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Lecture 10

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Department
Psychology
Course
PSYC 2002
Professor
Steven Carroll
Semester
Winter

Description
Lecture 10 independent measures Independent measures design - Here’s an example: - I recently helped put together a research proposal wherein I designed a series of experiments that could be used to evaluate the “Nouse” The point of the Nouse - My partners and I wanted to evaluate whether people using the Nouse could work at speeds comparable to non-Nouse users - Our goal was to develop this product as an assistive device technology (ADT) - It was important that the participants who used the Nouse actually be disabled: • We really wanted to see whether the technology levelled the playing field Independent groups - So we proposed a “between subjects” design: • Run a series of independent tests on each of the two groups of interest in the study, then compare the results Definition - Aresearch design that uses a separate group of participants for each treatment condition is called an independent-measures research design or a between-subjects design Between-subjects hypotheses - In a single sample t-test, how do you form a non-directional (i.e. two tailed) hypothesis? H 0 : µ = X H 1 : µ ≠ X - We hypothesize that our treated group comes from a population with a mean of X - Our alternative hypothesis is that our treated group comes from a population that does not have a mean of X - In a between-subjects / independent samples t-test, we typically hypothesize that our two groups come from two independent populations that nevertheless have equal parameters µ and ² - How do we state this? H µ µ H µ µ 0 : 1 - 2 = 0 , 1 : 1 - 2 ≠ 0 - Why don’t we phrase it like this? H 0 : µ 1 = µ 2 , H 1 : µ1 ≠ µ 2 - Because we want our hypothesis to state a number that can be used in Step 3 of the test - Note: if you suspect that the difference between the population means has some non-zero value, you could say something like: H µ µ H µ µ 0 : 1 - 2 = 5 , 1 : 1 - 2 ≠ 5 H 0 µ 1 - That’s another great reason to phrase the hypothesis this way instead of : = µ 2 Critical value - What change do you suppose are necessary in Step 2 of hypothesis testing? - At  = X two-tailed, t (df) = Y - What is df here? Df - We test everyone in groupAand we get a mean - We test everyone in group B and we get a mean - What do we know about means? • - How many means are we dealing with here? - So what is our df? Critical values - Df = ( n 1 - 1) + ( n2 – 1) - Df = n1 - 1 + n2 – 1 n n - Df= 1 + 2 - 1 – 1 n1 n2 - Df = + – 2 - At  = X two-tailed, t (n1 + n2 - 2) = Y Calculating t-observed - The same basic t-test idea holds here as well: observeddata−h ypot hesis T = error (M 1M –(µ2)µ ) 1 2 T = S (M1−M2) - M1 - M2 • M 1 is the mean of the first group M • 2 is the mean for the second group M 1 M 2 • - is the observed difference between our two sample groups - µ1 - µ2 • This value is derived from our null hypothesis. For example: H 0 : µ1 - µ 2 = 0 - S( M1 – M2) • Each group produces an s value • Each of these s values is an estimate of  in the respective populations ❑ ❑ S S • We are assuming 1 = 2 , so that both 1 and 2 are provid
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