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
- 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
- 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
- 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 : =
- What change do you suppose are necessary in Step 2 of hypothesis testing?
- At = X two-tailed, t (df) = Y
- What is df here?
- 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
- Df= 1 + 2 - 1 – 1
- Df = + – 2
- At = X two-tailed, t (n1 + n2 - 2) = Y
- 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
• M 1 is the mean of the first group
• 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 =
- 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