SPSS on two independent samples.
Two sample test with proportions.
Paired t-test (with more SPSS)
State of the course address:
The Final exam is Aug 9, 3:30pm – 6:30pm in B9201 in the
Burnaby Campus. (One or two hallways off from AQ on the
north side)
After this chapter, there are two must-cover topics: Analysis of
Variance (ANOVA, Ch. 8) , and Correlation/Regression (Ch. 1011).
Unless there are objections, I’d like to do Ch.10-11 first to give
people time to master Ch.7 before continuing that stream.
SPSS and two samples, Part 1: Red cars go the fastest.
We have a sample of 42 blue cars are 26 red cars going down
Burnaby mountain in the afternoon, and we’re trying to see
the red cars do, in fact, go faster than the blue cars.
We’re comparing two means, so this is a two-sample test.
We’re interested in one particular side (greater), this is a onetailed test.
We have the data set red cars, we’ll use that to determine the
rest.
Independent t-test data needs to be all in a single column
(speed). A second column is used as a grouping variable
to tell SPSS which sample each car belongs to.
To do a two-sample t-test, go to Analyze  Compare
Means  Independent Samples T-Test…
Put the response (speed) into the Test Variable(s) section.
Put the grouping variable (colour) into the Grouping Variable
spot, and click Define Groups.
Type “Red” into one group, and “Blue” into the other.
Be very careful of speling and cApitalization. It has to be
exactly the same as the names in the grouping variable.
Then click Continue and click OK
SPSS outputs a large table. The first part is the results from
testing the assumption of equal variance. This is what
tells us if pooled standard deviation
SP is reasonable.
The null assumption is equal variance holds. The significance is
.137, more than .050, so we’ll use
SP, the top row results.
The middle part is the actual hypothesis test results.
The p-value is .207/2 = .1035, which is greater than .050, so we
fail to reject the null hypothesis. There is no evidence against
the idea that blue cars go just as fast as red ones.
The top row uses the assumption of equal variances. Note that
this row has more degrees of freedom.
The rest of the values like standard error could be affected
either way, but df will always be bigger with pooled variance.
The last part is the confidence interval approach to the same
problem.
We’re interested in the difference, and a difference of zero is
in this confidence interval, again we fail to reject to null
hypothesis that the difference is zero.
Computers: Wizardous or Lizardous?
SPSS and two samples, Part 2: Red cars are for girls.
If we have data in a 0-1 format, we can do two-sample t-tests
on proportions as well.
The last variable in the Red Cars dataset is Gender, meaning
the gender of the driver, it’s coded 0 for male and 1 for female.
We want to know if there if the proportion of red car drivers
that are female is different than the proportion of blue car
drivers that are female.
(Two-tailed, two-sample t-test)
Basically, we want to know if two proportions are the same.
1 is “how many of the red car drivers were female”.
2 is “how many of the blue car drivers were female”.
Use the same grouping variable, but move the variable
gender into the Test Variable(s).
Click OK.
Can we assume equal variance?
Significance = .812, which is larger than .050, so yes.
Use the top row again.
Is there a significant difference?
NOTE THE CORRECTION FROM “REJECT” TO “FAIL TO REJECT”
The p-value (significance) is .908. If there was no difference in
gender proportion between red and blue cars, we’d see this
.908 of the time. It’s more than .050, so we fail to reject H0
Uff, stats… so much work.
Paired tests.
In every example so far of two samples, the individuals in
sample 1 have nothing do with those in sample 2.
A given red car isn’t matched up to a given blue car for
comparison.
We call these independent samples.
Sometimes there’s a natural link between observations in one
group and observations in another.
Observations form pairs, so we call these paired samples.
Often we’re looking at the before and after responses of
subjects.
Each pair of observations comes from the same person or
object, but at different times.
Twin or sibling studies are popular in nature vs. nurture
debates.
Each pair of observations comes from the same family, but
a different sibling.
SPSS and two sample tests – Part 3.
Is there an historical difference in gas prices across Vancouver?
We have the monthly average gas prices for 62 months in
Burnaby, Coquitlam, and Delta.
We want to know, is there a difference betweeen Burnaby and
Coquitlam prices. (Two-tailed test)
Each pair of observations has a link: They come from the
same month.
A common link means a paired t-test is
appropriate.
Some of the variation is going to be due to factors beyond
Vancouver, like the season and global economics and politics,
that could affect gas prices.
Since many of the effects happen at the same time, we roll
them into a time variable (month). Using the time variable like
this is a common practice.
Gas Prices
Burnaby
Coquitlam
Mean
133.2
137.8
Standard
Devation
Sample Size
11.0
16.9
Difference
-4.5
13.7
62
62
62
In a paired test, we only care about the difference between the
raw scores.
Then we do a one-sample t-test on the differences against the
null hypothesis that the mean difference is zero.
D is just stands for difference. There’s nothing else on the
top because it’s D – 0.
This formula is exactly the same as the one-sample t-test,
against a null hypothesis of zero.
D could also be written
1
-
2.
Plugging in values gives us t-score -2.59.
Since we used a sample of 62 differences, the degrees of
freedom is 62 – 2 =61. For the textbook, 61 is rounded down
to 60.
The two-tailed critical values in the textbook at df=60 are…
df
60
.20
1.296
.10
1.671
.05
2.000
.02
2.390
Against t= -2.59, we find .010 < p < .020.
.01
2.660
.001
3.460
In SPSS, paired t-tests can only be done on data that’s in two
side-by-side columns.
To get a paired t-test, go to
Analyze  Compare Means  Paired-Samples T Test…
Then drag the paired variables into the same pair. (Order
doesn’t matter for getting significance) Click OK.
If you want to change the confidence interval, press the
options button, change it, then click Continue.
When you’re ready, click OK on the main pop-up.
(Same as with the other t-test interfaces)
The table we want is the Paired Samples Test
The results agree with our by-hand results (up to rounding
error).
t = -2.613 (similar to -2.59)
p = .011, which is between .010 and .020, as we found.
Assuming alpha = .05, we would reject the null hypothesis
(using either
t vs. t*
or
p-value vs. .05)
If there’s a link between observations in two groups, it’s
important to acknowledge them.
We control for some of the confounding variables this way.
There is a numerical relationship between the gas prices in one
part of the city and gas prices in other places at the same time.
An independent samples t-test assumes that there is no
relationship.
Comparing Coquitlam and Burnaby prices as if they were
independent samples, we lose significance.
Month-to-month effects like the seasons and global pressures
become extra noise / extra variation, so we lose significance.
Next class: Type I and Type II Errors
Chapter 7 Wrap-Up, extra examples.