Chi-Square Goodness of Fit Test

A recent study in a national business journal asked consumers the following question: "In general, how would you rate the level of service provided by your supermarket?" A district manager of Piggly Wiggly supermarkets asked the same question about Piggly Wiggly supermarkets in her district. She took a random sample of 700 Piggly Wiggly shoppers. Research Question: Do the results of the Piggly Wiggly survey contradict the national study using a 5 percent significance level?The national study found that 30% of the respondents rated their supermarket as Excellent, 30% Good, 30% Fair, and 10% Poor. Conduct a Chi-Square Goodness of Fit test to determine whether the observations from the Piggly Wiggly study "fit" the national study.

# 1: Test Set-Up

This table shows the result of the Piggly Wiggly survey along with consumers' ratings of supermarkets from the national study. Find the Expected Frequencies. Note: Expected frequencies should be rounded off to a whole number. The total for the Expected Frequencies should equal the total of the Observed Frequencies.

Find the Expected Frequencies (E) based on the ratings from the National Study.

Rating	National Study	O	E*
Excellent	30%	190
Good	30%	205
Fair	30%	205
Poor	10%	100
Total	100%	700

*InExcel, format numbers as Numbers with 0 decimal places.

# 2: Select the Significance Level,

A 5 percent significance level has been selected. What is the critical value of Chi-Square? You can use either the Chi-Square Critical Values Table or Microsoft Excel. Report the degrees of freedom.

Place your answers in the boxes.

The Critical Value of Chi-Square =
Degrees of Freedom =

# 3: State the Null and Alternate Hypotheses

H0:
H1:

Model your answer on the examples shown in Clear-Sighted Statistics.Failure to do so will result in a major grading penalty.

# 4: Compose the Decision Rule(If your answer is longer than a short declarative sentence it is wrong.)

Model your answer on the examples shown in Clear-Sighted Statistics.Failure to do so will result in a major grading penalty.

Here is a graphic representation of the Chi-Square curve with the rejection region with 3 degrees of freedom.

# 5: Calculate the Test Statistic, p-value, Effect Size, and Statistical Power. Show your work.

s

Chi-Square Goodness of Fit Summary
Chi-Square =
p-value =
Effect Size =
Interpretation of ES:

Show your work here:

Calculating post hoc Statistical Power: use G*Power if you are using a Windows or Macintosh computer. If you are using a Chromebook or Tablet, use Statistical Kingdom's online tool. Do not use both tools.

Statistical Power: G*Power
Power =
P(Type II) =

Statistical Power: Statistical Kingdom
Power =
P(Type II) =

G*Power (Requires a Windows or Macintosh computer)

Test family:² tests

Statistical test: Generic² test

Type of power analysis: Post hoc: Compute power....

Input parameters:

1) Noncentrality parameter: Enter the calculated value of Chi-Square

2) err prob: Enter the selected significance level

3) Df: enter the degrees of freedom

Click on Calculate.

Statistics Kingdom: Statistical Power Calculators for Chi-Square Tests (Requires an internet connection(https://www.statskingdom.com/34test_power_chi2.html). Use these settings:

Statistics Kingdom Chi-Square Statistical Power Calculator
Test:	Enter Goodness of fit
Significance level ():	Set to the selected significance level
Effect:	Select Small, Medium, or Large
Categories:	Enter the number of categories
Digits:	Select number of digits for statistical power
Sample size: (n)	Enter total sample size
Effect Size (w):	Enter Effect Size

Note: The estimates of Statistical Power from G*Power and Statistical Kingdom Power will vary slightly.

# 6: Decide and Report:Your report should address what your decision regarding the Null Hypothesis means in the context of the research question, whether there is sufficient Statistical Power, and whether the results have practical significance.

Rating	National Study	O	E	(O-E)2/E	Formula		Effect Size, (Phi) or Cramer's V
Excellent	30%	190			=((C2-D2)^2)/D2		Threshold	Interpretation
Good	30%	205			=((C3-D3)^2)/D3		0.00 < 0.10	Negligible
Fair	30%	205			=((C4-D4)^2)/D4		0.10 < 0.20	Weak
Poor	10%	100			=((C5-D5)^2)/D5		0.20 < 0.40	Moderate
Total	100%	700	0	0.000	= Chi-Square: =SUM(E2:E5)		0.40 < 0.60	Relatively Strong
	5%	User Selected	CV		Enter formula		0.60 < 0.80	Strong
df	3	=COUNT(B2:B5)-1	p-Value	1.000	=CHISQ.DIST.RT(E6,B8)		0.80 to 1.00	Very Strong
			Effect Size,		=SQRT(E6/C6)
			Interpretation of Effect Size	Negligible	Formula: See A11
=IF(E9<0.1,I3,IF(E9<0.2,I4,IF(E9<0.4,I5,IF(E9<0.6,I6,IF(E9<0.8,I7,I8)))))
Critical Value of Chi-Square:
Use Chi-Square Table, or Excel: =CHISQ.INV.RT(,df)
Rating	National Study	Piggly Wiggly Study
Excellent	30%	27%	=C2/$C$6
Good	30%	29%	=C3/$C$6
Fair	30%	29%	=C4/$C$6
Poor	10%	14%	=C5/$C$6
Total	100%	100%	=SUM(C18:C21)