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Chi-squared test, ANOVA test and parametric

Explain what a Chi-Squared Test is used for and give an example how you could possibly use this test.

What is an ANOVA test? Create an example where this test could be used.

Compare and contrast parametric and non-parametric tests. What example can you give where the non-parametric test could be used?

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Explain what a Chi-Squared Test is used for and give an example how you could possibly use this test.
The probability density curve of a chi-square distribution is asymmetric curve stretching over the long right tail. The shape of the curve depends on the value of the degrees of freedom.
Chi square test
To test the characteristics of the variables are independent or not
The goodness of fit test
A goodness-of-fit test is an inferential procedure used to determine whether a frequency distribution follows a claimed distribution.
The chi square test can only be used on data that has the following characteristics:
Data is typically attributed (discrete). At the very least, all data must be able to be categorized as being in some category or another).
• The data must be in the form of frequencies
• The frequency data must have a precise numerical value and must be organized into categories or groups.
• The expected frequency in any one cell of the table must be greater than 5.
• The total number of observations must be greater than 20.

Example:
Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, Which test do you prefer? Why? (Data are from Consumer Reports 56, no. 8 [August 1991], p. 519.) Cola

Correct? Regular Cola Diet Cola Row Total
Yes, got it right 7 7 14
No, got it wrong 12 20 32
Col Total 19 27 46
Solution:
Null hypothesis: The correctness of the prediction different for the two types of cola drinkers.
Alternative hypothesis: The correctness of the prediction is not different for the two types of cola drinkers
Level of significance:
Alpha= 0.05
Observed frequency

Observed Frequencies
Correct Regular cola Diet cola Total
Yes 7 7 14
No 12 20 32
Total 19 27 46

Expected frequency
Expected Frequencies
Correct Regular cola Diet cola
Yes 5.7826087 8.2173913
No 13.217391 18.782609

Expected frequencies for contingency table under the assumption of independence
Test Statistics:
Where o ij is the observed frequencies and the e ij is the expected frequencies
Oi Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei
7 5.7826087 1.4820416 0.256293
12 13.217391 1.4820416 0.112128
7 8.2173913 1.4820416 0.180354
20 18.782609 1.4820416 0.078905
Total 0.62768

Critical value:
The critical value of chi-square at (2-1)X(2-1)df at 0.05, the level of significance is 3.841.
Conclusion:
Since the calculated value of chi-square is less than the critical value of chi-square so we accept the null hypothesis and conclude that the correctness of the prediction different for the two types of cola drinkers. ...

Solution Summary

The solution examines chi-squared tests, ANOVA and parametrics. The expert compares and contrasts parametric and non-parametric tests. An example is provided.

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