t-Test. Comparing Means From Two Sets of Data. Steps For Comparing Groups. Assumptions of t-Test. Dependent variables are interval or ratio. The population from which samples are drawn is normally distributed. Samples are randomly selected.
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Comparing Means From Two Sets of Data
Critical value of t(120) = 1.98, p = 0.05
Since our obtained t(98) = -1.36 is NOT greater than the critical value we ACCEPT the Null Hypothesis. The training had no effect upon shooting skill.
Note: The sign +/- of t does not matter.
Critical value t(40) = 2.201, p = 0.05
Since obtained t > critical t
We reject the Null and state that positive reinforcement significantly improves bowling ability.
When you have unequal numbers of subjects in each group the statistic uses a different equation to estimate the standard error of the differences between groups.
Critical value of t(16) = 2.120, p = .05. The groups are significantly different.
Note that the equation uses the correlation between pre and post samples.
The Dependent t-test is more powerful that the Independent Groups t-test.
The same subjects are in each group (DEPENDENT or PAIRED t-test).
Critical value t(29) = 2.045, p = 0.05
The groups ARE SIGNIFICANTLY Different.
Note: the correction formula adjusts the variance between groups. Since the same subjects are in each group you can expect less variance.
Repeated Measures experiments are more powerful than independent groups
Critical value of t(60) = 2.000, p = 0.05, so there is a significant difference. BUT DOES IT MEAN ANYTHING???
Type I Error: Stating that there is a difference when there isn’t.
Type II Error: Stating there is no difference when there is one.
From Table A.1 Zβ of .54 is 20.5%
20.5% + 50% = 70.5%
In this example Power (1 - β ) = 70.5%
Compute Sample Size N for a Power of .80 at p = 0.05
The area of Zβ must be 30% (50% + 30% = 80%) From Table A.1 Zβ = .84
If the Mean Difference is 5 and SD is 6 then 22.6 subjects would be required to have a power of .80
For an Independent t-Test you need a grouping variable to define the groups.
In this case the variable Group is defined as
1 = Active
2 = Passive
Use value labels in SPSS
Be sure to enter value labels.
Grouping variable GROUP, the level of measurement is Nominal.
Assumptions: Groups have equal variance [F = .513, p =.483, YOU DO NOT WANT THIS TO BE SIGNIFICANT. The groups have equal variance, you have not violated an assumption of t-statistic.
Are the groups different?
t(18) = .511, p = .615
2.28 is not different from 1.96
Is there a difference between pre & post?
t(9) = -4.881, p = .001
Yes, 4.7 is significantly different from 6.2