# Chi Square

Data Analysis through Statistics

quaLitative = what they’re like or categories

quaNitative = numbers

## Chi Square

Problem = want to know everything about populations

Solution = take sample to represent the population

Purpose = take our sample data and process to see if it is significant or by chance to draw a prediction about the population

## Process:

Step 1: Identify IV and DV

Step 2: Create a null hypothesis (Ho) and an alternative hypothesis (Ha)

• Ho = There is no difference or effect on the DV due to IV.

• Ha = There is a difference or effect on the DV due to IV.

Step 3: Determine the observed (o) and expected (e) values.

Step 4: Calculate X2

Step 5: Degree of freedom (df = n - 1); where n = # of categories in IV

Step 6: Compare X2 to critical value (p)

• 95% confidence = 0.05 p-value

• 99% confidence = 0.01 p-value

Step 7: Draw a conclusion

• If X2 > p then reject Ho. Data suggests there is a difference/effect on…

• If X2 < p then fail to reject Ho. Data suggests there is no difference/effect on…

## Example 1: Does age impact how many times heads is flipped?

Step 1:

• IV = age

• DV = # of heads flipped

Step 2:

• Ho = There is no effect on the # of heads flipped due to age.

• Ha = There is an effect on the # of heads flipped due to age.

Step 3:

 Observed Data (o) Age # Heads # Tails Total 14 3 7 10 not 14 2 1 3

Expected Date (e)

• 50%/5 → 1.5

Step 4:

X2 = (3 - 5)2 / 5 +(2 - 1.5)2 / 1.5

X2 = 0.8 + 0.17

X2 = 0.97

Step 5: df - 1

Step 6:

95% confidence

99% confidence

X2 = 0.97

X2 = 0.97

p = 3.84

p = 6.63

Step 7: X2 < p

Fail to reject null null hypothesis Ho. Our data suggests there is no effect on head flipping due to age.