Two-Sample t Test

Statistics > Basic Statistics > 2-Sample t

 

Tests whether two samples from a normal distribution could have the same mean when the standard deviations are unknown but assumed to be equal.

Use Two-Sample t Test to perform a hypothesis test and compute a confidence interval of the difference between two population means when the population standard deviations, s's, are unknown. For a two-sided two-sample t

H0: µ1 - µ2 = µ0     versus     H1: µ1 - µ2 ≠ µ0

where µ1 and µ2 are the population means and µ0 is the hypothesized difference between the two population means.

Independent-Sample t-Test is used to test if two unrelated samples come from populations with the same mean. When you have dependent samples, use Two-Sample Paired t Test.

 

Dialog box items

Samples in one column:
Choose if the sample data are in a single column, differentiated by factor levels in a second column.

oSamples: Enter the columns containing the sample data.

oFactor and Levels: Enter the columns containing the sample factor, and select the levels.

Samples in different columns:
Choose if the data of the two samples are in separate columns.

oFirst Sample: Enter the column containing one sample.

oSecond Sample: Enter the column containing the other sample

Summarized data:
Choose if you have summary values for the sample size, mean, and standard deviation.

oFirst Sample

-Sample size: Enter the value for the sample size.

-Sample Mean: Enter the value for the sample mean.

-Sample Std Dev: Enter the value for the sample standard deviation.

oSecond Sample

-Sample size: Enter the value for the sample size.

-Sample Mean: Enter the value for the sample mean.

-Sample Std Dev: Enter the value for the sample standard deviation.

Report:
The display of outputs of VisualStat.

 

Data

Data can be entered in one of two ways:

Both samples in a single numeric column with another grouping column (called factor) to identify the population. The grouping column may be categorical, numeric or text.

Each sample in a separate numeric column.

The sample sizes do not need to be equal. Missing values are ignored.

 

Charts

Displays a histogram, a histogram with a normal curve, and a boxplot.

Histogram:
Choose to display a histogram for each variable

Histogram with Normal Curve:
Choose to display a histogram with a normal curve for each variable

Boxplot of data:
Choose to display a boxplot for each variable

Options:
Choose the options you want.

oExclude missing values: Check to excludes rows that have missing values.

oInverted Bar: Check to reverse the axes.

 

Options

Alternative Hypothesis:
Enter Two-sided, Upper One-sided, or Lower One-sided. If you choose an One-sided hypothesis test, an upper or lower confidence bound will be constructed, respectively, rather than a confidence interval.

Confidence Level:
Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.

 

Example

Results of an experiment to test whether directed reading activities in the classroom help elementary school students improve aspects of their reading ability. A treatment class of 21 third-grade students participated in these activities for eight weeks, and a control class of 23 third-graders followed the same curriculum without the activities. After the eight-week period, students in both classes took a Degree of Reading Power (DRP) test which measures the aspects of reading ability that the treatment is designed to improve.

Source: http://lib.stat.cmu.edu/DASL/Datafiles/DRPScores.html

1.Open the DataBook compare.vstz

2.Select the sheet DRP Scores

3.Choose the tab Statistics, the group Basic Statistics and the command 2-Sample t

4.Select group Samples in one column

5.In Response, select Response. In Factor, select Treatment.

6.Click OK

 

Report window output

 

Two-Sample t Test

 

Two-sample T-Test of difference = 0 vs not = 0

alternative hypothesis: true difference in means is not equal to 0

                                     N     Mean    StDev  SE Mean     Corr    95% Conf Interval        t  df  p-value  Alt Hypothesis

Response-Control - Response-Treated  44  -9.9545  14.5512   4.3919  -0.1907  [-18.8176; -1.0913]  -2.2666  42   0.0286          Accept

 

 

 

Interpreting the results

 

VisualStat gives a table of confidence interval for the difference in population means. For this example, a 95% confidence interval is [-18.8176; -1.0913] which excludes zero, thus suggesting that there is a difference. Next is the hypothesis test result. The test statistic is -2.2666, with p-value of 0.0286, and 42 degrees of freedom. Since the $$p-value$ is little than commonly chosen a-levels, there is a difference between treated class and control class.

 

 

 

See Also:


One-sample t Test | One-Way Analysis of Variance | Report | Numeric Formats

Web Resource: NIST e-Handbook of Statistical Methods, 2006 | Probability and statistics EBook