L33 Psych 300 Chapter Notes - Chapter 9: Null Hypothesis, Sampling Distribution, Statistical Hypothesis Testing


Department
Psychological & Brain Sci (Psychology)
Course Code
L33 Psych 300
Professor
Nestojko
Chapter
9

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Chapter 09: the Single-Sample t
Test and the Paired-Samples t
Test
Review: Six Steps of Hypothesis Testing
Identify the populations, distribution, and assumptions: then choose the
appropriate hypothesis test
State the null and research hypothesis
Calculate mean and standard error of the sampling distribution (the comparison
distribution)
Determine the critical values (cutoffs) that indicate the points beyond which we
will reject the null hypothesis
Calculate the test statistic
Decide whether to reject or fail to reject the null hypothesis
Make a confidence interval (will learn this soon)
Calculate effect size
T
-statistic - the distance of a sample mean from a population mean in terms of the
estimated standard error
We use t
distributions when we do not know the population standard deviation
and are comparing only two groups
The two groups may be a sample and a population, or two samples as part of a
within-groups design or a between-groups design
The formula for the t
statistic for a single-sample t
test is the same as the formula
for the z
statistic for a distribution of means, except that we use estimated
standard error in the denominator rather than the actual standard error for the
population
We calculate estimated standard error by dividing by (N - 1) rather than dividing
by N, when calculating standard error
T-Test and Z-Test
If we know the mean and the SD of the population, use a z-test (single-sample
z-test, chapters 6-8)
But if we don’t know the SD of the population, use a t-test
Single-sample t-test (if we know the mean)
Two samples (if we don’t know the mean)
Within groups design: paired-sample t-test
Between groups design: independent samples t-test
How t-tests are different from z-tests:
In t-tests:
We will estimate the population SD using our sample data
The sampling distribution of means will no longer be a normal (z) shape;
it will be a t
distribution shape, and the particular shape will depend on
sample size (N)
Instead of using a z-table to look up critical cutoff values, we will use a
t-table, and in that tabel the critical cutoff values will depend on the
degrees of freedom (N - 1)
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