determining differences between groups
DESCRIPTION
Determining Differences Between Groups. T-tests ANOVA. Some background…. Researchers want to know the characteristics of a large group (i.e. all women). IMPOSSIBLE!! However a representative “sample” can be selected Results are then inferred to apply to the population. Background. - PowerPoint PPT PresentationTRANSCRIPT
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Determining Differences Between Groups
T-testsANOVA
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Some background…...
Researchers want to know the characteristics of a large group (i.e. all women). IMPOSSIBLE!!
However a representative “sample” can be selected
Results are then inferred to apply to the population.
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Background
This is called inferential statistics.
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Comparing Means
Standard Error of the Mean= SEM
The standard deviation of a sampling distribution of means
SD divided by the square root of “n-1”
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Normal Curves
Just like with scores and SD, 68% of sample means from a population fall within +1SEM of the population mean
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% of Sample Means in 1 SEM
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2 SEM?
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Example
Mean of a population is 50 and the SEM is 5
Very likely to select a sample with a mean of 45 but very unlikely to select a sample with a mean that is 35.
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Comparing Means
Most of the time researchers want to compare 2 or more samples
IE, difference in reading ability between 3rd grade boys and girls.
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More background
Initial stats approach is to assume that groups are NOT different, then test statistically.
This is the NULL HYPOTHESIS“ Boys and Girls reading abilities
do not differ”“Male heights are equal to
female heights”
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Comparing Means
Obviously two means from a sample will never be exactly alike.
We want to know if they are different due to chance or is there a real reason.
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Comparing means
We can obtain the probability that two means will differ simply due to chance.
If the probability is small we reject the null and accept the research hypothesis: “there is a difference between male and female height”
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In other words………...
If the probability is less than .05, groups are considered different
This is known as the Alpha level.
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Statistical Tests
To compare two means we use a t-test
We can use the normal curve to determine the a difference between two means is likely.
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Types of t-tests
Independent (unpaired): compare two different groups
Dependent (paired): same subjects in both groups. Some treatment has been applied.
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Grab a representative sample
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Compare Height Means and SD
Unpaired T-Test
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Results
“The probability that the mean difference we observe between the male and female heights is due to chance is .034, thus we reject the null and accept the research hypothesis”
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Other ways of saying it….
The probability of obtaining such an outcome is only 3.4 in 100
Our results are likely to occur by chance less than 3.4 percent of the time.
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P-Value
P less than .05 is significant (reject null, accept research)
P greater than .05 is not significant (accept null, reject research)
The p value is .05 a lot of times but you may see .01, .10, or an adjusted p value sometimes as you read.
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By the way………..
The significance of our example isn’t very meaningful since we probably already knew that males on average are significantly taller than females and there are reasons for our that.
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Directional Hypotheses
Maybe our research hypothesis should have been: “Males are taller than females”
Before: “Male and female heights are different” (two-tailed)
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Tails
One-tailed T-test We decide ahead of time that we
will subtract the mean of the females from the males (thus expect a positive difference)
If we get a negative difference it will not support our research hypothesis and we would reject the null
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Quick Assignment
Using the class data spreadsheet, perform a paired (dependent) t-test for thigh vs. triceps
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Assignment
Use the t-test excel spreadsheet on my web page
t-test
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Assignment1
ACT1=no test prepACT2=test preparationThese are two separate sets
of subject.Perform the appropriate t-
test
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Assignment2
Height1 = height in third grade
Height2 = height in sixth grade
Performed on same set of subjects
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Assignment3
Attitude 1=attitude toward school at beginning of the year
Attitude 2=attitude toward school at end of the year
Performed on same group of subjects
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ANOVA
Again, two typesRepeated MeasuresFactorialMore than two means to
compare
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Repeated Measures (ANOVA)
Used when performing repeated measures on the same group of subjects (analogous to a dependent t-test)
I.e. changes in strength over 12 weeks of training…………..
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Subjects
20 subjects have bench press 1RM assessed at 1, 4, 8 and 12 weeks
One way ANOVA used to determine changes across time
If significant, then post-hoc tests (Tukey, Scheffe)
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1RM changes
1 4 8 12
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“post hoc” t=tests
1 4 8 12
Wk 4 > 1 p= .03Wk 8 > 1 p = .03Wk 12 > 1 p = .01Wk 12 > 4 p = .03Wk 8 > 4 p = .02Wk 12 > 8 p = .15
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Factorial ANOVA
Used when have more than two groups of subjects (analogous to independent t-test)
Comparing three different types of teaching styles on 3 different groups of 3rd graders
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Higher level ANOVAS
Previous examples were one-way ANOVAs (only one independent variable)
Can have studies with multiple independent variables
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Variables
Dependent and Independent Variables
Dependent – what you are measuring or interested in.
Independent – usually categorical and what remains constant.
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Actually………
The training study should be a mixed factorial repeated measures ANOVA since you probably have a Control group.
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Results
Time (wks)
Training
Control
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Example
Two groups (control and training)
Measured strength, EMG, MMG every 4 weeks for 12 weeks
Measured strength, EMG, MMG of both legs
Measured strength, EMG, MMG at 7 different velocities
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Variables?
Independent?Dependent?A 2 x 2 x 4 x 7 mixed factorial
repeated measures ANOVA for each dependent variable (otherwise would have to do a MANOVA – two or more dependent variables)
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Other Higher Order Examples
You want to know how three separate third grade classes respond to 3 different teaching styles and you measured test scores at 3 different times during the year.
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Answer
3 (treatment) by 3 (week of year) factorial ANOVA (3 separate groups of subjects).
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Example
You are following a group of 1st graders throughout their elementary years and measuring the height of both the boys and girls.
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Answer
6 (years of elementary) x 2 (gender) repeated measures (same group of subjects) mixed factorial ANOVA
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Example
You are following a group of 1st graders throughout their elementary years and measuring the height (twice a year) of both the boys and girls.
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Answer
6 (years of elementary) x 2 (gender) x 2 (times measured) repeated measures mixed factorial ANOVA
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Columns of Data
Year1-1, Year1-2, Year 2-1, Year2-2, Year3-1……………
Would also have a gender column denoting which subjects are girls and which are boys (boys = 1, girls = 2)
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Assumptions
1. Data are normally distributed2. Random sampling3. Groups are independent of
each other (random assignment into treatment groups)
4. In studies using multiple samples, the populations represented are assumed to be equally variable
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Non-parametric Tests
Mann-WhitneyKruskal-WallisSign TestFriedmanChi-Square