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. 10-11). 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 S P is reasonable. The null assumption is equal variance holds. The significance is.137, more than.050, so we ll use S P, 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 H 0
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 Difference Mean 133.2 137.8-4.5 Standard 11.0 16.9 Devation 13.7 Sample Size 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.20.10.05.02.01.001 60 1.296 1.671 2.000 2.390 2.660 3.460 Against t= -2.59, we find.010 < p <.020.
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.