# T-Test

Significance Testing : Meaning
You have a sample data and you are asked to assess the credibility of a statement about population. Statistical significance evaluates the likelihood that an observed difference is due to chance.

It deals with the following question :

If we selected many samples from the same population, would we still find the same relationship between these two variables in every sample? Or is our finding due only to random chance?

Independent T-Test
The independent t test evaluates whether the means for two independent groups are significantly different from each other. It is used for just 2 groups of samples. If you have more than 2 groups of samples, you should use ANOVA.

Assumptions

1. Each score is sampled independently and randomly.
2. The scores are normally distributed within each of the two groups.
3. The variance in each of the groups is equal.

Case Study
How powerful are rumors? Frequently, students ask friends and/or look at instructor evaluations to decide if a class is worth taking. Kelley (1950) found that instructor reputation has a profound impact on actual teaching ratings.  [Source : Journal of Personality, 18, 431-439]

Experimental Design
Before viewing the lecture, students were given a summary of the instructors prior teaching evaluations.

There were two types of instructors : Charismatic instructor and Punitive instructor.

Null Hypothesis
It is a statement that you want to test. It usually states that there is no relationship between the two variables.

In this case, the null hypothesis states that there is no difference between the mean ratings of the charismatic-teacher-reputation condition and the punitive-teacher-reputation condition.

Alternate Hypothesis
It is contrary to the null hypothesis. It usually states that there is a relationship between the two variables.

In this case, the alternate hypothesis states that there is a difference between the mean ratings of the charismatic-teacher-reputation condition and the punitive-teacher-reputation condition.

Type I and II Errors

 Hypothesis Testing : Type I and II Errors

Interpretation
An independent-samples t-test was used to test the difference between the mean ratings of the charismatic-teacher-reputation condition and the punitive-teacher-reputation condition. The output from SPSS is shown below

Assumption Check

The columns labeled “Levene’s Test for Equality of Variances” tell us whether an assumption of the t-test has been met. The t-test assumes that the variance in each of the groups is approximately equal.

Look at the column labeled “Sig.” under the heading “Levene’s Test for Equality of Variances”. In this example, the significance (p value) of Levene’s test is .880. If this value is less than or equal to 5% level of significance (.05), then you can reject the null hypothesis that the variability of the two groups is equal, implying that the variances are unequal.

If the significance (p value) of Levene’s test is less than or equal to 5% level of significance (.05), then you should use the bottom row of the output (the row labeled “Equal variances not assumed”)

If the significance (p value) of Levene’s test is greater than 5% level of significance (.05), then you should use the middle row of the output (the row labeled “Equal variances assumed”)

In this example, .880 is larger than 0.05, so we will assume that the variances are equal and we will use the middle row of the output.
Conclusion

The column labeled “Sig. (2-tailed)” gives the two-tailed p value associated with the test. In this example, the p value is .018.

Since p-value .018 is less than .05, so we reject null hypothesis. That implies that there is a significant difference between the mean ratings of the charismatic-teacher-reputation condition and the punitive-teacher-reputation condition.