Stats Exam 3

Front 1

What is the goal of a Z-score?

Back 1

To determine whether the obtained difference between the data and the hypothesis is significantly greater than would be expected by chance

Front 2

Why/when do we use the t-test instead of the z-test?

Back 2

You use a t-test to test hypotheses about an unknown population mean when the value of standard deviation is not known.
The t-statistic is the same as the z-statistic except the t-statistic uses the estimated standard error as the denominator.

Front 3

When the population standard error of the mean cannot be computed, what do you use to estimate it? How?

Back 3

You would use the estimated standard error. You do this by replacing the sample variance (s^2) in place of the standard deviation.

Front 4

What is the definition of estimated standard error (Sm)?

Back 4

This is used an an estimate of the real standard error when the value of the standard deviation is unknown.
-It is computed from the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean (M) and the population mean (m).

Front 5

What are the two reasons to make the shift from standard deviation to varience?

Back 5

1. B/c on avg. sample variance (s^2) will provide an accurate and unbiased estimate of the population variance.
2. other versions of the t statistic that require variance in the formulas for estimated standard error.

Front 6

What is the definiton of a t-statistic?

Back 6

This is used to test hypotheses about an unknown population mean when the value of the standard deviation is unknown.
-The only difference between this and the Z-score is that the t-score has the estimated standard error in the denominator.

Front 7

what are degrees of freedom?

Back 7

describes the number of scores in a sample that are independent and free to vary. it is represented as (n-1)

Front 8

How does the shape of a t distribution compare to the shape of a normal distribution?

Back 8

The t distribution approximates the normal distribution but it tends to be flatter and more spread out.

Front 9

What is the relationship between the df and the shape of the t distribution?

Back 9

-The greater the value of df for a sample the better s^2 represents standard deviation^2 and the better the t statistic approximates the z-score.
-As df gets very large, the t distribution gets closer in shape to a normal z-score distribution.
-As a result, t statistics are more variable than z-scores.

Front 10

What are the 3 steps in calculating a t statistic?

Back 10

1.) calculate the sample varience. s^2= SS/df
2.) Then use the sample varience to compute the estimated standard error
3.) Now you are able to compute the t-statistic.

Front 11

What are the two basic assumption that are necessary for hypothesis tests with the t statistic?

Back 11

1.) The values in the sample must consist of independent observations. meaning the occurence of the first event has no effect on the probability of the second event.
2.) The population sampled must be normal

Front 12

What is the difference between Cohen's d and the estimated d? when do we use it?

Back 12

Cohen's d measures the effect size in terms of population mean difference and the population standard deviation. When the pop. mean w/treatment and the standard deviation are unknown we use replace them with the mean for the treated sample and the sample standard deviation. This gives us the "estimated d".

*an estimated d of 1.00 indicates that the size of the treatment is equivalent to one standard deviation.*

Front 13

What is an alternative method for measuring effect size?

Back 13

Determining how much of the variability in the scores is explained by the treatment effect. By doing this we will obtain a measure of the size of the treatment effect.

Front 14

What is r^2?

Back 14

This is the percentage of variance accounted for by the treatment. it is computed by doing r^2= t^2/t^2+ df.

*a less efficient way of computing this is by taking the difference between the two SS values and putting that over the total variability (which is the SS value of the treatment effect).

Front 15

What r^2 values are considered to be a small, med, and large effect?

Back 15

r^2=0.01 is a small effect
r^2=0.09 is a medium effect
r^2=0.25 is a large effect

Front 16

What are some factors that will decrease the likelihood of rejecting the null hypothesis?

Back 16

-Increasing the standard error
-Increasing the sample variance which would increase estimated standard error

*In general large variance means that you are less likely to obtain a significant treatment effect*

Front 17

how is the sample size (n) related to estimated standard error?

Back 17

They are inversely related!! the larger the sample is, the smaller the error is.
-This means that if all other factors are held constant, the large samples will produce bigger t statistics and increase the likelihood of rejecting the null hypothesis!!

Front 18

Does sample size effect Cohen's d or r^2?

Back 18

No!! Cohen's d is not influenced by sample size and r^2 is on slightly affected by changes in size of the sample.

Front 19

Under what circumstances do you use the Independent measures t-test?

Back 19

This is used when the study involves two seperate sample groups.
- The goal of an independent-measures research study is to evaluate the mean diff. between two populations (or two treatment conditions). It uses the diff between two sample means to evaluate the diff between two pop. means.

Front 20

What is the purpose of pooled variance and what does it correct for?

Back 20

This is used when the sample sizes are unequal and it corrects the biased assumption of the sample variances that the sample sizes are equal.
-Since the larger sample has a larger df value it will carry more weight when averaging the two variances.

Front 21

How do you compute the df for an independent measures t-test?

Back 21

By simply adding the df of sample 1 to the df of sample 2

Front 22

In the overall context of an Independent-measures test what can the t-statistic be reduced to?

Back 22

t= (data - hypothesis)/error

Front 23

What are the steps in determining a t-statistic using independent measures?

Back 23

1.) state the hypothesis and select the alpha level
2.) find the df and the critical region
3.) a. find the pooled variance
b. use the pooled variance to compute the estimated standard error
c. compute the t statistic
4.) Make a decision

Front 24

What is the estimated d for and independent measures research study?

Back 24

The estimated d= estimated mean diff/ estimated standard deviation (which is the sqr rt of the pooled variance)

Front 25

How do you compute r^2 for independent measures?

Back 25

The calculation is exactly the same as it was for the single sample t.

Front 26

What is the homogeneity of variance?

Back 26

this is the assumption that the two pop. being compared must have the same variance. Without satisfying this requirement you cannot accurately interpret a t statistic, and the hypothesis test becomes meaningless.

Front 27

How do you know if the homogeneity of variance assumption has been satisfied?

Back 27

You can use Hartley's F max test! This test can check the homogeneity of variance with more than two independent variables

Front 28

What is the F-max test anyway?

Back 28

It is based on the principle that a sample variance provides and unbiased estimate of the pop. variance.
- To compute this you 1st compute the sample variance for each sample and then put the largest of the smalles to get your F max value.
*a large value indicates a large diff between the sample variances while a small value (near 1.00) indicates that sample variances are similar and that the homogeneity assumption is reasonable.
- When the F max value is computed you need to find the critical region on table B.3
-to do this you need to know
a. k= # of seperate samples
b. df for each sample variance. (The Hartley test assumes that all samples are the same size)
*also note that this test would generally use the larger alpha level)

Front 29

Why use the dependent measures t test? what are the advantages?

Back 29

the main advantage of a repeated measures study is that it uses the same individuals in all treatment conditions.

-some advantages are.....
1. the repeated measures design typically requires fewer subjects than an independent measures design
2. A researcher can better study and observe behaviors that change or develop over time
3. It reduces or eliminates problems caused by individual diff. such as IQ, age, gender, etc.

Front 30

Under what circumstances do you use the dependent measures t test?

Back 30

You use this when there is one group of subjects that are being tested with two different conditions.

Front 31

What is the diff between the repeated measures and matched subjects design?

Back 31

The repeated measures design uses the same subjects in all treatment conditions.
-The matched subjects design tries to match subjects so that they are close to equivalent with respect to a specific variable that the researcher would like to control.
*The problem with this is that the more variables you try and control the less likely it is that you will find subjects that fit the criteria*

Front 32

Under what circumstances should you avoid using the dependent measures t-test?

Back 32

The primary disadvantage of this design is that it allows time related factors and order effects to change the participants score from one treatment to the next.
- You should NOT use a repeated measures design if there is any reason to expect strong time-related effects or strong order effects. Your best strategy would be to use and Independent measures design (or matched-subjects) so each individual participates in only one treatment and is measured only one time.

Front 33

How do you compute df for a dependent measures test?

Back 33

you only have one group of subjects so its only (n-1)

*n refers to the number of D scores, not the number of x scores. (D scores being the difference between the x scores of each sample)*