Join Yash Patel for an in-depth discussion in this video Scenario and context, part of SPSS for Academic Research.
- [Instructor] Imagine a situation in which you have paired observations. Your task it to determine whether the difference between these observations is significantly different from zero. This is a classic research scenario that most all early stat students encounter. First of all, what are paired observations? This is when the participants are either tested at two different time points, or under two different conditions on the same dependent variable. More than likely, you'll have to use this test to see if there are changes over time, or conditions between two related groups.
You can only have two time points for this particular test. There is usually some type of intervention between time point one and time point two. Here's how the design works. Essentially, you start off with all of the randomly selected participants. Then you measure the dependent variable at time point one and time point two. The participants do not change. The question that you want to answer is are the scores on the dependent variable different between the two time points? Is this difference statistically significant? In example of this is an instructional intervention where a pretest is given before the intervention, and a post test is given after.
If there is a significant difference between the two time points, there may be some use for the intervention. Analogously, you can use this type of test if you have a research design that wants to determine whether there are differences in the score of a dependent variable between two treatment conditions. That is, if you want to measure the same dependent variable under two different situations. For example, if you wanted to measure the difference in sprinters' 100 meter time after a carb supplement, or after a protein supplement, you can use a paired T test.
Please take note that participants have to be the exact same through both conditions. You may want to reduce bias caused by chronological order of the treatment conditions. For example, your sprinters may be tired from the carb sprint and may not do as well on the protein sprint. Or maybe there's some mental bias related to the supplement after trying it out, who knows? Anything could happen. A lot of things can change between the two conditions that aren't part of your experiment. So what you can do is break up sprinters into two groups.
These two groups have to be of equal size, so for instance, Group One and Group Two. You can then expose group one to Condition One and Group Two to Condition Two. Then you can expose Group One to Condition Two and Group Two to Condition One. You can then used a paired T test to determine whether the times are different between the two conditions. There are also other ways to use this test, but you don't really see the other ones as often, so I'm going to skip over them now for this beginner level course. I really like the sprint time for athletes example, so let's go with that one.
We'll use a sample size of 50 observations per condition, and construct a 95% confidence interval. We'll have the dependent variable of sprint time, and the factor of conditions with two treatments. The treatments are the carb supplement and the protein supplement. We'll imagine that measurements are taken in the same time frame that the supplements are ingested, or within about 30 minutes. With that information, let's move forward with the assumptions and hypotheses.
- Quantitative vs. qualitative analysis
- Sample size considerations
- Normal distribution
- Estimating the population mean
- One-sample t-test
- Paired-sample t-test
- One-way and two-way ANOVA
- Repeated measure ANOVA