Statistical Hypothesis Testing and Variance Estimation in Psychological Research: A Comprehensive Analysis Using t Tests
A comprehensive analysis of statistical hypothesis testing and variance estimation in psychological research using t-tests.
Sophia Johnson
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Statistical Hypothesis Testing and Variance Estimation in Psychological
Research: A Comprehensive Analysis Using t Tests
WEEK FOUR INDIVIDUAL ASSIGNMENT
Last week, we worked on comparisons involving either one individual’s score being
compared to a population or a sample of people’s scores being compared to a population.
We called these comparisons z tests and in both situations we had information about the
population’s mean and variance. Remember also, that I said that this was rarely the kind of
research that was done in the field of psychology but a good foundation that we needed to
understand.
This week, we’ll move closer to the type of research that you’ll read in the professional
literature. We’re still making comparisons but in real life, we seldom have information on
the population’s mean and variance. If the population’s variance is not known, a solution is
to estimate it based on the sample’s variance. While it might seem easy then to just use the
sample’s variance directly; mathematically, it can be shown that the sample’s variance will,
on average, be a bit smaller than its population’s variance so we tweak it just a little. Last
week, we calculated variance as the sum of square deviations from the mean divided by the
number of participants in the sample: SD2 = SS/N.But the estimated population variance is
figured as the sum of squared deviations from the mean divided by the number of
participants minus one: SD2 = SS/N-1. Not a big tweak, just a little one. This “tweak” is
called degrees of freedom.
With these new comparisons (where we don’t know the population’s variance), some
things to keep in mind:
• The comparisons are called t tests (not z tests) and there are two kinds of t tests.
One, a t Test for Dependent Means and Two, a t Test for Independent Means. I’ll
leave it to your assigned readings to explain the difference between the two.
• Estimating the population variance loses some accuracy so we make up for that by
setting the cutoff score a little more extreme
• You will use the t table at the end of our textbook to determine your cutoff score.
So for this week’s Individual Assignment, Part One will require you to demonstrate that you
can calculate the estimated population variance. This is Formula (7-1) on your Major
Formulas Handout. Part Two, will require you to go through the Five-Step Hypothesis
Testing Process for a t Test for Dependent Means and Part Three will require you to go
through the Five-Step Hypothesis Testing Process for Independent Means. Again, I’ll walk
you through an example of each one and then give you a scenario to do on your own.
PART ONE: CALCULATING AN ESTIMATED POPULATION VARIANCE
FORMULA (7-1)
First, my EXAMPLE:
Research: A Comprehensive Analysis Using t Tests
WEEK FOUR INDIVIDUAL ASSIGNMENT
Last week, we worked on comparisons involving either one individual’s score being
compared to a population or a sample of people’s scores being compared to a population.
We called these comparisons z tests and in both situations we had information about the
population’s mean and variance. Remember also, that I said that this was rarely the kind of
research that was done in the field of psychology but a good foundation that we needed to
understand.
This week, we’ll move closer to the type of research that you’ll read in the professional
literature. We’re still making comparisons but in real life, we seldom have information on
the population’s mean and variance. If the population’s variance is not known, a solution is
to estimate it based on the sample’s variance. While it might seem easy then to just use the
sample’s variance directly; mathematically, it can be shown that the sample’s variance will,
on average, be a bit smaller than its population’s variance so we tweak it just a little. Last
week, we calculated variance as the sum of square deviations from the mean divided by the
number of participants in the sample: SD2 = SS/N.But the estimated population variance is
figured as the sum of squared deviations from the mean divided by the number of
participants minus one: SD2 = SS/N-1. Not a big tweak, just a little one. This “tweak” is
called degrees of freedom.
With these new comparisons (where we don’t know the population’s variance), some
things to keep in mind:
• The comparisons are called t tests (not z tests) and there are two kinds of t tests.
One, a t Test for Dependent Means and Two, a t Test for Independent Means. I’ll
leave it to your assigned readings to explain the difference between the two.
• Estimating the population variance loses some accuracy so we make up for that by
setting the cutoff score a little more extreme
• You will use the t table at the end of our textbook to determine your cutoff score.
So for this week’s Individual Assignment, Part One will require you to demonstrate that you
can calculate the estimated population variance. This is Formula (7-1) on your Major
Formulas Handout. Part Two, will require you to go through the Five-Step Hypothesis
Testing Process for a t Test for Dependent Means and Part Three will require you to go
through the Five-Step Hypothesis Testing Process for Independent Means. Again, I’ll walk
you through an example of each one and then give you a scenario to do on your own.
PART ONE: CALCULATING AN ESTIMATED POPULATION VARIANCE
FORMULA (7-1)
First, my EXAMPLE:
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Document Details
University
Southern New Hampshire University
Subject
Psychology