Support the Monkey! Tell All your Friends and Teachers

Help / FAQ



Example The following table is published in a memoir written by 'Karl Pearson'

Test whether the color of son’s eyes is associated with that of father’s.

Solution: The null hypothesis : The eye color of sons and eye color of father’s are independent. If this is true the expected frequencies are

The table value of c2 at 0.05 level of significance for df = 1 is 3.841 which is extremely poor compared to the calculated 133.37. Thus we reject the null hypothesis saying that there is high association between the sons’s eyes and that of the father.


Example In an experiment on the immunization of goats from anthrax, the following results were obtained. Derive the you inference on the efficacy of the vaccine.
       
  Died of anthrax Survived Total
       
Inoculated 2 10 12
       
Non-inoculated 6 6 12
       
Total 8 16 24

Solution: The null hypothesis : Inoculation of vaccine and survival are independent attributes. The expected frequencies would be :

The nos. of degree of freedom n = ( c - 1 ) ( r - 1 )

            = ( 2 - 1 ) ( 2 - 1 )

            = 1

From the table c20.05, n = 1 = 3.841. Thus the calculated value is less than table value. Hence the hypothesis is accepted,

Note : Brandt and Snedecor gave a simple formula for 2 ´ 2 contingency table, in order to calculate c2. Representing th ( 2 ´ 2 ) fold contingency table as :

We Multiply diagonal frequencies and find the difference between the two products ( b1c2 - c1b2 )

Square this i.e. ( b1c2 - c1b2 )2

Multiply by the grand total i.e. ( b1c2 - c1b2 )2 ´ T

Divide the above result by the product of all the sub totals i.e. T1 ´T2 ´ Tb ´ Tc

Index

8.1 Population
8.2 Sample
8.3 Parameters and Statistic
8.4 Sampling Distribution
8.5 Sampling Error
8.6 Central Limit Theorem
8.7 Critical Region
8.8 Testing of Hypothesis
8.9 Errors in Tesitng of Hypothesis
8.10 Power o a Hypothesis Test
8.11 Sampling of Variables
8.12 Sampling of Attributes
8.13 Estimation
8.14 Testing the Difference Between Means
8.15 Test for Difference Between Proportions
8.16 Two Tailed and one Tailed Tests
8.17 Test of Significance for Small Samples
8.18 Students t-distribution
8.19 Distribution of 't' for Comparison of Two Samples Means Independent Samples
8.20 Testing Difference Between Mens of Two Samples Dependent Samples or Matched Paired Observations
8.21 Chi-Square
8.22 Sampling Theory of Correlation
8.23 Sampling Theory of Regression

Chapter 1





All Contents Copyright © All rights reserved.
Further Distribution Is Strictly Prohibited.


Search:
Keywords:
In Association with Amazon.com