PSYC*1010 Chapter 9: Intro to the t Statistic Flashcards
When are t statistics used as a replacement for z-scores?
When the population standard deviation/variance is unknown
T or F: z-tests are more versatile than t-tests.
False. t-tests are more versatile.
When is estimated standard error used?
When population standard deviation/variance is unknown
What does the estimated standard error provide a measurement of?
An estimate of the standard distance between the sample mean and the population mean
How is estimated standard error denoted?
s (subscript M)
What is the difference between the t statistic formula and the z-score formula?
The structure is the same, but the t formula uses the notation for sample data rather than population parameters
What are degrees of freedom?
The number of scores in a sample that are independent and free to vary
Does an increase in degrees of freedom indicate an increase or a decrease in the sample’s ability to represent the population?
Increase
T or F: The greater the value of degrees of freedom, the better t will approximate the z-score.
True
What is a t distribution?
The complete set of t values computed for every possible random sample of a specific size
What determines how well a t distribution approximates a normal distribution?
Degrees of freedom/sample size
The distribution of sample means will create an almost perfectly normal distribution if one of what two criteria are met?
- n>30
- The samples were selected from a normal population
T or F: There is a different sampling distribution of t for each possible number of degrees of freedom.
True
Does the t distribution have more or less variability than a z-score distribution?
More
How do the shapes of a t distribution and normal z distribution tend to differ?
The t distribution tends to be flatter and more spread out, and a normal z distribution has more of a central peak
What is the main reason for the shape disparity in z and t distribution?
In the z formula, only the numerator varies between samples (denominator uses population parameters which are consistent for all sample sizes), but for the t formula both the numerator and denominator vary
What does it mean for t tables to be abridged?
They don’t include entries for every possible df value
How is the t value determined if the degrees of freedom aren’t listed in the table?
Look up the critical t for both surrounding values and use the larger value for t
What is a t statistic?
The difference between the sample mean (from data) and the population mean (hypothesized from H0), divided by the estimated standard error
What is the conclusion of a hypothesis test if the t statistic is larger (+ or -) than expected if H0 was true?
H0 is rejected
What is the conclusion of a hypothesis test if the t statistic is smaller (+ or -) than expected if H0 was true?
H0 fails to be rejected
What is the unknown population?
The population that exists after the treatment is administered
How is the null hypothesis obtained in a t test?
A theory, logical prediction, or simply wishful thinking
What are the two assumptions of a t test?
- The values in the sample consist of independent observations
- The population sampled is normal (or n>30)
What does it mean for two observations to be independent of each other?
If the occurrence of one has no effect on the probability of the second
T or F: The sample size and magnitude of variability both have a large effect on the t statistic.
True
Will a larger standard error produce a larger or smaller t statistic?
Smaller
What two factors determine the magnitude of standard error?
- Sample size
- Sample variance
Will a larger sample produce a larger or smaller standard error?
Smaller
Will a larger variance produce a larger or smaller standard error
Larger
Does an increase in percentage of confidence increase or decrease the value of t?
Increase
How does the size of a sample influence the confidence interval?
The bigger the sample, the smaller the interval
What are the two types of t tests?
- Independent-measures t-test (between subjects design)
- Repeated-measures t-test (within subjects design)
