Psychology Statistics (Chapter 8)

The Null Hypothesis (H0)

states that in the population there is no change, no
difference, or no relationship. In the context of an experiment, predicts that the independent variable (treatment) will have NO EFFECT on the dependent variable in the population

Example: Ho: μinfants handled = 26 pounds

The Alternative Hypothesis (H1)

States that in the population there is a change, a
difference, or a relationship. In the context of an experiment, predicts that the independent variable (treatment) WILL have an effect on the dependent variable in the population

H1: uinfants handled ≠ 26 pounds

The Null Hypothesis (H0)

states that in the population there is no change, no
difference, or no relationship. In the context of an experiment, predicts that the independent variable (treatment) will have NO EFFECT on the dependent variable in the population

Example: Ho: μinfants handled = 26 pounds

The Alternative Hypothesis (H1)

States that in the population there is a change, a
difference, or a relationship. In the context of an experiment, predicts that the independent variable (treatment) WILL have an effect on the dependent variable in the population

H1: uinfants handled ≠ 26 pounds

Harking

hypothesising after results are known, which can lead to biased conclusions and reduce the validity of the research findings.

Hypothesis Test

a statistical method that uses sample data to evaluate a hypothesis about a population parameter

Step 1 of hypothesis testing

State the hypothesis, both the null and the alternative hypothesis

Step 2 of hypothesis testing

Set the criteria for a decision, choose the alpha and find the critical z that goes along with the alpha

Step 3 of hypothesis testing

Collect Data and Compute the Sample Statistic (test statistic), use the z-score formula for distribution of the sample mean (Z = M - μ/σM)

Step 4 of hypothesis testing

Make a decision, Once we have z-score for the sample
→ compare it to z-score critical

Reject or fail to reject the null hypothesis based on the comparison with the critical value.

Alpha Level/Level of Significance (α)

probability value used to define very unlikely
sample outcomes if the null hypothesis is true

What is the critical z for two tailed testing

0.05 (5%)/2= 0.0250/2.5%= Z:±1.96

0.01 (1%)/2 = 0.049/0.5%% = Z:±2.58

0.001 (0.10%)/2 = 0.0005/0.05% = Z:±3.30

Anything more than positive/negative 1.96 means the null hypothesis can be rejected

Test statistic

when the sample data are converted into specific statistic used to test the null hypothesis

Critical Region

composed of extreme sample values that are very unlikely to be obtained if the null hypothesis is true. Boundaries for the critical region are determined by the alpha level in the tail.

If sample data fall in the critical region, the null hypothesis is rejected (thte sample is statistically significant)

Type 1 error

Occurs when a research rejects a null hypothesis that is actually true.

Researcher says there IS an effect when there ISN’T an effect. Akin convicting an innocent person in a murder trial

Type 2 error

Occurs when a research fails to reject a null hypothesis that is actually false.

Researcher says there ISN’T an effect when there IS an effect. Akin to letting a guilty person go free in a murder trial.

Assumptions of random testing

1. Random Sampling – in order for generalization of data

2. Independent Observations – there is no consistent, predictable relationship between one observation (subject A) and another (subject B)

3. Value of σ does not change – the treatment effect is assumed to be a constant added/subtracted from every score

4. Normal Distribution – so that we can use the unit normal table to find probabilities

Cohen’s D formula

mean difference / standard deviation

d = (M - μ / σ)

Cohen’s D variation

0.20 or less = very small

0.20 = small

0.50 = medium

0.80 or more = larger

Directional hypothesis test

the statistical hypothesis (H0 and H1)
specify either an increase or a decrease in the population mean. They make a
statement about the direction of the effect

Step 1 of a directional hypothesis test

State the hypothesis, both the null and the alternative hypothesis AND a directional prediction is incorporated

H0 = μ ≤ μ0 (or μ ≥ μ0)

H1: μ > μ0 (or μ < μ0)

example (increase):
Ho: μ infants handled ≤ 26 pounds (there is no increase in weight)

H1: u infants handled > 26 pounds (there is an increase in weight)

Step 2 of a directional hypothesis test

the critical region is located entirely in one tail of the distribution (increase means above the mean, decrease means below the mean)

What is the critical z for one tailed testing

0.05 (5%) = 1-0.05 =0.95 = Z:±1.65

0.01 (1%) = 1 - 0.01 = 0.99 = Z:±2.33

0.001 (0.10%) = 1 - 0.001 = 0.999 = Z:±3.09

Anything more than positive/negative 1.65 means the null hypothesis can be rejected