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Chapter 9

# Chapter 9.docx

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University of Guelph

Psychology

PSYC 1000

Anne Bergen

Fall

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Chapter 9
The Single-Sample t Test and the Paired-Samples t Test
There are three types of t tests
o Single-sample t test
Used when we are comparing a sample mean to a population
but do not know the populations standard deviation
o Paired-sample t test
Used when we are comparing two samples and every
participant is in both samples
o Independent-samples t test
When we are comparing two samples and every participant is
in only one sample
The t Distributions
We use a t distribution instead of a z distribution when sampling requires us
to estimate the population standard deviation from the sample standard
deviation or when we compare two samples to another
Estimating Population Standard Deviation from the Sample
The formula for standard deviation when estimating from a sample
o Look at page 205
Calculating Standard Error for the t Statistic
The formula for standard error when were estimating from a sample
o Sm= s/(square root) N
Using Standard Error to Calculate the t Statistic
The t statistic indicates the distance of a sample mean from a population
mean in terms of the standard error
o There is a formula page 206
Close to z statistic formula
The Single-Sample t Test
A single sample t test is a hypothesis test in which we compare data from one
sample to a population for which we know the mean but not the standard
deviation
The t Table and Degrees of Freedom
Degrees of freedom is the number of scores that are free to vary when
estimating a population parameter from a sample
o The formula is df= N-1 As sample size increases the t distributions more and more closely
approximate the z distribution
The Six Steps of the Singe-Sample t Test
Step 1
o Identify the populations, distributions and assumptions
Step 2
o State the null and research hypothesis
Step 3
o Determine the characteristics of the comparison distribution
Step 4
o Determine the critical val

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