# PSYC 241 Lecture Notes - Lecture 8: Standard Deviation, Sample Size Determination, Statistical SignificancePremium

5 pages88 viewsSpring 2017

Department

PsychologyCourse Code

PSYC 241Professor

Kristen LeightonLecture

8This

**preview**shows page 1. to view the full**5 pages of the document.**Lesson 8: Introduction to Hypothesis Testing

● Hypothesis Testing

○ Goal: rule out chance (sampling error) as a plausible explanation for results

○ Hypothesis testing helps determine whether a treatment has an effect

○ To evaluate research in which:

■ 1. A sample is selected from the population

■ 2. The treatment is administered to the sample

■ 3. The people in the sample are measured after treatment

○ If people in sample are noticeably different from those in original population, we have

evidence of treatment effect

○ It is also possible, however, that the difference between sample and population is due

to sampling error

○ A statistical hypothesis is an assumption about a population parameter

○ Best way to determine whether hypothesis is true would be to examine entire

population

■ Impractical --> impossible

○ Random sample is proxy for population

○ Use this sample to test hypothesis

○ Two possible explanations:

■ 1. The difference between sample and population can be explained by sampling

error

■ No treatment effect

■ 2. The difference is too large to be due to sampling error

■ Treatment effect

● Cannot "prove" things to be true

● Much easier to show that something is false

● Dilemma for researchers:

○ We want to support our hypotheses, but the techniques available are better for showing

that something is false

● Null Hypothesis

○ Two types of statistical hypotheses:

■ 1. Null hypothesis: No difference

■ H0

■ No difference between sample statistics and population parameters or

■ No difference between samples

--> no difference between populations

● Any minor differences due to chance

● Alternative Hypothesis

○ 2. Alternative hypothesis: Difference

■ H1 or Ha

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■ Difference between sample statistics and population parameter or

■ Difference between two samples

--> difference between populations

● Difference due to some non-random cause

● Even though we are using samples to test our hypothesis, the hypotheses are always stated

based on populations

● Statistical Notation

○ H0: µ0 = µ1

■ No difference in population means

○ H1: µ0 doesn't equal µ1

○ Ha: µ0 doesn't equal µ1

■ Population means are not equal (two-tailed, non-directional)

■ Non-directional tests are more stringent; more conservative

● Directional Tests

○ If researchers predicts a specific direction for the treatment effect (increase or

decrease), can incorporate the directional prediction into the hypothesis test

○ The result is called a directional test or a one-tail test

○ Directional test includes directional prediction in statement of hypotheses and location

of the critical region

○ For example, if the original population has a mean of 80 and treatment is predicted to

increase the scores, the null hypothesis would state that after treatment:

■ H0: mean is equal to or < 80 (there is no increase)

● Statistical Notation

○ H1: µ0 < µ1

○ H1: µ0 > µ1

○ Ha: µ0 < µ1

○ Ha: µ0 > µ1

■ One mean is greater (or less than) the other (one-tailed, directional)

● The Null hypothesis, the Alpha Level, the Critical Region, and the Test Statistic (can be written on

calculation sheet)

○ 5 steps in hypothesis testing:

■ Step 1: State Hypothesis

■ State the hypotheses; select an α (alpha) level

■ Null hypothesis, H0, always states that the treatment has no effect

■ Alpha level establishes a criterion, or "cut-off," for making a decision

about the null hypothesis

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