# PSYC209 Lecture 9: Testing Means - Two independent-sample t Test with confidence interval

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Instructor – Amey Rachel

Textbook – Essential Statistics for the Behavioral Sciences by Gregory Privitera

Between-subjects design

- A research design in which different participants are observed one time in each group

or at each level of one factor

- Two ways to do this

o Observe the same participants twice

o Select two different groups

Independent sample

- A type of sample in which different participants are independently observed one time in

each group

- Two ways to select two independent samples

o Select a sample from a population

Used to conduct quasi-experiments

o Select independent samples

Select one sample from the same population and randomly assign

participants in the sample to groups

Used in experiments that include randomization, manipulation and a

comparison/control group

Two-independent sample t test

- A statistical procedure used to compare the mean difference between two independent

groups

- This test is specifically used to test hypotheses concerning the difference between two

population means, where the variance in one or both populations is unknown

We make four assumptions for a two-independent sample t test

- Normality

o We assume the data in each population being sample are normally distributed

- Random sampling

o We assume that the data we measure were obtained from samples that were

selected using a random sampling procedure

- Independence

o We assume that each measured outcome or observation is independent,

meaning that one outcome does not influence another

- Equal variance

o We assume that the variances in each population are equal to each other

o This assumption is usually satisfied when the larger sample variance is not

greater than two times the smaller

Two ways to state that there is no difference between two population means