Hypthoesis Testing

Hypothesis Testing

Sample data is used to evaluate a hypothesis (a proposition on limited evidence) about a population

• goal is to rule out sampling error -possibility of being the result for the research study

1. A sample is selected from the population

2. the treatment is administered to the sample

3. after treatment, the individuals in the sample are measured

Hypothesis Testing (State the Hypothesis)

NULL Hypothesis: no change; no difference; the treatment has no effect

• H_0: μ_apple a day = 6

ALTERNATIVE Hypothesis: a change; a difference; the treatment has an effect

• H_1: μ_apple a day ≠ 6

• Hypothesis Testing (Set the Criteria for a Decision)

α level: probability value your willing to accept or reject based on your α level

• p-value > .05, retain H_0; Sample results are not extreme → there is not effect

example)

p-value = .12 (p is above α = .05), No effect (retain H_0)

.12 > .05

• p-value ≤ .05, reject H_0; Sample results are extreme (critical region) → there is an effect

example)

p-value = .02 (p is below α = .05), Has effect (reject H_0)

.02 ≤ .05

Critical Region (for p-value → normals unit table): Danger Zone for results (area in the curve is so extreme, it’s beyond α = .05)

• if sample land in this zone (inside) → reject H_0

• if sample don’t land in this zone (outside) → retain H_0

Hypothesis Testing (Collect Data and Compute Sample statistics)

1. Summarise the data with appropriate descriptive statistics (i.e., mean)

2. After, compare sample mean with population mean via z-Score (FORMULA [z-Score for a sample mean; test how far sample mean is from population mean] SHOWN IN IMAGE)

When H_0 (no change) is TRUE

• APPROVE H_0 → Correct decision (yay!)

• REJECT H_0 → Type I Error [P(Type I Error) =α] → saying there’s a change when there isn’t

When H_1 (change) is TRUE

• APPROVING H_1 → Correct decision (yay!)

• REJECTING H_1 → Type II Error [P(Type II Error) = β] → Saying there’s isn’t a change when there is

Directional (one-tailed) Hypothesis Tests

Statistical Hypothesis H_0 and H_1 specify either an increase or decrease in the population mean score

• make a statement about the direction of the effect

• z cutoff for a one tailed test is + or -

Power of a Hypothesis Test

defined as the probability that the test will either accept or reject H_0

FACTORS EFFECTING POWER:

• Sample size

• Alpha level

• One-tailed versus two-tailed test