Chapter 8 Independent Sample T-Test

Front 1

Independent Sample T-test

Back 1

We collect data from two independent samples
(control and experimental group)

Want to know if there's a difference between the sample means

Front 2

Assumptions of Test

Back 2

the populations standard deviation and variance are equivalent.
(group 1; SD and V = group 2; SD and V)

Front 3

Level of Measurement (independent samples t-test)

Back 3

WE GO BY THE GROUP LEVEL

Our sample is not dependent on each other, so we cannot go by the individual level

Front 4

Sampling distribution of the mean difference

Back 4

The mean is 0
SD = ?

Front 5

Pooled Variance

Back 5

Done if the sample means are not equivalent

Front 6

Degrees of Freedom

Back 6

Pooled as well

sample 1 + sample 2 - 2 = pooled DF

this gives us an estimate of their combined degrees of freedom

Front 7

Null and Alternative Hypothesis

Back 7

Null: Mu1 = Mu2
(we assume the two interdependent samples are equivalent)

Alt: Mu1 (doesn't equal) Mu2
(they may also be proven not to be equivalent)

Front 8

Standard error of the mean difference

Back 8

The pooled variance is divided by sample size 1 and 2, then added together and square rooted.

The variance square rooted gives us the Standard deviation of the two, or the standard error of the mean difference.

Front 9

T-value for mean difference

Back 9

subtract the means from each other, and divide that by the standard error of the mean difference.

This gives us the value that represents where we fall on the spectrum of the sample distribution of the mean difference (Mean = 0, SD = ?)

Front 10

critical value

Back 10

We give a 5% chance on a two tailed test as to whether were getting this wrong. If this value passes this critical value it means it a reasonable enough difference away from the (mean of the sample distribution of the mean difference (0)) to say that there was a difference between the two groups.

Front 11

T-table

Back 11

using the degrees of freedom you find out what the critical value is.

Front 12

Confidence Intervals

Back 12

Sample mean + t-crit (standard error)

Dif of Sample means - t crit (standard error)

You take these two values, and if the mean of the sample distribution of the mean difference (0) is not within those values, you can then reject the null.

Front 13

DATA (SAS)

Back 13

name of data set

Front 14

INPUT (SAS)

Back 14

gives variable names

Front 15

CARDS; put in data ; (SAS)

Back 15

gives data on card sheets next to each other

Front 16

PROC MEANS DATA = data_02;
VAR cog1 cog2 diff;
RUN; (SAS)

Back 16

looks at the means of your variables

Front 17

PROC TTEST DATA = data_02;
PAIRED cog1 * cog2;
RUN; (SAS)

Back 17

dependent samples t-test

mean difference and appropriate standard error immediately

Front 18

PROC TTEST DATA = data_02;
VAR diff;
RUN;
(SAS)

Back 18

One Sample t-test

compares difference to 0

Front 19

Pr > t
(SAS)

Back 19

significance value, probability of observing value greater than t-value

(if its greater than .05 we reject null)

Front 20

$ (SAS, AND R)

Back 20

tells SAS its a categorical variable

Front 21

PROC MEANS DATA = ex2;
CLASS group;
VAR score;
RUN;

(SAS)

Back 21

calculates means for both groups in independent samples t-test

Front 22

PROC TTEST DATA = ex2;
CLASS group;
VAR score;
RUN;

(SAS)

Back 22

tells you grouping variable and outcome variable score

tells you the results of independent samples ttest

Front 23

cog1 < -- c(data) (R)

Back 23

arranges data as column

Front 24

diff (cog1-cog2) (R)

Back 24

gives you difference

Front 25

summary diff (R)

Back 25

summary of dif

Front 26

sd diff (R)

Back 26

standard d of dif

Front 27

t.test(diff, mu=0) (R)

Back 27

one sample t-test

Front 28

t.test(cog2,cog1, paired=true) (R)

Back 28

dependent samples t-test

Front 29

t.test(score~group) (R)

Back 29

Independent sample t-test