Chapter 14: F-tests

What happens as the MS between groups gets bigger?

The F statistic increases, and therefore, it becomes less and less likely that the null of "no difference between the means" is true

Once you run an F test and see that the F statistic is higher than 1, and the significance is low, what do you have to do next?

The F test being significant does NOT tell you which group is higher or lower --> it only tells you that there is a significant difference. Now, you have to run individual T tests between each pair of groups to see which variables differ significantly from one another

When you do the T-test after an ova, which S squared / variance value do you use?

The S squared value that yyou use with the WITHIN-CONDITION MS

Explain + Equation for Total SS:

Total Sum of Squares = the sum of squares of deviation of all the individual scores from the grand mean

What's the difference between a 1-way and 2-way anova? What do we use in class?

1-way anova = 1 independent variable, with 3 or more levels of dependent variables 2-way anova = 2 independent varaibles, each with multiple levels

You might use a F test instead of a T test, because T tests can only compare _____________, while F tests can compare MORE/LESS than that?

2 means More than 2 means

For a F statistic, when the null hypothesis of no difference between the means is true, what should the value of F be?

A little higher than 1: Df / (df-2)

Statitical decisions should NEVER be based on significance value alone..... -->

A) one should also condiser the effect size and its corresponding confidence interval and BESD B) when calculating the effect size correlation, one uses the formula used for T tests, but degrees of reedom are defined form the groups being compared

Explain + equation for Between Groups SS:

Between Groups SS = the sum of squares of the deviations of the group means from the grand mean

***** What is the formula for the F statistic?

F = MS between / MS within

The F test is a signal to noise ratio that divides up variability using Analysis of Variance (ANOVA) What is the F Ratio? What is the signal, and what is the noise? Explain ****

F ratio = Between Groups Variation / Within Groups Variation Signal to Noise Ratio: Signal = Between Groups = how much do the means of each group differ from the Grand Mean Noise = Within Groups = inter-group variation = variation within each individual group (nothing to do with the grand mean)

For a F-test, what is the null, and what is the alternate? The F test is also referred to as a "__________" Test

H0: u(A) = u(B) = u(C) = ...... H1: Not all of the of the means are equal

What question does an F test answer?

Is the variation / variability between conditions different from the variation within conditions?

What happens if you try doing an ANOVA (1-way), however your IV only has 2 levels?

It's essentially the exact same result as a T test, except you will get an F statstic instead of a T statastic. Your F statistic will be T squared. So, you just have to take the square root of it, and get your T (which you can do, becasue there are only 2 groups)

What statistic combines each of the SS scores with their DF? What is the formula? What does it measure? ***

Mean Square = MS MS = SS / DF Mean Square is anova's way of measuring the total variance MS between is signal, MS within is noise

What is an "omnibus F" versus a Focused Test?

Omnibus = Any F test with numerator DF > 1 Focused Test = all F tests with numerator DF = 1, and all T tests

"One Degree of Freedom Effects" VS "multiple Degree of Freedom Effects"

One DF = focused tests = F test where DF = 1, and T tests Multiple DF = omnibus tests = F tests with DF > 1

*** what was the formula for computing the Effect Size R from T? Given that, what is the fromula for computing the effect size R from F?

R(effect Size) = Root (t^2 / t^2 + DF) R (effect size) = Root (F / F + DF.within)

For the SS total, SS between, and SS within, how do you find the DF? **** what formula relates these 3?

SS total = N - 1 = total number of measurements minus 1 SS Between = K - 1 = total number of groups, minus 1 SS Within = N - K = Total number of measurements, minus total number of groups Total = Between + Within

T and F statistic: Shape of graph? Any Skew? Intrinsically 1 or 2-tailed?

T = normal distribution bell curve, no skew, 2-tailed F = skewed right distribution, intrinsicially 1-tailed

an F test does NOT specifically tell you which groups differ from each other. That means, you must do a t-test. Which of these tests are "tests of simple effects" and waht does that mean?

T-test Test of simple effects = comparisons of specific group means

How is F related to T? What is ALWAYS true? What is not always true? --> however, when is this always true?

T^2 always = F --> whenever you square T, you will always get F However, taking the square root of F will NOT always give you T --> However, when there are only 2 groups being compared, then taking the square root of F always produces T

**** Lets say you have data for 3 different groups. Explain.... The total Variance The Between Groups Variance The Within Groups Variance

Total Variance = Take all of the data from 3 groups, put it all on one big group, and now you have the GRAND MEAN of the entire sample / Total Variability of the group Between = essentially, you are looking at each group individually, and comparing BETWEEN group A (or B, or C) and the Grand Mean. --> It's the variability / difference between the Grand Mean and the mean of each group Within = has nothing to do with the grand mean. You are only looking WITHIN an individual group. Each individual group has it's own mean, and you are looking at the variability of the individuals within that group

The purpose of ANOVA is to divide up variation of all observations into separate sources of variation. What is the total variation referred to as? What is the formula for this? ***

Total variation = Sum of Squares (SS) Total SS = Between Group SS + Within Group SS

The F test is a signal-to-noise ratio that divides up / tests __________ in a procedure called ___________ ******

Variance (between means) Analysis of Variance (ANOVA)

With the F ratio being Between Group Variation / Within group variation...... When do we fail to reject the Null (the group means are equal)? What is the value of F? When do we REJECT the null - the means are not equal? What is the value of F?

When the F ratio = 1, that means that the within group variation is equal to the between group variation, which means that the means are equal, and the null can NOT be rejected When the F ratio is GREATER than 1, this means that there is much greater variation BETWEEN groups than within each group, which means that the means are not all the same, and we can REJECT the null

Explain + equation for Within Groups SS:

Within groups SS = the sum of squares of the deviations of the individual scores from their group means

The T-test is a "signal-to-noise" ratio. Is the F test also a signal-to-noise ratio?

Yes, the F-statistic is also a signal-to-noise

When computing R effect size for a F statistic, the denominator is "F / DF.within" How do you find "DF within" ?

You take the degrees of freedom (N-1) from each group, and then add them up

MS Between is a reflection of both the ________ and the __________

size of the effect size of the study