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CHISQ.DIST.RT

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

Syntax:

CHISQ.DIST.RT(x, deg_freedom)

x is required, and is the value that you want to use to evaluate the distribution.

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

Example:

If x contains 7.815 and deg_freedom contains 3:

CHISQ.DIST.RT(7.815, 3)

returns 0.049993903

This example finds the probability of observing a chi-square value that is greater than or equal to 7.815 with 3 degrees of freedom.

x:

Deg_freedom:

Result:

0.049993903

Application:

Market Research Survey

A market researcher wants to know if there's a relationship between a person's age group and their preferred social media platform. They conduct a survey and collect the following observed data:

Table 1: Observed Frequencies

	Age Group	Platform A	Platform B	Platform C	Total
	A	B	C	D	E
1	18-29	15	35	50	100
2	30-49	40	25	20	85
3	50+	50	10	5	65
4	Total	105	70	75	250

The Chi-Squared Test

The chi-squared test requires us to compare the observed frequencies (the data we collected) with the expected frequencies. The expected frequencies are what we would expect to see if there was no association between age group and social media preference.

The formula for the expected frequency of each cell is:

$E_{ij} = \frac{( Row Total _{i} ) \times ( Column Total _{j} )}{Grand Total}$

Using this formula, we can calculate the expected frequencies for each cell:

Table 2: Expected Frequencies

	Age Group	Platform A	Platform B	Platform C
	A	B	C	D
1	18-29	42	28	30
2	30-49	35.7	23.8	25.5
3	50+	27.3	18.2	19.5

Calculating the Chi-Squared Statistic ( $χ^{2}$ )

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

$χ^{2} = \sum \frac{( O _{ij} - E _{ij} ) ^{2}}{E _{ij}}$

Where:

Oij is the observed frequency
Eij is the expected frequency

Let's calculate the value for each cell and then sum them up:

	Cell	Calculation	Result
	A	B	C
1	(18-29, Platform A)	(15−42)2/42	17.357
2	(18-29, Platform B)	(35−28)2/28	1.75
3	(18-29, Platform C)	(50−30)2/30	13.333
4	(30-49, Platform A)	(40−35.7)2/35.7	0.518
5	(30-49, Platform B)	(25−23.8)2/23.8	0.061
6	(30-49, Platform C)	(20−25.5)2/25.5	1.186
7	(50+, Platform A)	(50−27.3)2/27.3	18.875
8	(50+, Platform B)	(10−18.2)2/18.2	3.695
9	(50+, Platform C)	(5−19.5)2/19.5	10.782
10	Total ( $χ^{2}$ )	Sum of all results	67.557

Our calculated χ2 statistic is 67.557.

Using the CHISQ.DIST.RT Function

Now we can use the CHISQ.DIST.RT function to find the probability of getting a chi-squared statistic as extreme as 68.98, assuming the null hypothesis (that there is no relationship) is true.

The function takes two arguments: x (the chi-squared statistic) and deg_freedom (degrees of freedom).

The degrees of freedom (df) are calculated as:

df=(number of rows−1)×(number of columns−1)

In our example:

Number of rows (Age Groups) = 3
Number of columns (Platforms) = 3

df=(3−1)×(3−1)=2×2=4

The function call would be:

CHISQ.DIST.RT(67.557, 4)

The result of this function is the p-value, which is approximately 7.44x10−14.

Conclusion

The output of CHISQ.DIST.RT is the p-value. The p-value is the probability of observing the data we have, or data that is more extreme, if the null hypothesis is true.

Null Hypothesis (H0): There is no association between a person's age group and their preferred social media platform.
Alternative Hypothesis (Ha): There is a significant association between a person's age group and their preferred social media platform.

The p-value of approximately 7.44x10−14 is extremely small, and much less than the typical significance level of 0.05. Because the p-value is so low, we reject the null hypothesis.

The conclusion is that there is a statistically significant association between a person's age group and their preferred social media platform. The market researcher can be confident that the differences in social media preferences among the age groups are not due to random chance.