We can only predict probabilistically

E.g., People high on I.Q. likely to do well in school

Predictions with much greater certainty

E.g., Physical laws, such as Newton’s 

Descriptive statistics tell us where people stand on a variable:

65% of this class supports the president

Inferential statistics allow inferences about relations among variables:

Democrats are more likely to support the president than republicans

Observation: A subject’s standing on a variable

Distribution: A collection of observations showing the frequency of each possible value

Statistic: Number that summarizes some property of a distribution

Central tendency: Mean, median, mode

Dispersion: Standard deviation, variance

Inference: Drawing conclusions from statistic to entire population—which is the goal of science

Statistical test: Convert observations to a statistic that has known distribution, e.g., t or z

1. Decide on the sort of inference you wish to make, e.g., comparison of two means

2. Determine which statistical test is appropriate, e.g., independent group t-test

3. Collect data, e.g., observations for subjects assigned to two groups

4. Compute descriptive statistics, e.g., means and standard deviations.

5. Compute t statistic from basic quantities, means and standard deviations.

6. Compare your value to t to the theoretical t distribution, i.e., see if the value exceeds the critical value.

7. This gives you the probability of finding your value of t by chance.

8. Use the .05 rule of thumb to make your inference about whether the means are the same or different in the population to which you wish to generalize.

Measurement: The assigning of numbers to characteristics of things or quantifying variables

Nominal: Player numbers on a team, race

Ordinal: Order of finishers in a beauty contest

Interval: Fahrenheit temperature

Ratio: Kelvin temperature, length

Reliability: Consistency in measurement of a constant property

Internal consistency: Similar assessment across equivalent forms of assessment, e.g., same weight on different bathroom scales.

Coefficient alpha: Measure of consistency

Test-retest: Similar assessment across time, e.g., same weight on repeated trials on one scale.

Classical test theory: Observed = True + Error

Validity: Interpretation of a measure, e.g., marks on an answer sheet represent intelligence, which is the ability to perform certain types of cognitive, problem solving tasks.