# Two Means

#### Description

The red and blue points in this graph represent data from two samples of 10 values from each of two normally distributed populations. (Only the *x*-coordinates of the points are relevant.) You are interested in whether the means of the two distributions are significantly different.

The sketch shows a normal curve for two populations each with a mean and standard deviation corresponding to the mean and standard deviation of the two samples. The standard error (the standard deviation divided by the square root of the number in the sample) for each sample is shown as the half-width of a vertical rectangle. the *t* statistic and *p* value for an unpaired difference of means is shown.

#### Questions

- Press one of the hide buttons so that just one sample and distribution are shown. Drag one data point back and forth from left to right. Describe the effect on the normal curve of dragging the point when it is close to the mean as compared to when it is far from the mean. What does your observation say about whether the standard deviation is resistant to outlier effects?
- Select all of the red points, and drag one of the selected points. (This should have the effect of moving all the points at once.) Describe the effect that this has on the mean and standard deviation of the sample. Describe the effect on the
*p*value for the difference of means. Explain what you see. - What will be the effect on the
*p*value of dragging just one point far from the mean of its sample? Predict first! Explain what you observe.