1. Grade Curve A = 85+D = 50-62 B = 77-84F = 49 and below C = 63-76

2. Sampling Distributions & Hypothesis Testing

3. Sampling Distributions What we know, so far What we know, so far Why Statistics is important Why Statistics is important Basic means to describe a set of data Basic means to describe a set of data (i.e. Descriptive Statistics): Measures of Central Tendency Measures of Central Tendency Measures of Variability Measures of Variability Graphs Graphs Z-Scores Z-Scores

4. Sampling Distributions Where we’re going Where we’re going Statistics designed to help us infer characteristics of a population from the characteristics of our sample (i.e. Inferential Statistics) OR comparing two samples Statistics designed to help us infer characteristics of a population from the characteristics of our sample (i.e. Inferential Statistics) OR comparing two samples How do these statistics relate to the research questions that we’re asking? How do these statistics relate to the research questions that we’re asking? How can we phrase these questions so that our statistics will answer them? How can we phrase these questions so that our statistics will answer them?

5. Sampling Distributions In our experiment, we want to say that change due to our IV exceeds variability naturally occurring in the sample, or that effect of IV was “due to chance” In our experiment, we want to say that change due to our IV exceeds variability naturally occurring in the sample, or that effect of IV was “due to chance” Every sample contains variability due to individual differences on whatever is being measured Every sample contains variability due to individual differences on whatever is being measured I.e. in a sample of people with AIDS, some will be healthier than others based on their T-cell count, degree of overall health before contracting AIDS, and how they’ve taken care of themselves after contracting it I.e. in a sample of people with AIDS, some will be healthier than others based on their T-cell count, degree of overall health before contracting AIDS, and how they’ve taken care of themselves after contracting it

6. Sampling Distributions

7. We are conducting an experimental treatment for people suffering from AIDS to try to improve their quality of life (QOL) We are conducting an experimental treatment for people suffering from AIDS to try to improve their quality of life (QOL) What is the Independent Variable? The Dependent Variable? What is the Independent Variable? The Dependent Variable? We compare the QOL of our subjects for those receiving the Tx to those not receiving it We compare the QOL of our subjects for those receiving the Tx to those not receiving it

8. Sampling Distributions Our Tx is successful to the extent that our treated S’s QOL exceeds the healthiest of our untreated S’s Our Tx is successful to the extent that our treated S’s QOL exceeds the healthiest of our untreated S’s I.e. We want to say our subjects went from being “sick”, to being “well”, not just from being more “sick” to less “sick” I.e. We want to say our subjects went from being “sick”, to being “well”, not just from being more “sick” to less “sick” We want to say that the subjects in our two groups are qualitatively, not merely quantitatively, different We want to say that the subjects in our two groups are qualitatively, not merely quantitatively, different

9. Sampling Distributions Sampling Error – variability of a statistic from sample to sample due to chance Sampling Error – variability of a statistic from sample to sample due to chance Can potentially bias our results if it isn’t equivalent across treatment and control groups Can potentially bias our results if it isn’t equivalent across treatment and control groups I.e. if only the subjects in the Tx group for our hypothetical study were convinced as to the benefits of our Tx (sampling error), because they knew the PI personally beforehand, they may be more motivated than most other people and do better (the effect of sampling error) I.e. if only the subjects in the Tx group for our hypothetical study were convinced as to the benefits of our Tx (sampling error), because they knew the PI personally beforehand, they may be more motivated than most other people and do better (the effect of sampling error) Random Assignment reduces sampling error by equating groups on these chance factors Random Assignment reduces sampling error by equating groups on these chance factors

10. Sampling Distributions The essential question in any experiment is: The essential question in any experiment is: Are the changes in subject performance due to the effect of our independent variable, or to sampling error? Are the changes in subject performance due to the effect of our independent variable, or to sampling error? I.e. Are the improvement in the treated group in our AIDS intervention due to our intervention, or to unequal sampling error across our groups? I.e. Are the improvement in the treated group in our AIDS intervention due to our intervention, or to unequal sampling error across our groups? All statistics for the rest of this course (i.e. t- tests, ANOVA, etc.) are essentially proportions of variance due to the effect of our IV versus variance due to some kind of sampling error All statistics for the rest of this course (i.e. t- tests, ANOVA, etc.) are essentially proportions of variance due to the effect of our IV versus variance due to some kind of sampling error

11. Sampling Distributions You can obtain many possible samples of any given population You can obtain many possible samples of any given population Those sample will tend to differ due to chance Those sample will tend to differ due to chance Therefore you can create a distribution of these samples in the same way you create a distribution of individuals that differ on a given variable Therefore you can create a distribution of these samples in the same way you create a distribution of individuals that differ on a given variable This distribution of every possible sample from a population is called the sampling distribution This distribution of every possible sample from a population is called the sampling distribution Like the population of samples Like the population of samples

12. Sampling Distributions Just as you can determine the probability of obtaining a given score from a distribution of scores, you can find the p(sample) from its sampling distribution Just as you can determine the probability of obtaining a given score from a distribution of scores, you can find the p(sample) from its sampling distribution sample of individual scores:standard deviation::sampling distribution:standard error sample of individual scores:standard deviation::sampling distribution:standard error

13. Sampling Distributions There are many ways to characterize a sample in a sampling distribution (i.e. mean, median, mode, z-scores), but the mean is the most common There are many ways to characterize a sample in a sampling distribution (i.e. mean, median, mode, z-scores), but the mean is the most common Sampling Distribution of the Mean Sampling Distribution of the Mean Sampling Distribution of the Median Sampling Distribution of the Median Sampling Distribution of the Mode Sampling Distribution of the Mode

14. Sampling Distributions Population: 1, 2, 3 Population: 1, 2, 3 SampleMean 1, 1 1.0 1, 2 1.5 1, 3 2.0 2, 1 1.5 2, 2 2.0 2, 3 2.5 3, 1 2.0 3, 2 2.0 3, 3 3.0

15. Sampling Distributions Sampling Distribution of the Mean Sampling Distribution of the Mean