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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 PsychologicalResearch: A Comprehensive Analysis Using t TestsWEEK FOURINDIVIDUAL ASSIGNMENTLast week, we worked on comparisons involving either one individual’s score beingcompared 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 thepopulation’s mean and variance. Remember also, that I said that this was rarely the kind ofresearch that was done in the field of psychology but a good foundation that we needed tounderstand.This week, we’ll move closer to the type of research that you’ll read in the professionalliterature. We’re still making comparisons but in real life, we seldom have information onthe population’s mean and variance. If the population’s variance is not known, a solution isto estimate it based on the sample’s variance. While it might seem easy then to just use thesample’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. Lastweek, wecalculated variance as the sumof square deviations from the mean divided by thenumber of participants in the sample:SD2= SS/N.But the estimated population variance isfigured as the sum of squared deviations from the mean divided by the number ofparticipantsminus one:SD2= SS/N-1.Not a big tweak, just a little one. This “tweak” iscalled degrees of freedom.With these new comparisons (where we don’t know the population’s variance), somethings 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’llleave 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 bysetting 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 youcan calculate the estimated population variance. This is Formula (7-1) on your MajorFormulas Handout. Part Two, will require you to go through the Five-Step HypothesisTesting Process for a t Test for Dependent Means and Part Three will require you to gothrough the Five-Step Hypothesis Testing Process for Independent Means. Again, I’ll walkyou through an example of each one and then give you a scenario to do on your own.PART ONE: CALCULATINGAN ESTIMATED POPULATION VARIANCEFORMULA (7-1)First, my EXAMPLE:

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Document Details

University
Southern New Hampshire University
Course
PSY 315
Subject
Psychology

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