Test of Proportions

test of proportion

assess whether a sample from a population represents the true proportion from the entire population

• how does observed data compare to expected data

Chi Square Test Assumptions

• Independent groups
• Nominal level of measurement
• Sample size sufficiently large to detect meaningful difference (data NOT sparse)

• value of the cells in expected count should be >5 in at least 80% of cells

• no cell should have expected count <1

Chi-Square Test

• Nonparametric statistic used to determine if a distribution of observed frequencies differs from theoretically expected frequencies.
• Asks: Is the data as expected?
• Based off chi-square distribution
• Degrees of freedom (df)

chi square critical value

3.84

chi square OR example

OR = 3.6 > 1.0; the rate of participants being responsive is 3.6 times higher with the new medication than the standard treatment only

McNemar assumptions

• groups are paired/matched

• 2 groups of data

• nominal level of measurement

• • Sample size sufficiently large to detect meaningful difference (data NOT sparse)

  • value of the cells in expected count should be >5 in at least 80% of cells

  • no cell should have expected count <1

mcnemar examples

. To look at a subject's responses to a question and see how many subjects answered correctly or incorrectly before and after exposure to specific information
2. To examine the effects of a particular treatment program by looking at the presence or absence of an outcome result, such as pain, before and after treatment

df

= (# rows - 1) x (# columns - 1)