 # Descriptive Statistics

## Presentation on theme: "Descriptive Statistics"— Presentation transcript:

Chapter 13: Understanding Results—Statistical Inferences Chapter 14: Generalizing Results

Descriptive Statistics
Used to present data in summary form.

Inferential statistics
Used to determine whether an independent variable had a reliable effect on a dependent variable Replication: repeating experiment to try to get the same results second time Groups must be equivalent Achieved by experimental control and/or randomization

Random error Variation due to differences among subjects within each group Responsible for some difference in the means

Research and Null Hypotheses
Research hypothesis H1: Population means are not equal Null hypothesis HO: Population means are equal The assumption that the independent variable has had no effect

Statistical significance
The probability the difference in sample means is due to error Statistically significant outcome: has a small likelihood of occurring if the null hypothesis is true

Level of significance Probability of error chosen by researcher
Usually set at .05 or less Alpha level indicated by Greek letter α Noted as p  .05; p  .01, etc p: probability

Null-Hypothesis Significance Testing
Null-hypothesis significance testing assesses the probability of obtaining a given difference between sample means t-test: commonly used significance test

The t-test Interpreting the t-test value:
If probability is high (over .05), fail to reject the null hypothesis If probability is low (.05 or less), reject the null hypothesis

Do we have a winner? Data Analysis for an Experiment Comparing Means
Round Chopsticks? Did the independent variable (shape of chopsticks) have an effect on the dependent variable (number of pasta pieces transferred)? Square Chopsticks?

Null Hypothesis Significance Testing: The t Test
One-tailed versus two-tailed tests One-tailed test = research hypothesis specified a direction of difference between the groups Two-tailed test = research hypothesis did not predict direction of difference

Chopsticks Challenge Hypothesis #1: Performance when using round chopsticks is different (better or worse) than performance when using square chopsticks (two-tailed) = .19 Hypothesis #2: Performance when using round chopsticks is better than performance when using square chopsticks (one-tailed) = .09

Do we accept the null hypothesis if the independent variable did not have an effect?
Instead we fail to reject the null hypothesis.

Type I and Type II Errors
Decision to reject the null hypothesis is based on probabilities rather than certainties. Decision may or may not be correct

Type I error Occurs when the null hypothesis is rejected, but the null hypothesis is true

Type II error Occurs when the null hypothesis is false, but it is not rejected

Experimental sensitivity
Occurs when an experiment detects an effect of the independent variable (when, in fact, the independent variable truly has an effect)

Experimental power Occurs when a statistical test allows researchers to correctly reject the null hypothesis Determined by 3 factors: Size of the effect Sample size Level of statistical significance