Inputs to Get P Value

How to Get the P-Value in a Chi-Square Test

The P-value in a Chi-Square test tells you the probability of observing your results (or something more extreme) if the null hypothesis is true. A smaller P-value suggests the observed differences are unlikely due to chance.

Steps to Calculate the P-Value

Calculate the Chi-Square Statistic (( \chi^2 )):

Use the formula:
```
χ² = Σ [(O - E)² / E]
```
where:
- ( O ): Observed value.
- ( E ): Expected value.
Determine Degrees of Freedom (df):

For one variable:
```
df = (number of categories - 1)
```
For contingency tables:
```
df = (rows - 1) × (columns - 1)
```
Use Software or a Chi-Square Table to Find the P-Value:
- Input ( \chi^2 ) and df into statistical software or look up the P-value in a Chi-Square table.
- Compare the P-value to the significance level (( \alpha )).

Example 1: Red and Blue Candies

Observed Counts (O): Red = 40, Blue = 20.
Expected Counts (E): Red = 30, Blue = 30.

Calculate ( \chi^2 ):

χ² = [(40 - 30)² / 30] + [(20 - 30)² / 30]
   = [10² / 30] + [(-10)² / 30]
   = (100 / 30) + (100 / 30)
   = 6.67

Determine df:

df = (number of categories - 1)
   = 2 - 1
   = 1

Use software to calculate the P-value:
- For ( \chi^2 = 6.67 ) and ( df = 1 ), ( P = 0.0098 ).
Compare P to ( \alpha ) (e.g., 0.05):
```
P = 0.0098 < 0.05
```
Conclusion: The result is statistically significant.

Example 2: Contingency Table

Testing candy preference by age group:

	Red Candies	Blue Candies	Total
Kids	50	30	80
Adults	20	40	60
Total	70	70	140

Calculate expected values for each cell:

Expected = (row total × column total) / grand total

Example for Kids-Red:

Expected = (80 × 70) / 140 = 40

Compute ( \chi^2 ):

χ² = Σ [(O - E)² / E]
   = [(50 - 40)² / 40] + [(30 - 40)² / 40] + ...
   = 2.5