Testing
In Hypothesis this module, we will discuss how to do the t-test using Excel for one, two, and paired sample experiments. We'll also describe how sample size, the population mean under the alternative hypothesis, and significance level affect Type I and Type II errors, and power. OPTIONS 1 = One sample t-Test 2 = Two sample t-Test
PAIR= Paired t-Test ERROR= Type I and Type II errors (using standard Normal instead of t) POWER= Power Curves (using standard Normal instead of t)
One Sample t-Test
Excel does not have a one-sample t-test function. In the example below, you will go through the steps of performing this test. EXAMPLE: An experiment is performed to see if dietary chromium has an effect on the activity level of the liver enzyme GITH in rats. Fourteen rats were fed special low-chromium diets, and the activity level of this enzyme was measured for each rat (shown in column A below). It is believed that this level follows a Normal distribution.
Low Cr Diet 42.3 51.5 53.7 48.0 56.0 55.7 54.8 52.8 51.3 58.5 55.4 38.3 54.1 52.1
Suppose we know that rats on a regular diet have a mean level of 0 = 53.2. We wish to test, for rats on the low chromium diet, whether this mean is different. In terms of the hypotheses, H0: =53.2 vs. HA: 53.2. In the box below, calculate the values for the test. The functions and values indicated to the right are hints. n 0 mean s SE t df p-value crit. val. COUNT 53.2 AVERAGE STDEV use D21 and SQRT(D18) use D20, D19, and D22 D18-1 TDIST(ABS(D23), D24, 2) 0.05 TINV(D26, D24)
Based on the p-value or critical value, what decision do you make? What is your scientific conclusion? Next construct a 95% confidence interval for the true mean . Use the numbers you calculated above, and note that the value of t.025 required is the same as the critical value used for the test. Is 0 in the confidence interval? Confidence Interval lower upper D20-D27*D22 D20+D27*D22
As with any t-test, it is important to make sure that the data are not severely skewed or that there is an unusual observation that may affect the results. Thus, a histogram, boxplot, or Normal QQ-plot would be appropriate.
steps of performing this
is an unusual appropriate.
Two-Sample t-Test
For the two-independent-sample, one can do the calculations step by step or else one can use the t-test procedures available in Data Analysis. We will do the analysis both ways here. EXAMPLE: Now suppose that we do not know the activity level of the enzyme in rats fed a normal diet. Ten additional rats are fed a normal diet, and their levels are measured and are shown next to the low chromium diet results. If we let 1 refer to the mean level for the low-Cr rats, and 2 refer to the mean level for the normal rats, the hypotheses are H0: 1=2 vs HA: 1 2.
Liver Enzyme Activity Low Cr Normal 42.3 53.1 51.5 50.7 53.7 55.8 48.0 55.1 56.0 47.5 55.7 53.6 54.8 47.8 52.8 61.8 51.3 52.6 58.5 53.7 55.4 38.3 54.1 52.1
In the box below, calculate the values for the test. The functions and values indicated to the right are hints.
Low Cr n mean s SE SS df pooled SE t p-value alpha crit. val.
Normal COUNT AVERAGE STDEV use s and n from rows 21 and 19, and SQRT DEVSQ (the complicated formula--filled for you) SQRT((D23+E23)/(D19+E19-2)*(1/D19+1/E19)) (D20-E20)/D25 TDIST(ABS(D26), D24, 2) 0.05 TINV(D28, D24)
#DIV/0!
Based on the p-value, what decision do you make? What is your scientific conclusion? Note that we used pooled SE because we think variability in all rats is similar. Next construct a 95% confidence interval for the true mean difference 1-2. Use the numbers you calculated above, and note that the value of t.025 required is the same as the critical value ...
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