CHISQ.INV.RT

Calculates the inverse of the right-tailed probability of the chi-squared distribution.

Syntax:

CHISQ.INV.RT(probability, deg_freedom)

probability is required, and is the right-tailed probability associated with the chi-squared distribution.

deg_freedom is required, and is the degrees of freedom of the distribution.

Example:

If probability contains 0.05 and deg_freedom contains 3:

CHISQ.INV.RT(0.05, 3)

returns 7.814727903

This example finds the chi-square value that corresponds to a right-tailed probability of 0.05 in the chi-squared distribution with 3 degrees of freedom.

Probability:

Deg_freedom:

Result:

7.814727903

Application:

Testing for Independence

Let's imagine a company that sells three different products: Product A, Product B, and Product C. They want to determine if there is a relationship between the product a customer buys and their gender (male or female).

Null Hypothesis (H0): Product choice is independent of gender.

Alternative Hypothesis (Ha): Product choice is not independent of gender.

The company surveys 180 customers and collects the following observed data in a contingency table:

Table 1: Observed Frequencies

		Product A	Product B	Product C	Total
	A	B	C	D	E
1	Male	30	35	40	105
2	Female	25	30	20	75
3	Total	55	65	60	180

To perform the chi-squared test for independence, we first calculate the expected frequencies for each cell, assuming the null hypothesis is true (i.e., that gender and product choice are independent). The formula for an expected frequency is:

$E_{ij} = \frac{( row total for i ) \times ( column total for j )}{grand total}$

i = Gender

j = Product A, Product B or Product C

So, for i -> Male, and j -> Product A, Eij = 32.08

Table 2: Expected Frequencies

		Product A	Product B	Product C	Total
	A	B	C	D	E
1	Male	32.08	37.92	35	105
2	Female	22.92	27.08	25	75
3	Total	55	65	60	180

Next, we calculate the chi-squared test statistic using the formula:

$χ^{2} = \sum \frac{( Observed - Expected ) ^{2}}{Expected}$

This calculation results in a test statistic of approximately 2.58.

Now, we need to find the critical value to compare our test statistic against. We'll use the CHISQ.INV.RT function for this.

Significance Level (Probability): We choose a standard alpha level of 0.05.
Degrees of Freedom: The degrees of freedom are calculated as (r−1)(c−1). In our case, this is (2−1)(3−1)=1 x 2=2.

Using the CHISQ.INV.RT function in a spreadsheet or statistical software:

CHISQ.INV.RT(0.05, 2)

This function will return the critical value, which is approximately 5.99.

Conclusion

Calculated Chi-Squared Statistic: 2.58
Critical Value (from CHISQ.INV.RT): 5.99

Since our calculated chi-squared test statistic (2.58) is less than the critical value (5.99), we fail to reject the null hypothesis. There is not enough statistically significant evidence to conclude that product choice is dependent on gender.

Result for $χ^{2}$ :

2.58

Result for CHISQ.INV.RT(0.05, 2):

5.99