNWAR
DEPARTMENT OF AGRICULTURAL ECONOMICS
MAY 29, 2021
1

Introduction
A specific, testable and precise prediction about what the researcher assumes to
happen in his/her study
Hypothesis is usually considered as the principal instrument in research
Involves proposing a possible relationship between two variables i.e. the
dependent and independent variable
A complete hypothesis must include three components i.e. the variables, the
population and the relationship between the variables
2

Characteristics of Hypothesis
Should be clear and precise
Should be capable of being tested
Should state relationship between variables (if relational hypothesis)
Should be limited in scope and must be specific
Should be stated as far as possible in most simple terms
Should be consistent with most known facts
3

Contd…
Should be amenable to testing within a reasonable time
Must explain the facts that gave rise to the need for explanation
4

Types of Research Hypothesis
Generally, there are four types of research hypothesis which are:
1. Null Hypothesis
2. Alternate Hypothesis
3. Directional Hypothesis
4. Non-directional Hypothesis
5

Purpose of Hypothesis Testing
A statistical process of testing an assumption regarding a phenomenon or
population parameter
It is a critical and crucial part of the scientific method
Is a systematic approach to assessing theories through observations and
determining the probability that a stated statement is true or false
For an analyst who makes predictions, hypothesis testing is a difficult way of
backing up his prediction with statistical analysis
Also helps to determine whether there is sufficient statistical evidences that
support a certain hypothesis about the population parameter or not
6

Null Hypothesis
Null hypothesis is normally referred to as hypothesis of no difference and it is
denoted by Ho
Assumes that there is no difference between the hypothetical population and
the one, from which the sample under study has been drawn
A/c to this hypothesis, “there is no difference between the effects of two
treatments or there is no association between two attributes”
7

Contd…
It declares that there is no true difference in the sample statistic and
population parameter under consideration,
Hence it is called ‘null’ which means invalid, void, or a mounting to nothing
and the difference found is accidental, arising out of instabilities of sampling
Rejecting a null hypothesis does not necessarily mean that the experiment did
not produce the required results, but it sets the situation for further
experimentation
8

Contd…
For example, the hypothesis may be set in a form “maize variety A will give the
same yield per hectare as that of the variety B or there is no difference between
the average yields of maize varieties A and B”
Symbolically, Ho: μ1=μ2
Thus, these hypothesis form a basis to work with and such a working
hypothesis is known as null hypothesis.
It is called null hypothesis because if nullifies the original hypothesis i.e. variety
A will give more/less yield than variety B
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States of Nature and Decisions on Null Hypothesis
Decision on Null
Hypothesis
States of Nature
Null Hypothesis True Null Hypothesis False
Accept Correct Decision
Probability=1 − 𝛼
Type II error committed
Probability=𝛽
Reject Type I error committed
Probability=𝛼
(𝛼 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑐𝑒 𝑙𝑒𝑣𝑒𝑙)
Correct Decision
Probability=1 − 𝛽
(1 − 𝛽 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 𝑝𝑜𝑤𝑒𝑟 𝑜𝑓 𝑎 𝑡𝑒𝑠𝑡)
Note. Adapted from “Formulating and Testing Hypothesis” by Muhammad, K. S. (2016). Basic Guideline for Research. pp.
51-71.
10

Contd…
In the choice of null hypothesis, the following considerations are usually kept in
view:
A. 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.
B. If the rejection of a certain hypothesis when it is actually true involves great
risk, it is taken as null hypothesis because the probability of rejecting it when
it is true is 𝜶 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.
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Alternative Hypothesis
Hypothesis that contradicts the null hypothesis i.e. 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.
An alternative hypothesis and a null hypothesis are mutually exclusive, which
implies that only one of the two hypotheses can be true
A/c to this hypothesis, there is a relationship between the two variables being
studied (one variable has an effect on the other) and the results are not due to
chance
In simple words, null hypothesis means there is no effect while alternate
hypothesis means there is an effect
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Contd…
Usually represented by Ha/H1
For example: “There is a significant difference between the yields of two maize
varieties”
Symbolically, H1: μ1≠μ2 (two tailed or non-direction alternative)
If the statement is that A gives significantly less yield than B or A gives
significantly more yield than B. Such statement is known as alternate hypothesis
Symbolically, H1: μ1 < μ2 (left tailed) H1: μ1 > μ2 (right tailed)
13

Directional Hypothesis
Directional hypothesis is also known as one-tailed hypothesis which predicts
the nature of the effect of the independent variable on the dependent variable
States which way you think the results are going to go
For example: “Mansuli variety of rice will have more yield than that of Basmati
variety”; the hypothesis compares the two groups and states which one will have
more/less, be faster/slower and so on
14

Contd…
Under correlational study, the directional hypothesis would state whether a
positive or a negative correlation is expected, stating how the two variables will
be related to each other
 E.g.: There will be a positive correlation between the number of tillers and
yield of rice, number of irrigation and plant growth etc.
 The directional hypothesis can also specify a negative correlation
 E.g.: the higher the inflation rate in the country, lower the purchasing power of
the people.
15

Contd…
Here the researcher is intellectually committed to a particular outcome and
the anticipated direction of the relationship between variables is also specified
i.e. the investigator predicts not only the existence of a relationship but also its
nature
Such type of hypothesis is generally use by scientific journal
If the normal or t-distribution is used, one side or one tailed test only is
employed to estimate the required probabilities
16

Contd…
Figure 1. Directional/One-tailed Test
To reject H0: μ1 ≤ μ2 and accept H1: μ1 > μ2 0, using the normal distribution,
a normal deviate greater than +1.64 (i.e. right tailed) is required for significant
at the 0.05 level.
17

Contd…
Likewise, to reject H0: μ1 ≥ μ2 and accept H1: μ1 < μ2, the corresponding
normal curve is less than -1.64 (i.e. left tailed)
The choice between a non-directional or directional alternative hypothesis
should be determined by the rationale that gives rise to the study and should be
made before the data are gathered.
The major advantage of a directional alternative hypothesis is that it takes less
of a deviation from expectation to reject the null hypothesis
18

19
Figure 1. Directional/One-tailed Test
Figure 1. Non-Directional/Two-tailed Test

Non-directional Hypothesis
States that “The independent variable will have an influence on the dependent
variable, but the direction of the outcome is not specified”
For e.g.: “There will be a difference in the yield of two varieties of rice namely,
Basmati and Mansuli being cultivated”
A non-directional hypothesis only states that there exists a difference between
the two group/items but does not specify which will be greater/smaller,
positive/negative, faster/slower etc.
Similarly, in case of correlational study, we simply state that variables will be
correlated but do not state whether the relationship will be positive or negative,
e.g. there will be a significant correlation between variable X and variable Y
20

Contd…
We may wish to test the null hypothesis H0:μ1− μ2 = 0 against the alternative
H1:μ1− μ2 ≠ 0. This means that if H0 is rejected, the decision is that a difference
exists between the two means.
No confirmation about the direction of the difference is made. Such test is a
non-directional test.
Sometime called a two-tailed or two-sided test, because if the normal
distribution or t-distribution is used, the two tails of the distribution are employed
in the estimation of probabilities
21

Contd…
Figure 2. Non-directional/Two-tailed Test
Consider a 5% significance level. If the sampling distribution is normal, 2.5%
of the area of the curve falls to the right of 1.96 standard deviation units above
the mean, and 2.5% lies to the left of 1.96 standard deviation units lower the
mean.
22

Procedure For Hypothesis Testing
1. Making a formal statement
2. Selecting a significance level
3. Deciding the distribution to use
4. Selecting a random sample and computing an appropriate value
5. Calculation of the probability
6. Comparing the probability
23

Tests of Hypotheses
IMPORTANT PARAMETRIC TESTS
The important parametric tests are:
(1) z-test
(2) t-test
(3) Chi-Square-test, and
(4) F-test
(All these tests are based on the assumption of normality i.e., the source of data
is considered to be normally distributed)
24

z-test
Based on the normal probability (z) distribution and is used for judging the
significance of several statistical measures, particularly the mean
z-test is generally used for comparing the mean of a sample to some
hypothesized mean for the population in case of large sample (>30)
Besides, this test may be used for judging the significance of median, mode,
coefficient of correlation and several other measures
25

t-test
t-test is based on t-distribution and is considered an appropriate test for judging
the significance of a sample mean or for judging the significance of difference
between the means of two samples in case of small sample(<30)
In case two samples are related, we use paired t-test (aka. difference test) for
judging the significance of the mean of difference between the two related
samples.
It can also be used for judging the significance of the coefficients of simple and
partial correlations
26

Contd…
t-statistic is calculated from the sample data and then compared with its
probable value based on t-distribution (to be read from the table that gives
probable values of t for different levels of significance for different degrees of
freedom) at a specified level of significance for concerning degrees of freedom
for accepting or rejecting the null hypothesis
27

Chi-Square-test
Chi-Square-test is based on chi-square distribution and as a parametric test is
used for comparing a sample variance to a theoretical population variance
It can also be used to make comparisons between theoretical populations and
actual data when categories are used.
Thus, the chi-square test is applicable in large number of problems.
The test is, in fact, a technique through the use of which it is possible for all
researchers to:
(i) test the goodness of fit
(ii) test the significance of association between two attributes,
(iii) test the homogeneity or the significance of population variance.
28

F-test
F-test is based on F-distribution and is used to compare the variance of the
two-independent samples.
This test is also used in the context of analysis of variance (ANOVA) for
judging the significance of more than two sample means at one and the same
time.
It is also used for judging the significance of multiple correlation coefficients
F-statistic is calculated and compared with its probable value (to be seen in the
F-ratio tables for different degrees of freedom for greater and smaller variances at
specified level of significance) for accepting or rejecting the null hypothesis
29

Conclusion
Research hypothesis is a specific, testable and precise prediction about what the
researcher assumes to happen in their study
There are four types of research hypothesis (null, alternate, directional and non-
directional hypothesis)
Hypothesis testing is done to determine whether there is sufficient statistical
evidence that supports a certain hypothesis about the population parameter or not
Null hypothesis is the hypothesis of no difference i.e. same
30

Contd…
Directional hypothesis predicts the nature of the effect of the independent
variable on the dependent variable i.e. direction of outcome is specified
Non directional hypothesis predicts the influence of independent variable on
the dependent variable, but the direction of the outcome is not specified
Test for hypotheses testing: t-test, z-test, chi-square test, F-test
31

References
Agresti, A., & Finlay, B. (1997). Statistical Methods for the Social Sciences (3rd ed.). Prentice
Hall.
CFI. (2020). Null Hypothesis. Retrieved from Corporate Finance Institute:
https://corporatefinanceinstitute.com/resources/knowledge/other/null-hypothesis-2/
Development of the Research Hypothesis and Types of Hypothesis. (2018). Retrieved from
THEINTACTONE: https://theintactone.com/2018/02/26/br-u1-topic-3-development-of-the-
research-hypothesis-and-types-of-hypothesis/
McLeod, S. (2018, August 10). What is a hypothesis. Retrieved from Simply Psychology:
https://www.simplypsychology.org/what-is-a-hypotheses.html
Muhammad, K. S. (2016). Formulating and Testing Hypothesis. In Basic Guideline for Research
(pp. 51-71).
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