Testing Two Samples

Returning to Figure 4-8, we want to know whether the mean values of the two sets of data are statistically the same or not. In the tools menu, select DATA analysis. In the window that appears, select t-Test Two-Sample Assuming Equal Variances. Click OK. The next window asks you in which cells the data are located. Write B5 B12 for Variable 1 and... 

Analysis of Rayleigh s Data t-Test Two-Sample Assuming Equal Variances ... 

The F test in Equation 4-12 told us that the standard deviations of Rayleigh s two experiments are different. Therefore, we can select the other t test found in the TOOLS menu in the DATA ANALYSIS choices. Select t-Test Two-Sample Assuming Unequal Variances and fill in the blanks exactly as before. Results based on Equations 4-8a and 4-9a are displayed in cells E15 to G26 of Figure 4-8. Just as we found in Section 4-3, the degrees of freedom are df =7 (cell F21) and Calculated = 21.7 (cell F22). Because Calculated s greater than the critical value of t (2.36 in cell F26), we reject the null hypothesis and conclude that the two means are significantly different. 

There are two basic test configurations. The first is a blind flange setup where the sample is clamped between a glass tube containing the liquid and a temperature-controlled heater. In this test, two samples can be tested under identical conditions. The second is a retaining cup clamped onto the sample. Figure 9.7 illustrates the two types of test cells. 

From the box, select / -Test or t-Test Two-Sample for Variances and click OK. 

For the first eight years that Chemistry and the Environment was offered, no formal laboratory was associated with the course. When the course did not have a formal laboratory, projects occasionally involved laboratory experiments or various types of field testing. Two sample projects are described below, and a listing of addition project topics with chemistry and civic connections appears in Table 2.3 as well as in previous publications.9,10... 

Anova Two-Fador WSh RepScation Anova Two-Fador Without RepTicatior Correlatim Covariance Descriptive Statistics E)g onential Sofioothing F-Test Two-Sample for Variances Focjfier Analysis... 

The brewer and his customer make a subjective assessment of beer flavour each time they taste but for a more objective appraisal it is usually desirable to submit the beer, with suitable controls, to a taste panel. Taste panels may be used to (/) select qualified judges, (//) correlate sensory with chemical and physical measurements, (Hi) study processing effects, maintain quality, evaluate raw material selection, establish storage stability, and reduce costs, (fv) evaluate quality, and (v) determine consumer reaction [Ij. The types of test used include (/) difference tests, (ii) rank order, (Hi) scoring tests, (iv) descriptive tests, (v) hedonic scaling, and (v/) acceptance and preference tests [1]. Difference tests are most commonly used in the brewing industry, the results of which are readily analysed by statistics. Several forms of difference test are used. The A-not-A form of test is perhaps the simplest. Assessors are first familiarized with a standard A and then presented, in a random manner, either with A again or with the comparative sample B. In the paired-comparison test two samples are presented simultaneously (AA, AB, BA, or BB) and assessors report either there is a difference or there is no difference . 

For Rayleigh s data in Figure 4-5, Fcaicuiated (cell B19) > F abie (cell B20) therefore the two standard deviations are different. In Data Analysis, select /-Test Two-Sample Assuming Unequal Variances and proceed as above with cell El6 for the output. We find 7 degrees of freedom in cell F23 and /calculated = 21.7 in cell F24, just as we found in the Example in Section 4.3. The critical value of / is 2.36 in cell F28, and the probability that the two means come from the same population is 1.12 X 10 in cell F27. We conclude that the two means are significantly different. 

Table 2.14 summarises the appropriate probabilities, critical values, and testing conditions for the different hypothesis cases. Testing two sample variances forms the foundation for various methods that can be used to compare different data subsets to determine their significance. 

In order to test two sample proportions, assume that a large number of samples has been taken, so that the normal approximation to the binomial distribution can be used. The null hypothesis can be written as Ho- fi=r2. 

Identify significant differences between genotypes/drug treatments using ANOVA, post hoc f-tests (two samples assuming equal variances). 

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