Evaluating Hypotheses

Chapter 9

Homework: 1-9

Descriptive vs. Inferential Statistics

Descriptive quantitative descriptions of

characteristics ~

Inferential Statistics

Making conclusions (inferences) about parameters e.g., X confidence intervals: infer lies

within interval also quantitative ~

Hypothesis Testing

Most widely used inferential statistics Hypothesis

testable assumption or inference about a parameter or distribution

should conclusion (inference) be accepted?

final result a decision: YES or NO qualitative not quantitative ~

Hypothesis Testing

Example: IQ scores = 100, = 15 Take random sample of students

n = 10 Hypothesis:

sample is consistent with population with above parameters

sample is the same as population ~

Evaluating Hypotheses

Proving / Disproving Hypotheses

Logic of science built on disproving easier than proving but ultimately want to prove

State 2 mutually exclusive hypotheses if one is true, other cannot be true ~

Hypothesis Evaluation

Null Hypothesis: H0

there is no difference between groups Alternative Hypothesis: H1

also called “experimental” hypothesis

there is a difference between groups ~

Steps in Hypothesis Evaluation

1. State null & alternative hypothesesH0 and H1

2. Set criterion for rejecting H0

level of significance: 3. collect sample; compute sample

statistic & test statistic4. Interpret results

is outcome statistically significant? ~

Hypothesis Evaluation

Example: IQ and electric fields question: Does living near power lines affect IQ

of children? H0 : there is no difference

Living near power lines does not alter IQ. = 100

H1 : Living near power lines does alter IQ. 100 ~

Hypothesis Evaluation

Outcome of study reject or “accept” null hypothesis

Reject Ho accept as H1 true

“Accepting” null hypothesis difficult or impossible to “prove” Ho

actually: fail to reject Ho i.e., data are inconclusive ~

Evaluating Ho and H1

Hypotheses about population parameters

Test statistic especially designed to test Ho

Procedure depends on… particular test statistic used directionality of hypotheses level of significance ~

Directionality & Hypotheses

Directionality affects critical values used Nondirectional

two-tailed test Ho : = 100; H1 : 100 change could be either direction Do not know what effect will be

may increase or decrease IQ ~

Directionality & Hypotheses

Directional one tailed test Have prior evidence that suggests

direction of effect predict that effect will be larger

or smaller, but only 1 Ho: < 100 H1: > 100 ~

Errors

“Accept” or reject Ho

only probability we made correct decision

also probability made wrong decision Type I error

incorrectly rejecting Ho e.g., may think a new antidepressant is

effective, when it is NOT ~

Errors

Type II error incorrectly “accepting” Ho e.g., may think a new antidepressant is

not effective, when it really is Do not know if we make error

because we do not know true population parameters ~

Actual state of nature

H0 is true H0 is false

Decision

Accept H0

Reject H0

Correct

CorrectType I Error

Type II Error

Errors

Level of Significance ()

Probability of making Type I error complement of level of confidence

.95 + .05 = 1 = .05

conduct experiment 100 times 5 times will make Type I error

Want probability of Type I error small ~

Statistical Significance

If reject H0

Outcome is “statistically significant” difference between groups is ...

greater than expected by chance alone due to sampling, etc.

Does NOT say it is meaningful ~

Statistical Power

Power probability of correctly rejecting H0

= probability of Type II error complement of power *power = 1 - ~

Practical Significance

Degree to which result is important result can be statistically significant but not important in real world

Effect size measure of magnitude of result difference between means of 2 groups e.g., IQ: 1 point small effect, 15 large ~

Procedure for Evaluating Hypotheses

Experiment Draw random sample compute statistic determine if reasonably comes from

populationIf no, reject H0

Use test statistic to make decision 3 important distributions

variable, sample statistic, test statistic~

Test Statistic distribution of test statistic

has known probabilities General form

test statistic = sample statistic - population parameterstandard error of sample

statistic

difference actually obtained: X - divided by difference by chance alone ~

Steps in Hypothesis Evaluation

1. State null & alternative hypothesesH0 and H1

2. Set criterion for rejecting H0

level of significance:

3. collect sample; compute sample statistic & test statistic

4. Interpret results is outcome statistically significant? *If so, is it practically significant? ~