1. More inferential statistics

3. Chi square tests compare observed frequency distributions, either to theoretical expectations or to other observed frequency distributions. Differences Between Distributions

4. E.g. The F2 generation of a cross between a round pea and a wrinkled pea produced 72 round individuals and 20 wrinkled individuals. Does this differ from the expected 3:1 round:wrinkled ratio of a simple dominant trait? Smooth Frequency Wrinkled E E HBI: Chi-Square One Sample Test (goodness of fit) Excel: Chitest – under Function Key – Statistical

5. E.g. 67 out of 100 seeds placed in plain water germinated while 36 out of 100 seeds placed in “acid rain” water germinated. Is there a difference in the germination rate? PlainAcidPlain Proportion Germination Acid Proportion Germination Null Hypothesis Alternative Hypothesis Differences Between Distributions HBI: Chi-Square Two or More Sample Test (independence) Excel: Chitest – under Function key - Statistical

6. Differences Between Distributions Are there differences in the numbers of male and female Cardinals at different times of the year? SexSpringSummerFallWinter Male1631357143 Female86774038 This is a special case for a Chi-Square Test known as a Contingency Table (as was the previous example)