matched t test experimental designs n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Matched t test Experimental Designs PowerPoint Presentation
Download Presentation
Matched t test Experimental Designs

Loading in 2 Seconds...

play fullscreen
1 / 26

Matched t test Experimental Designs - PowerPoint PPT Presentation


  • 292 Views
  • Uploaded on

Matched t test Experimental Designs . Repeated measures Simultaneous Successive Before and after Counterbalanced Matched pairs Experimental Natural. Chapter 12. The one-way independent ANOVA An. O. Va. = Analysis of Variance. More than two groups .

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Matched t test Experimental Designs' - johana


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
matched t test experimental designs
Matched t testExperimental Designs
  • Repeated measures
    • Simultaneous
    • Successive
      • Before and after
      • Counterbalanced
  • Matched pairs
    • Experimental
    • Natural
chapter 12

Chapter 12

The one-way independent ANOVA

An. O. Va. = Analysis of Variance

more than two groups
More than two groups
  • So far we have considered only one or two (sub) populations
  • What if there are more?
  • One could compare A to B, B to C, C to D etc.
example
Example
  • Three groups of manic-depressive patients are compared.
  • One group is given only psychotherapy, one group is given medication, and one group is given psychotherapy and medication.
  • After treatment, each patient is given a wellness test.
  • Are there differences between these treatments?
how many pairs can be derived from k levels
How many pairs can be derived from k levels?
  • This quickly gets out of hand in cases where there are many subpopulations (or groups).
  • If there are k populations
  • There are
  • pairs to compare.
  • We need another way.
one way analysis of variance
One way analysis of variance
  • That way is the one way analysis of variance
  • One way = There is only one independent variable.
  • The independent variable is called a factor.
  • The factor takes on different values
  • Each value is called a level
  • Each level denotes a population
  • A single test compares k levels.
another reason to use anova
Another reason to use ANOVA
  • Suppose there is no significant difference between the k levels.
  • If there are k levels then there are
  • different combinations
  • So, as k increases so does the number of combinations.
  • Given a .05 significance level
  • One now has many chances to reach it and make a type I error.
  • Somehow this must be taken into account
so how do we develop this anova
So how do we develop this ANOVA ?
  • We want to develop a test statistic (like z or t) for the ANOVA.
  • We don’t know anything about it
  • So we must start with something we do know
  • Like, the t test
  • We will start by rewriting the t test, then generalize it to more than two levels
generalizing the t test
Generalizing the t test
  • sp2 is the weighted average of two variances.
  • Since we now have k groups or levels, we could just as easily average over k variances.
  • Denote as MSW
  • Call this generalized sp2 the mean square within = MSW
  • This is a pool of k variances.
  • The rationale for the mean square terminology is that a variance is an unbiased mean of a sum of squares.
  • Within refers to the fact that the variances are within each group.
generalizing the t test1
Generalizing the t test
  • Next, for no particular reason, square both sides.
  • Then rearrange.
  • So, how do we compute MSW?
generalizing the t test2
Generalizing the t test
  • For equal sized groups, MSW is simply the average of each group’s variance.
generalizing the t test3
Generalizing the t test
  • Next generalize the numerator
  • It is a measure of the difference between the means
  • However, we can’t subtract k things
  • But, a difference is also a measure of spread
  • We need a measure of spread that can be applied to k things
  • This might be…?
generalizing the t test4
Generalizing the t test
  • We will use the variance
  • Replace n times the difference of means with n times a variance of means
  • Call this variance the mean squares between = MSbet
large or small
Large or small?
  • t2 : should it be large or small?
  • MSbet: should it be large or small? 2 reasons
  • MSW: should to be large or small? 2 reasons

0

give t 2 a new name
Give t2 a new name
  • t2 will be called the F-ratio.
  • F has a distribution that can be used in a way, similar to, the way we use the normal distribution.
  • How does this distribution differ from the normal and t distributions?
    • Mode can’t be 0.
    • Symmetry
    • Tails
    • Is a one tailed in the graph.
    • Like two tailed test in terms of directionality.

0

f ratio the numerator
F ratiothe numerator
  • The numerator is the actually the variance of the general population!
  • Recall the definition of the standard error (which assumes that the null hypothesis is true).
f ratio interpretaion
F ratioInterpretaion
  • What happens if the null hypothesis is not true?
f ratio interpretaion1
F ratioInterpretaion
  • Look at the formula for the variance of the mean
  • If the null hypothesis is not true, then the differences can be arbitrarily large, depending on the differences between the subpopulations.
f ratio interpretaion2
F ratioInterpretaion
  • MSbet and MSW behave differently
  • In the bottom figure, spreading of the means has an effect (increase) on F numerator, but has no effect on the denominator
  • So, if the null hypothesis is not true, F is …?
example computing the f ratio
ExampleComputing the F ratio
  • Three groups of manic-depressive patients are compared.
  • One group is given only psychotherapy, one group is given medication, and one group is given psychotherapy and medication.
  • Each group has 50 individuals.
  • After treatment, each patient is given a wellness test.
example computing the f ratio1
ExampleComputing the F ratio
  • Plug and chug.
  • But we are still missing the mean of the group means.
example computing the f ratio2
ExampleComputing the F ratio
  • The mean of group means is easy to compute.
  • Plug it in and do the arithmetic.
  • Now we need a Fcrit.
f ratio degrees of freedom
F ratioDegrees of freedom
  • Like the t test, the shape of the F distribution depends on df
  • There are two
  • dfbet = k-1=3-1=2
  • dfW = NT-k = 150 - 3 = 147
f distribution the tables
F distributionthe tables
  • Since there are two df, there will be many combinations
  • Hence, the tables are limited to a few  levels
  • One per table
  • See tables A7, A8, A9
  • Let’s use  =.05
  • Table A7 gives ______
  • Compare Fcrit to F.
exercises
Exercises
  • Page 334
  • 1,2,3,5,6,7