TWO SAMPLE T-TEST

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For the yield variable, we want to compare the effects of one diet with the other. First investigate whether there is any difference between the mean yields of the cows on diet 1 and those on diet 2, i.e. whether diet has any effect.

The test for the difference is called the two-sample t-test. In Excel there are three two-sample t-tests, one for samples with unequal variance, one for samples with equal variance and a third for paired samples. The samples here are not paired and assume for the moment that the samples have unequal variances.

Select Tools > Data Analysis > t-test: Two sample assuming unequal variances from the menubar. output Insert the input range for each of the diets into the dialogue box (put the reference to the yield of the first 45 cows in variable 1 range and similarly highlight those on diet 2 for variable 2 range). Then select the output range and click OK. On the right, variable 1 is diet 1 and variable 2, diet 2.

A slightly more powerful test can be used if you can assume that the standard deviations are the same under both treatments. output
In Excel, this is done by selecting t-test: Two sample assuming equal variance in the Analysis ToolPak. For the milk data the results are almost identical since the variances of the two samples are very similar. In general, this test produces a smaller confidence interval for the difference in means, shown by the p-value i.e. P(T<=t) two-tail.

The Paired Two-Sample for Means t-test is used when there is a natural pairing of observations in the samples, for example, when a sample group is tested twice - before and after a treatment.

Read in the tobacco data. Selecting t-test: Paired Two-Sample for Means from the Data Analysis menu and entering Test1 and Test2 in the variable ranges gives the output on the right.

Next, read in the grass data to compare the different conditioned treatments for drytime. histograms Set up four columns labeled : noncond, machine1,machine2,machine3 and copy and paste the drytime data to each of these columns. (first 6 values under noncond, the next six under machine1, and so on).
Using the Histogram tool in the Analysis ToolPak plot a histogram for each of the four samples.

As it is a relatively small sample size assume a Normal distribution. You can test the pairs of treatments as before using t-test: two sample assuming equal variance. For example see right:

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Basic statistics in Excel   23.2.99   Page: 19 of 25