Hypothesis Testing is important part of research, based on hypothesis testing we can check the truth of presumes hypothesis (Research Statement or Research Methodology )

1. Hypothesis Testing
Kalyan Acharjya
kalyan.acharjya@gmail.com

2. Outlines
● What is Hypothesis?
● Characteristics of Hypotheses.
● Hypotheses Types & Terminologies.
● Null & Alternate Hypotheses.
● Flowchart of Hypotheses Testing.
● Chi-Square Test.
● Conclusion.
2

3. What is Hypothesis?
● A Hypothesis is a premise or claim that we want to test.
● Hypothesis (Latin)= Hupo (Under)+Thesis (placing)-Greek.
● A supposition or proposed explanation made on the basis of limited
evidence as a starting point for further investigation.
● A hypothesis is a speculation or theory based on insufficient evidence that
lends itself to further testing and experimentation.
● Presume assumption based on observations or experiences (Not Verified).
3

4. Characteristics of Hypothesis
● Hypothesis should be clear & precise.
● Hypothesis should be capable of being tested.
● Hypothesis must explain the facts that give rise to the need for
explanation.
● Hypothesis should be amenable to testing within a reasonable time.
● Hypothesis should be consistent with most known facts.
● Hypothesis should state relationships between variables.
4

5. Hypothesis Types
★ Null Hypothsis
★ Alternate Hypothesis / Research Hypothesis
A Null Hypothesis (Ho) - that says there is no statistical significance
between the two variables in the hypothesis.
When the samples result donot support the null hypothesis, then
concluded something else is true, termed as Alternate Hypothesis (Ha).
5

6. Hypothesis Testing Flowchart
Hypothesis
Significance
Sample
Values
Testing
Method
P Value
Decision
6

7. Some Terminologies
The level of Confidence (C): Probability of confidence (May be Null
Hypothesis likely to be reject).
The level of Significance (alpha) - The probability of rejecting the null
hypothesis when it is true. Normally referred in percentage (usually 5%).
Decision Rule-Test Hypothesis - The decision rule compares the sample
mean to the hypothesized mean. If the sample mean is "close" to the
hypothesized mean, we accept the null hypothesis.
Type I & Type II error:
7

8. 8
Two Tailed & One Tailed Test

9. Some Terminologies..Continue
Analyze Sample Data: Degrees of freedom, expected frequencies, test statistic,
and the P-value associated with the test statistic.
•Degrees of freedom. The degrees of freedom (DF) is equal to:
DF = (r - 1) * (c - 1)
where r is the number of levels for one categorical variable, and c is the
number of levels for the other categorical variable.
•Expected frequencies: Er,c = (nr * nc) / n, where Er,c is the expected
frequency count for level r of Variable A and level c of Variable B, nr is the total
number of sample observations at level r of Variable A, nc is the total number
of sample observations at level c of Variable B, and n is the total sample size.
9

10. Test statistic: Chi Square Test
•The test statistic is a chi-square random variable (chi square) defined by the
following equation-
P-value: The P-value is the probability of observing a sample statistic as
extreme as the test statistic (Variable and degrees of freedom on Chi-Square
Distribution).
Interpret Results: When P value < alpha (Level of significance) implies null
hypothesis is rejected.
10


E
EO 2)(2

11. Chi-Sqaure Test-Example
•“Is Demonetization will help to boost the Indian Economy?” Opinion poll surveyed a simple
random sample of 1000 people. Respondents were classified by gender (male or female) and by
voting preference (Yes, No, or Neutral). Results-
•Is there a gender gap? Do the men's preferences differ significantly from the women's preferences?
Use a 0.05 level of significance.
Poll Results
Row Total
Yes No Neutral
Male 200 150 50 400
Female 250 300 50 600
Column total 450 450 100 1000
11

12. Chi-Sqaure Test-Solutions Contd..
•State the Hypotheses: The first step is to state the null hypothesis and an alternative
hypothesis.
H0: Gender and voting preferences are independent.
Ha: Gender and voting preferences are not independent.
•Formulate an analysis plan. For this analysis, the significance level is 0.05. Using
sample data, we will conduct a chi-square test for independence.
12

13. Numerical Continue..
•Analyze sample data: Compute the degrees of freedom, the expected
frequency counts, and the chi-square test statistic.
DF = (r - 1) * (c - 1) = (2 - 1) * (3 - 1) = 2
E r,c = (nr * nc) / n
E1,1 = (400 * 450) / 1000 = 180000/1000 = 180
E1,2 = (400 * 450) / 1000 = 180000/1000 = 180
E1,3 = (400 * 100) / 1000 = 40000/1000 = 40
E2,1 = (600 * 450) / 1000 = 270000/1000 = 270
E2,2 = (600 * 450) / 1000 = 270000/1000 = 270
E2,3 = (600 * 100) / 1000 = 60000/1000 = 60
= Σ [ (Or,c - Er,c)2 / Er,c ]
= (200 - 180)2/180 + (150 - 180)2/180 + (50 - 40)2/40
+ (250 - 270)2/270 + (300 - 270)2/270 + (50 - 60)2/60
= 16.2
where DF is the degrees of freedom, r is the number of
levels of gender, c is the number of levels of the voting
preference, nr is the number of observations from level r
of gender, nc is the number of observations from level c of
voting preference, n is the number of observations in the
sample, Er,c is the expected frequency count when
gender is level r and voting preference is level c, and Or,c
is the observed frequency count when gender is level r
voting preference is level c.
13
Poll Results
Row Total
Yes No Neutral
Male 200 150 50 400
Female 250 300 50 600
Column
total
450 450 100 1000
2
2
2

14. Numeric Continue…
Based on the chi-square statistic and the degrees of freedom, we determine
the P-value.
The P-value is the probability that a chi-square statistic having 2 degrees of
freedom is more extreme than 16.2.
By using the Chi-Square Distribution Calculator to find P( > 16.2) = 0.0003.
Results: Since the P-value (0.0003) is less than the significance level (0.05),
we cannot accept the null hypothesis. Thus, we conclude that there is a
relationship between gender and voting preference.
Null Hypothesis is rejected.
14
2

15. Conclusions:
• The outcome of the research is based on formulation of hypothesis.
•Hypothesis testing is a significant part of any research work.
•The objective of Hypothesis Testing to verify the Null Hypotheses, not prove it.
•Chi-square is one statistic use to find the P value (Hypothesis Testing).
•If P Value is less than level of significance, then reject the null hypothesis.
•The other most popular test statistics are z2 test and t test.
15

16. References:
Book:
 Website link (Numeric Example)
http://stattrek.com/chi-square-test/independence.aspx?Tutorial=AP
16

17. Thank You
17
Kalyan Acharjya
kalyan.acharjya@gmail.com