Chi square test for more than two rows, Applied Statistics

 

Using Chi Square Test when more than two Rows are Present

 

To understand this, let us consider the contingency table shown below. It gives us the information about the stage of the economy and the number of PCs sold on a weekly basis.

 

 

Weekly sale of PCs

Total

High

Medium

Low

Economy at Peak

Economy at Trough

Economy Rising

Economy Falling

20

13

18

14

14

 

12

9

10

5

9

8

44

26

39

31

Total

65

43

32

140

For calculating the proportion of sales during a weekly high, when the economy was rising we employ the formula of joint probability for two independent events A and B. The event A stands for proportion of sales durings a high irrespective of the stage of the economy and is given by (65/140), whereas the proportion of sales when the economy was rising irrespective of the weekly sales is (39/140). Since these two events happen to be independent events, the joint probability that they will occur simultaneously is

                   =  (65/140)(39/140)

                   =  2535/19600

Similarly the proportion of sales, when the weekly sales are low and the economy at its peak is given by the product of

                   =  (32/140)(44/140)

                   =  1408/19600

Since these figures give us the expected proportions to calculate the theoretical proportions, we multiply the above values with the total number of observations. Therefore, the theoretical proportion for the cell (economy rising, high) is given by

                   (2535/19600) x 140 = 18.107

and for the cell (economy at peak, low) the theoretical proportion is

                   (1408/19600) x 140 = 10.06

Generalizing this, the expected frequency for any cell (intersection point of the concerned row and the column) is given by the product of the sum of the elements in that row (usually denoted by TRi, i = 1, 2) and the sum of the elements in that column (denoted by CRj, j = 1, 2, 3) divided by the total number of observations. Mathematically it is expressed as

 

1594_chi square test.png

After this step, we proceed in the same manner as we do in case of contingency table having two rows and a given number of columns.

Posted Date: 9/15/2012 6:07:16 AM | Location : United States







Related Discussions:- Chi square test for more than two rows, Assignment Help, Ask Question on Chi square test for more than two rows, Get Answer, Expert's Help, Chi square test for more than two rows Discussions

Write discussion on Chi square test for more than two rows
Your posts are moderated
Related Questions
how can we use measurement error method with eight responses variables (we do not have explanatory variable in the data )?.the data analyse 521 leaves ..

Among the students doing a given course, there are four boys enrolled in the ordinary version of the course, six girls enrolled in the ordinary version of the course,and six boys e

A researcher hypothesized that the pulse rates of long-distance athletes differ from those of other athletes. He believed that the runners’ pulses would be slower. He obtained a ra

A country''s national accounts are assumed to look as follows: GDP 1180 VAT and taxes 140 Commodity subsidies 60 Raw material and consumables 530 1. Calculate GVA 2. Calculate t

Evaluate Gross Reproduction Rate: From the data given below compute : i)   General  Fertility  Rate ii)  Specific  Fertility  Rate iii)  Total  Fertility  Rate iv)

Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coi

From the information given, what seems to be the main flaw in each of the following statistical generalisations? (i) Banking industry employees are facing a crisis, if their

Statistical Definition of probability: Ques: (a) (i)  Distinguish Statistical Definition of probability from the Classical Definition.                  (ii) State the A

The file Midterm Data.xls has a tab labeled "Many vs. S&P" which presents historical price data for several assets, a volatility condition (VIDX = 1 if the NYSE volatility is grea

For the following questions we are interested in a comparison of the 16 years education vs. > 16 years. (Recall we did the analysis on the log scale, so these are actual means on t