What is a Hypothesis??

• An Assumption to be tested

• An un-proved theory

• A claim to be checked/tested

Our Conclusions based on The p-value / (L.O.S.) comparison

Types of Hypotheses

Ho: Null Hypothesis Mostly contains: A Claim or A tradition or A hopeless Statement e.g. Ho: =10 m. Ho: There is no-difference b/w two quantities Ho: There is no association b/w two variables etc.

Ha: Alternate Hypothesis

Research Hypothesis OR Test Hypothesis Mostly contains: Denial of A Claim or A New tradition or A hopeful Statement e.g. Ha: ≠10 m. Ha: There is a difference b/w two quantities Ha: There is an association b/w two variables etc.

Responses and Tests

Two Quantitative Variables

Scatter Diagram

Correlation Regression Models

e.g.

Age v/s Weight

Two Qualitative Variables

Cross Tabulation Chi-square Test of Association

e.g.

Sex v/s CauseCRF

One Qualitative & One

Quantitative Variable

Box-plots (EDA) T-test /Z-test

ANOVA e.g.

Sex v/s Age

Types of Hypothesis & Recommended Tests

• Hypothesis related to single or two averages (Recommended z-test and t-test) • Hypothesis related to single or two proportions (Recommended z-test and t-test) • Hypothesis related to single & two variances (Recommended Chi-square and F-test respectively) • Hypothesis related to test of association b/w two

qualitative variables (The Bi-variate contingency table) (Recommended Chi-square test)

• Hyp. related to compare more than 3 Averages • (Recommended Test is ANOVA)

Story of “Significance”

1- If p-value < =0.05 2- Null Hypothesis (Ho) Rejected… 3- Result will be “Significant” 4- We are in Research

1- If p-value > =0.05 2- Null Hypothesis (Ho) accepted… 3- Result will be “Insignificant” 4- We are not in Research

Exploratory Analysis for Quality ranks from Field Managers of a Pharma Co.

Str

uct

ur

Adm

in

Teach

ing

5

4

3

2

Boxplots of Teaching, Administration & Structure

(means are indicated by solid circles)

Ho: There is no significant difference b/w 3 Averages Ha: Atleast one Average is Significantly different from others

P-value<=0.05

We Reject Ho.

Result is significant due

to the 3rd Average

Single Sample t-test in SPSS

Single Sample t-test in SPSS (Output)

Ho: =4 Ha: 4

Since, p-value (0.039)<(0.05); we will

reject Ho. And conclude that 4

C.I. doesn’t contains ‘zero’.

Result is Significant

Two Sample t-test in SPSS

Two Sample t-test in SPSS

Since, p-value(s) are not less than (0.05); we will not reject Ho.

And conclude that Two averages are equal

Two averages Ho: There is No difference b/w Two Averages Ha: There is a Significant Difference b/w both averages

Results are Insignificant

Chi-Square Test of Association

• To Determine whether the Association is Present b/w Two QUALITATIVE variables or Not.

• A Contingency table can help us to understand the concept of “Association”.

• A contingency table is a Bivariate Frequency table usually showing a joint Distribution of two qualitative variables.

2 Test of Association (An Example)

Consider the following table which is representing Gender (Male/Female) and the Eyesight Status (Glasses/No Glasses):

Gender/EyeSight

Male (M) Female (F) R.Total

Glasses (G)

No Glasses (NG)

Column Total

Gender/EyeSight

Male (M) Female (F) R.Total

Glasses (G) 05 12 17

No Glasses (NG) 09 19 28

Column Total 14 31 45

Ho: There is No Association b/w Gender and Eyesight Ha: There is An Association b/w Gender and Eyesight

ChiSquare Results: 2=0.037 p-value=0.848

Since 0.848>0.05 We accept Ho.

Gender/EyeSight

Male (M) Female (F) R.Total

Glasses (G) 05 19 24

No Glasses (NG) 09 12 21

Column Total 14 31 45

ChiSquare Results: 2=2.535 p-value=0.111

Since 0.111>0.05 We accept Ho.

Gender/EyeSight

Male (M) Female (F) R.Total

Glasses (G) 05 26 31

No Glasses (NG) 12 12 24

Column Total 17 38 55

ChiSquare Results: 2=7.267 p-value=0.007

Since 0.007<0.05 We Reject Ho.

Correlation

• A correlation is useful when you want to see the relationship between two (or more) Quantitative Variables.

• Correlation is the measure of Linear Association b/w two Quantitative Variables.

• Range of Correlation is -1 r +1 showing the amount of association on either directions with r0 showing weak or no relationship.

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Correlation Example

• For a Doctor, its important to see the impact of one Quantitative Variable on to another Quantitative Variable.

• For e.g. The following results showing the Pearson’s correlation b/w Age and Weights of Urology patients.

14

Showing 6.6% association b/w Age and Weight

0.781 > 0.05 So, there is no

correlation b/w variables

Recommended Books of Statistics

• Title: Introductory Statistics, 5th Ed.,

By Neil A. Weiss, Publisher Pearson Addison Wesley

• Probability and Statistics for Engineers and Scientists, 8th Ed.

By Walpole, Myer’s and Myer’s and YE

Thankyou