Statistics: t-test

No Significant Difference

param. pop1 pop2
mean: 3.75 3.00
variance: 1.00 1.00
pop size: 10.0 10.0

Significant Difference

param. pop1 pop2
mean: 4.00 3.00
variance: 1.00 1.00
pop size: 10.0 10.0

Role of Variance

param. pop1 pop2
mean: 4.00 3.00
variance: 2.00 1.00
pop size: 10.0 10.0

Role of Population Size

param. pop1 pop2
mean: 4.00 3.00
variance: 2.00 1.00
pop size: 20.0 20.0

Statistics: t-test

The t-test is employed when one wishes to determine if two samples have statistically different means. The t statistic is calculated as:

where the pooled variance, , is calculated as:

If t is greater than the critical value, then the two samples have statistically different means. The critical value can be determined given the sample sizes, the level of significance chosen (typically a = 0.05), and a critical value table.

Statistics: t-test

Adjust the means, variances, and sample sizes to the right:

Increasing the difference between the means of the samples will increase the t value; decreasing the difference will decrease the t value. Increasing the variance will decrease the t value, whereas decreasing the variance will increase the t value. Changing the population sizes will affect both the t value and the critical value.