# PSYC 2040 Chapter Notes - Chapter 2: Repeated Measures Design, Central Limit Theorem, Standard Deviation

by OC766356

School

University of GuelphDepartment

PsychologyCourse Code

PSYC 2040Professor

Naseem Al- AidroosChapter

2This

**preview**shows half of the first page. to view the full**2 pages of the document.**Chapter 2 â€“ The t-test

General Rationale

- Two main questions the test explores:

- How reasonable it is to assume that a sample originated from a population with a given

mean

- How reasonable it is that the two samples came from populations with identical means

- Standard normal distribution such that 95% of the area lies between â€“ 1.96 and + 1.96

would be significant at the .05 (probability of a type 1 error at this level is .05)

- Standard normal distribution such that 99% of the area lies between â€“ 2.58 and + 2.58

would be significant at the .01 level (probability of a type 1 error at this level is .01

Inferences Involving a Single Sample Mean

- Used to determine how likely it is that a sample with a given mean (statistic) could

originate from a population with a given mean (parameter)

- Can only do this if it is normally distributed, if the sample is large enough you can

assume it is because of the central limit theorem

- If the standard deviation is unknown it can be calculated from the sample data, this

standard deviation is then referred to as the biased estimate

Inferences Involving Two Sample Means

- Used to determine if the difference between two sample means was large enough to

suggest that the two samples were drawn from populations with different means

- Use the critical ratio equation to determine if they are truly different, and if so at what

level (.05, .01, .001)

- * note critical ratio is no longer used

The Density Function for t

- The density function is an equation that describes that shape of the distribution and can

be used to determine the area under the curve between any two points

- The equation has two variables df and t

- The nature of the function changes as a function of df, as df increases the t distribution

get more like the standard normal distribution

Determining is Variances are Heterogeneous or Homogenous

- F-Ratio used to determine whether or not the variances in the underlying populations are

the same or different

- SPSS uses levenes to test this

Probability Values and One and Two Tailed Tests

- One-Tailed test: only concerned about differences in one direction (either positive or

negative), significance gets divided by two

- Two-Tailed: concerned with either a positive or negative outcome

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