Week 9, Inferential Statistics:
t-tests & correlations.
Lecture notes
Key topics:
- Plato's Cave and the approximation of reality by science.
- Descriptive v. "inferential" statistics
- The central limit theorem and sampling distributions
- t test, critical ratio, and statistical significance.
- Correlations and assessing shared variance
This week we will discuss the t-test and correlation coefficient. Along the way we will learn a set of basic statistical concepts, some of which are cited in italics here.
Lecture notes: Statistics notes # 2
Readings
Chapter 5 and readings on interpreting “relative risk” statistics, and interpreting data about risks + benefits of mammography .
Discussion group Assignment
(Click for a Word copy of Week 12 assignment).
Calculate a t-test, begin writing your Research Paper results section.
Your assignment this week is to compute a t-ratio by hand, and answer some questions about it on the next page. You will use the formula from class & class notes, or you can use the formula from the text.
By now, you have written your introduction and overall research design. You
must do an experiment where you compare two groups, not a measurement / correlational
study.
We have made up two data sets you can use for your paper (the second is below;
you can also make up your own data set if you like). Each data set gives 20
scores, representing 10 participants in each of two groups (experimental &
control group). You should use a t-test to analyze the difference between
these groups.
For next week, you will complete the results section for your paper, so begin
working on that now; look at the paper assignment for guidance.
This (completely made up) data set tests the effect of self-confidence training (the Independent Variable) on Fear and Loathing of Statistics, the Dependent Variable.
The results compare an experimental group – who got statistical self-confidence training before class – to a control group, who got a “placebo” condition that had nothing to do with self-confidence.
The hypothesis is that participants who got the self-confidence training will show less Fear and Loathing of Statistics than students who got class as usual.
Steps: (Answer each item; show your work and, if you are using your own data, include a data table).
Derive a t value for the difference between groups. Use the example from the class notes to see how to derive the numbers you need for the formula (or the book formula).
Derive your degrees of freedom [df]; df = (ngroup1 - 1)+(ngroup2 - 1).
Decide what your criteria will be for statistically significance [alpha value]; usually this is p < .05.
Find the value on the t table given here that corresponds to your df, at your alpha. This is the critical value that your t must be over to be considered statistically significant.
Compare your t to the critical value, using the absolute value of t;
- Draw a line (labeled ‘a’) where the critical value would be if df = 120.
- Draw line ‘b’ where your critical value is, given your df. (The central limit theorem tells you to assume more error (a more "flat" distribution) as your df go down).
- Draw line ‘c’ where your t value came out as.
- Is your value statistically significantly greater than 0?
- Was the hypothesis supported?
The Central Limit Theorum & Normal Distribution Click here for a movie showing a quinconx device and briefly explaining the binomial distribution and the normal distribution. Click the image for the very cool (to stats types...) quinconx progam
illustrating the Central
Limit Theorum. that I will discuss in class. (You
may have to download it then open it). |
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