1 Chapter 11: Bivariate Statistics and Statistical Inference “Figures don’t lie, but liars figure.” Key Concepts: Statistical Inference

2 Making Inferences  We calculate the odds…  Crossing a busy street and not getting hit?  The movie will be good?  A child will be safe if left with parents in which there was previous child abuse?  Probability (the odds, chances of)  The chances of an event based on the ratio of favorable outcomes to total outcomes.  Getting heads on a coin flip 1/2 =.5 (50%)  Getting an Ace from cards: 4/52 = 7.7%

3 What are the odds (con’t.)  Average height: male – 5’9”; female 5’5”  Which groups are all male and all female?  Is the sample representative of the population?  How certain are you of your answer?  Could all 3 groups be the same sex? Group 1: 5’8, 5’6, 5’4, 5’2, 5’4, 5’5, 5’6, 5’1 Group 2: 5’9, 6’1, 5’8, 5’7, 5’8, 5’9, 6’2, 5’6 Group 3: 5’6, 5’8, 6’0, 5’2, 5’7, 5’5, 5’7, 5’6

4 Statistical Inference  Variation – differences in behavior, attitudes, values, characteristics, etc.  There is variation in the population  e.g., some people like chocolate, others like vanilla.  A sample is picked from the population.  We study the sample to make inferences about the population.  To do so, the sample must reflect the population in the characteristics under study.  If 30% prefer chocolate in the sample, we’d like to conclude that 30% prefer chocolate in the population.

5 Statistical Inference (con’t.)  BUT, sometimes the sample does not reflect the population – the extent to which it doesn’t is SAMPLE ERROR.  We can calculate the chances that the relationship between variables in the sample is due to sample error.  Influences on sample error  Luck – someone wins the lottery even if the odds are 40 million to 1.  Sample size – smaller samples will have more chances of error.  Homogeneity – less variation in the population yields smaller sample error.

6 Hypothesis Testing  Testing the relationship between two or more variables.  Statistical tests are used to find the probability that the relationship between variables is due to sampling error or to chance. TypeExample Null hypothesis (H o ) – No relationshipThere is no relationship between income and mental health. Two-tailed hypothesis (H 1 ) – There is a relationship There is a relationship between income and mental health. One-tailed hypothesis (H 1 ) – Directional relationship The greater the income the greater the mental health.

7 Statistical Inference (con.)  p-value  The probability that a relationship between variables or a mean difference found in a sample is a result of sample error.  p =.05 means there is a 5% chance that the relationship found in the sample is a result of sample error.  p =.05 means there is a 95% that the relationship is NOT due to sample error, and actually reflects the differences in the population.  Rejection level: If the p value is <.05, we reject the null hypothesis and accept the alternative hypothesis. (Why.05? – Convention).