PSYC1111 Study Guide - Final Guide: Statistical Hypothesis Testing, Stout, Statistical Parameter
t-Test Statistics
t-Test or Student’s t-test
• Developed in 1908 by William Sealy Gosset, a chemist working for the Guinnes
reery i Duli “tudet as his pe ae
• T-test was a cheap way to monitor the quality of stout
• The t-test was a cheap way to monitor the quality of stout
• The t-test work was published in the journal Biometrika in 1908 under the name
studet
Introduction
• Z-test is appropriate i situatios i hih oth the ea μ and the standard error
σ of the population mean are not known
• More common: the unknown population mean, z-test cannot be used
• Instead, t-test is used
o Very similar to z-test
o Does not require any knowledge of the population standard deviation
o Widely used in behavioral sciences
▪ Experiments involving a single sample
▪ Experiments involving two samples (or conditions)
The t Statistic
• Can be used to test hypotheses about completely unknown population
• All that is required for a hypothesis test with a t is a sample and a reasonable
hypothesis about the population mean
Example
• Do birds avoid moths with eye spot patterns?
• How long do they spend in cage with no eye-spot patterns
Hypotheses:
• H0: eye-spot patterns have no effect on the behavior of birds
• Therefore H0 = μ For the general hypothesis of moth-eating birds, the null hypothesis
states that μ = 30
Information we have:
• Hypothesis about the population mean (30 min)
• Sample size (16)
• Sample scores that produce a sample mean
The iforatio e do’t hae:
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• The population standard deviation σ (the information needed to calculate the
standard error for the sample mean
The steps for calculating single sample t-test:
1. Determine the hypothesised or population mean
2. Compute the sample mean
3. Compute the SS (sum of squares)
4. Compute the variance (S)
5. Compute the standard error of the mean
6. Compute t
7. Determine degrees of freedom (df)
8. Determine the critical value (i.e. significance level)
Example 2: Do infants prefer to look at attractive faces compared to less attractive faces?
• Newborns prefer to look at attractive faces
• Adults rated faces
• Testing time was 20 secs
• Results
o Average looking time 13 secs for attractive faces, SS=72
• Hypotheses
o Null hypothesis: M (attractive faces) = 10 sec
o Alternative hypothesis: M (attractive face) sec
Degrees of Freedom
• Monday you can wear 7 hats
• Tuesday you can wear only 1 of 6
• Constraint: estimation of the mean
• The sum of all values must equal n x mean (n = the number of values in the data set)
• If n = 10, the sum of the 10 values must equal the mean x 10
• If, for example, the mean of 10 values is 3.5, this constraint requires that the sum of
the 10 values must equal 10 x 3.5 = 35
• The first value in the data set is free to vary (whatever that value is, it still possible
for the sum of all 10 numbers to equal 35)
• Other 8 values can also vary
• The 10th value is not free to vary!
Degrees of Freedom
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