How To Find Out If Your Customers Are Becoming More or Less Predictable In Their Spending With the Chi-Square

Variance Test in Excel

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What Is the Chi-Square Variance Test?

● The Chi-Square Variance Test Determines Whether the Variance of a Population Has Changed ● Marketers Use the Chi-Square Variance Test To Find Out If the Range of Customer Spending Has Changed, Indicating That Something Has Affected the Customers’ Buying Habits.

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The 5 Steps of the Chi-Square Variance Test in Excel

1) Determine the Required Level of Certainty and Alpha 2) Take a Large (>30), Representative, Random Sample and Measure Its Standard Deviation 3) Calculate the Chi-Square Statistic 4) Calculate the Curve Area Outside the Chi-Square Statistic 5) Analyze Using the Chi-Square Statistic Rule

1) Determine the Required Level of Certainty, and Alpha

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2) Take a Large (n > 30), Random, Representative Sample From a Population of Known Population Standard Deviation (σ).

Calculate the Sample Standard Deviation (s) From This Sample.

3) Calculate the Chi-Square Statistic

4) Calculate the Curve Area Outside the Chi-Square Statistic

There Are 2 Possibilities:

a) Sample Standard Deviation (s) is Greater Than Population Standard Deviation (σ)

b) Sample Standard Deviation (s) is Less Than Population Standard Deviation (σ)

4a) Sample Standard Deviation (s) is Greater Than Population Standard Deviation (σ)

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http://blog.excelmasterseries.com/5% Alpha Region In Outer Right Tail in Yellow

Curve Area Outside Chi-Square Statistic in Red in Outer Left Tail Is Smaller Than the Yellow 5% Alpha Region

4b) Sample Standard Deviation (s) is Less Than Population Standard Deviation (σ)

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http://blog.excelmasterseries.com/5% Alpha Region In Outer Left Tail in Yellow

Curve Area Outside Chi-Square Statistic in Outer Left Tail in Red

Is Larger Than the 5% Yellow Alpha Region

5) Analyze With the Chi-Square Statistic Rule

The Population Standard Deviation (σ) Has Moved In The Direction of the Sample Standard Deviation (s) If The Curve Area Outside the Chi-Square Statistic (the Red Area) is Smaller Than Alpha Region (the Yellow Area)

In Other Words

If the Red Region Fits Inside the Yellow Region, the Population Standard Deviation (σ) Has Moved, Otherwise σ Hasn’t Moved.

Population Standard Deviation Has Shifted to Right (Increased)Because Curve Area Outside Chi-Square Statistic in Red in Outer Right Tail Is Smaller Than the Yellow 5% Alpha Region

Population Standard Deviation Has NOT Shifted to the Left (Decreased)Because Curve Area Outside Chi-Square Statistic in Outer Left Tail

in Red Is Larger Than the 5% Yellow Alpha Region

The Test We Ran

An Internet marketing manager wanted to determine if the number of items purchased on individual orders had become more spread out (order size standard deviation had increased).

She took a representative, random sample of 50 recent orders and measured the sample’s standard deviation in the number of items purchased per order to be 1.9 (n = 50 and s = 1.9).

The standard deviation in number of items purchased per order had remained at 1.6 for a long time (σ = 1.6).

The Internet marketing manager wanted to determine within 95% certainty whether the population order size standard deviation had increased (Alpha = 1 – 95% = 0.05).