4 - Qualitative Data

Question 1

How do we determine the significance of the difference between observed and expected results?

Answer 1

• Use chi-square
• x^2 = sum of (O - E)^2 / E
• O = observed; E = expected
• Chi-square statistic has positive values only, therefore only one parameter (degrees of freedom) is needed to specify any chi-squared distribution

Question 2

What is degrees of freedom?

Answer 2

Number of categories - 1

Question 3

What is used for a 1 df chi-square?

Answer 3

• A continuity correction (Yate’s correction) is recommended; not required when df > 1
• x^2 = sum of ([O - E] - 1/2)^2 / E

Question 4

What can be concluded if calculated chi square doesn’t exceed critical chi-square?

Answer 4

The difference between observed and expected values are small and are due to chance alone

Question 5

What are some assumptions for chi-square?

Answer 5

• Random sampling not essential for calculation, but may obviously impact the interpretation (bias)
• Observations must be independent
• Categories must be mutually exclusive
• Distribution of chi-square depends on # of tx being compared; this dependency is quantified in a df parameter v (equal to # of rows in the table minus 1, times # of columns in the table minus 1)
• For v = 1 contingency tables, computing chi-square using standard formula leads to p-values smaller than they ought to be (results are biased towards Ha) so Yate’s correction is used

Question 6

How do you calculate expected frequency?

Answer 6

(row total * column total) / grand total

Question 7

What conclusion can be made when calculated chi-square exceeds critical chi-square?

Answer 7

Reject null hypothesis and conclude there is an association between drug therapy and thrombus formation at alpha = 0.05