t-tests Flashcards
(13 cards)
population and sample
We use inferential statistics, to predict population characteristics using limited data selected from the population
population (all of the individuals of interest) –> the sample is selected from the population –> sample (the individuals selected to participate in the research study) –> the results from the sample are generalized to the population
scales of measurement
Nominal data – nominal or categorical classification of data (e.g., sex categorized as male and female)
Ordinal data – data can be ordered but differences between values are not equal (e.g., movie or restaurant ratings)
Interval data – ordered, constant scale, but no natural zero (e.g., temperature, dates)
Ratio data – ordered, constant scale, natural zero (e.g., income, age, length)
variable requirements in a t-test
independent variable – nominal with TWO CATEGORIES
(ex: gender - m/f; groups -experimental/control)
dependent variable – interval or ratio
(ex: income, gpa, score on a test)
T-test can determine whether the mean scores on the dependent variable differ significantly between the two categories of the independent variable
t-test
a statistical procedure to compare two means
guinness and t-test
W.S. Gossett was Guinness brewery’s chemist who was charged to make sure that new batches of beer correspond to the Guinness’ standards
Gossett invented a new statistical test, the t-test, to compare each new batch to the company standards and published it under the pseudonym “a student” in 1908 (this is where student’s t-test comes from)
types of t-tests
single sample t-test
independent samples t-test
related samples t-test (matched t-test)
single sample t-test
used to compare a sample mean with a known population mean
ex:
sample - nyu psych majors
population - ny psych majors
independent variable - college
dependent variable - grades
obtain sample mean at NYU and compare to known population means of all of NY
null hypothesis - there is no difference between the grades of NYU psychology major students and other NY college psychology major students
independent samples t-test
used to compare two means from two independent samples
The members of one group do not include, and are not related to, the members of the other sample
example:
Massachusetts high schools vs ny high schoolers
independent variable - students’ location (mass vs ny)
dependent variable - SAT scores
2 independent samples, unrelated students from each state
null hypothesis - there is no difference between the average SAT score of massachusetts students and new york students
related samples t-test (matched t-test)
used to compare two means from related samples
The members of the two samples are either measured repeatedly or matched in terms of a certain characteristic
example:
APUG students performance on test before/after study session with professor
independent variable - students’ session (before and after)
dependent variable - test scores
measuring the group twice (before/after implementation)
null hypothesis – there is no difference between the performance on the test before the study session and after the study session
How do we determine which t-test to use when you have two means to compare?
do you know the population mean?
yes – single sample t-test
no – are the two samples
independent?
yes – independent
samples t-test
no -- related samples t-
test
Conducting a t-test: 5 steps
- Calculate the means of the two groups
- Calculate the standard error of the difference between the two means
- Find the calculated value of t
- Find the critical value of t from a table of t-values
- Determine whether the null hypothesis should be rejected by comparing the calculated value of t to the critical value of t
a. If the calculated value of t > critical value of t, reject the null hypothesis (i.e., there is a group difference!)
finding the critical value of t
Calculate the degrees of freedom = total number of participants minus the number of conditions
Specify the alpha-level, usually 0.05
Consult the critical values of t-table in appendix A-2
If the value obtained with the t-test is greater than the critical value of t then the difference is “statistically significant”
APA staples results section
The hands-on group scored higher (M=30.95, SD=5.45) than the lecture group (M=24.05, SD=6.18). This difference was significant, t(38) = -3.75, p<0.001
It appears that students who are taught by the hands-on method do better than students who are taught by the lecture method
