Chi square test for more than two rows, Applied Statistics

Assignment Help:

 

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.


Related Discussions:- Chi square test for more than two rows

Show a simple linear regression analysis, In the early 1990s researchers at...

In the early 1990s researchers at The Ohio State University studied consumer ratings of six fast-food restaurants: Borden Burger, Hardee's, Burger King, McDonald's, Wendy's, and Wh

The weekly treatment , A researcher is interested in comparing the effectiv...

A researcher is interested in comparing the effectiveness of three different parts of therapy for anger problems. 8 participants are randomly assigned to 3 treatment conditions: Co

..National Account- Descriptive Statistics, A country''s national accounts ...

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

Significance of correlation, Significance of Correlation The study of c...

Significance of Correlation The study of correlation is of immense use in practical life. Correlation analysis contributes to the understanding of economic behavior, aids in lo

Calculate mean and standard deviation, Select and generate your assignment ...

Select and generate your assignment portfolio. The S&P/ASX 200 index is comprised of several sub-indices, including the following: 0) XPJ: The S&P/ASX 200 A-REIT Index 1) XDJ

Large-sample and small-sample simulations, Show that when h = h* for the h...

Show that when h = h* for the histogram, the contribution to AMISE of the IV and ISB terms is asymptotically in the ratio 2:1. Compare the sensitivity of the AMISE(ch) in Equa

Find the conditional distribution of turning diameter, 1. Assume the random...

1. Assume the random vector (Trunk Space, Length, Turning diameter) of Japanese car is normally distributed and the unbiased estimators for its mean and variance are the truth. For

Mean absolute deviation, Mean Absolute Deviation To avoid the problem o...

Mean Absolute Deviation To avoid the problem of positive and negative deviations canceling out each other, we can use the Mean Absolute Deviation which is given by

Enumerate the set, Grid is the set of pairs {1, 2, 3, 4} x {1, 2, 3, 4}. ...

Grid is the set of pairs {1, 2, 3, 4} x {1, 2, 3, 4}. Image is the power set of Grid. An element of Image is a subset of Grid and can be represented by a diagram on a 4 by 4

Chi-square analysis, Chi-square analysis can be used with both Goodness-of-...

Chi-square analysis can be used with both Goodness-of-Fit Tests and with Tests for Independence. There are specific instances when each test should be used based on the information

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd