How to Calculate P Vaule: Chi Square Test of Independence — Academic Writing for Students
Welcome back friends! In this post, I’ll educate you for how to calculate the P value with the help of Chi Square test of independence.
So, if you are looking forward to find the chi square P value or learn how to read the P value table, then read this detailed post.
In this report, a deep analysis has been provided on the basis of Ipsos poll results and the contingency table provided by the poll. In April 2006, a survey was being done on 1,005 adults to know their views whether the U.S. tax code is fair or unfair. Almost 60% of all people were agreed that the code is unfair.
Chi-square test based on the contingency table provided
Below is the contingency table provided from the Ipsos poll survey result: -
We need following values in order to apply the Chi-square test on the survey report: -
X1 = number of successes in group 1
X2 = number of successes in group 2
n1 − X1 = number of failures in group 1
n2 − X2 = number of failures in group 2
X = X1 + X2, the total number of successes
n − X = (n1 − X1) + (n2 − X2), the total number of failures
n1 = sample size in group 1
n2 = sample size in group 2
n = n1 + n2 = total sample size
If we compare the contingency table, then the respective values would be: -
X1 = 225, X2 = 180, n1 — X1 = 280, n2 — X2 = 320, X = 405, n — X = 600, n1 = 505, n2 = 500, n = 1005
Now, the formula for estimate overall proportion is as follow,
Putting respective values we get P = 405/1005 = 0.403(Daniel, 1990) (This is the answer of the B. part of the assignment)
So, the P value i.e. the expected overall proportion of people including the people having income group of more and less than $50,000 who accept that the U.S. Tax code is fair is around 0.403. To find the value of χ 2 , the following formula is being used,
Where fo and fe are the observed frequency and expected frequency respectively. fe is being calculated by multiplying P by the respective value of n, as follows(Conover, 2000),
For fair and <$50,000 = 0.403×505 = 203.5
For fair and >$50,000 = 0.403×500 = 201.5
For unfair and <$50,000 = (1- 0.403)x505 = 301.5
For unfair and >$50,000 = (1–0.403)x500 = 298.5
Depending upon the observed and expected frequencies, we got a new table as shown below: -
Below is the computation of χ 2 as per the calculated values of observed and expected frequencies,
Now according to the null hypothesis, the population proportions of fair and unfair people in both income groups are equal when,
And the hypothesis is against the proportions in the following condition,
Now, the value of χ 2 in our case is around 7.644. When we take α = 0.05and when we value that comes in the 1 degree of freedom row, corresponding to the value of 0.05, then it comes around 3.841, which is smaller than 7.644. So, we conclude that there is no significance in the proportions of people who are agreed or disagreed to the U.S. Tax code in both less than and more than $50,000 income group (Dixon, 1983).
So, friends! This was the detailed post for how to calculate the P value with the help of Chi Square test of independence.
Works Cited
Conover, W. J. (2000). Practical Nonparametric Statistics. In Wiley 3rd edition.
Daniel, W. W. (1990). Applied Nonparametric Statistics. In PWS Kent 2nd edition.
Dixon, W. J. (1983). Introduction to. In McGraw-Hill 4th edition.
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Originally published at https://academicwritingforstudents.com on November 18, 2020.