### 2 Sample T

## 2 Sample T,Sample T

Just like 1 Sample T, 2 sample T test is also used to verify if the process is having any centering related problems for continuous Y.

2 Sample T

Just like 1 Sample T, 2 sample T test is also used to verify if the process is having any centering related problems. It is a Mean based test where Y is continuous and X is Discreet. But here the similarity ends. 2 sample T test is used to make a comparison of Mean of 2 data sub-groups or populations. The 2 data sub-groups or populations must be independent. The resultant output shows if the mean of both populations or sub-groups is different or not.

Minitab Navigation -> Stat – Basic Stats – 2 sample T

Comparison within Sub-Groups

Select the first option by selecting Y in “samples” and Sub-groups in “Subscripts”

1

Two-Sample T-Test and CI: Total Breakage, Breakage Grading

Two-sample T for Total Breakage

Breakage

Grading N Mean StDev SE Mean

Bad 128 12.49 2.41 0.21

good 80 9.73 1.82 0.20

Difference = mu (Bad) – mu (good)

Estimate for difference: 2.764

95% CI for difference: (2.183, 3.345)

T-Test of difference = 0 (vs not =): T-Value = 9.39 P-Value = 0.000 DF = 198

Breakage Grading – Subgroups

N – Count of data subgroup wise

Mean – Mean of data subgroup wise

St Dev – SD of data subgroup wise

SE Mean: Standard Error of Mean of data subgroup wise

Difference = Difference within Subgroups

Estimate for differences – Gives the difference between both population mean

95% CI for difference: CI of Estimate for difference with 95% probability

T value – Helps in determination of P-value for T-test

P – P-value < 0.05 Alternate is true.i.e. Mean of first is not equal to mean of second

P-value ≤ 0.05 Null is True.i.e, Both means are equal.

DF – Degree of Freedom.

Comparison in between groups

Select the Second option by selecting first group in “First” and Second group in “Second”

2

The output is in the same form as shown above.

Comparison through Pre-Determined values

We can also compare the two populations or sub-groups if we have specific figures of Sample Count, Mean and Standard Deviation of both groups available. Just select the third option and give the values. Minitab gives the resultant output similar to the one given above.

Importance of Equal Variance Option

The lowest option in the window is “Assume Equal Variance”. Checking this option makes Minitab assume that both the groups have equal variance. The resultant output is very much different as shown below:

Output with option “Assume Equal Variance” selected

Two-sample T for Total Breakage

Breakage

Grading N Mean StDev SE Mean

Bad 128 12.49 2.41 0.21

good 80 9.73 1.82 0.20

Difference = mu (Bad) – mu (good)

Estimate for difference: 2.764

95% CI for difference: (2.146, 3.382)

T-Test of difference = 0 (vs not =): T-Value = 8.81 P-Value = 0.000 DF = 206

Both use Pooled StDev = 2.2002

Output with option “Assume Equal Variance” not selected

Two-Sample T-Test and CI: Total Breakage, Breakage Grading

Two-sample T for Total Breakage

Breakage

Grading N Mean StDev SE Mean

Bad 128 12.49 2.41 0.21

good 80 9.73 1.82 0.20

Difference = mu (Bad) – mu (good)

Estimate for difference: 2.764

95% CI for difference: (2.183, 3.345)

T-Test of difference = 0 (vs not =): T-Value = 9.39 P-Value = 0.000 DF = 198

The difference between both outputs is the “Pooled St Dev” value given above and the difference in the values of

1. 95% CI for Difference

2. T-value

3. DF

Other Options

1. There are several other options in Minitab for data analysis through 1 Sample T. We can give specific values also such as Mean, sample count and SD

2. As mentioned earlier, we can change the P-value also in Minitab present in the “Options”. It also has 3 options for Alternate:

a. Less Than: Gives the upper limit of the CI

b. Not Equal: Default option. Gives the CI

c. Greater Than: Gives the lower limit of the CI

These options can also be used by changing the 95% probability value of the CI and by comparing it against a target value

Graphical Representation

The output numerical data can also be represented in graphical manner. Minitab gives 3 options – we can use either one of them and even all of them also:

• Individual value plot

• Boxplot

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