Ttest

The most widely used test is that for detecting a deviation of a test object from a standard by comparison of the means, the so-called t-test. Note that before a f-test is decided upon, the confidence level must be declared and a decision made about whether a one- or a two-sided test is to be performed. For details, see shortly. Three levels of complexity, a, b, and c, and subcases are distinguishable. (The necessary equations are assembled in Table 1.10 and are all included in program TTEST.)... 

Comment-. All models yield the same l-value, but differ in the number of degrees of freedom to be used. The difference between the means is barely significant in two cases. Suggestion acquire more data to settle the case. Program TTEST automatically picks the appropriate equation(s) and displays the result(s). Equation (1.21) is used to scan the parameter space (Xmean Sx, n) in the vicinity of the true values to determine whether a small change in experimental protocol (n) or measurement noise could have changed the interpretation from Hq to H or vice versa. 

Both cases are amenable to the same test, the distinction being a matter of the number of degrees of freedom/. The F-test is used in connection with the t-test. (See program TTEST.)... 

Purpose Display the type I error (a) and the type II error (/3) both as (hatched) areas in the ND(/iREp, Urep) and the ND(/ttest, test) distribution functions and as lines in the corresponding cumulative probability curves. 

This PROC TTEST runs a two-sample f-test to compare the LDL change-from-baseline means for active drug and placebo. ODS OUTPUT is used to send the p-values to a data set called pvalue and to send the test of equal mean variances to a data set called variance test. The final pvalue DATA step checks the test for unequal variances. If the test for unequal variances is significant at the alpha =. 05 level, then the mean variances are unequal and the unequal variances p-value is kept. If the test for unequal variances is insignificant, then the equal variances p-value is kept. The final pvalue data set contains the Probt variable, which is the p-value you want. 

Case 3. Paired ttest for Comparing Individual Differences... 

One man given 2.7 pg/kg became confused and developed hallucinations. The most common complaints of the other volunteers were of dry mouth, blurred vision, and drowsiness Several developed restlessness, an inability to sleep despite drowsiness, and anorexia. Of six men given 2.3 pg/kg, one had a decrease in performance in the Number Facility Test of more than 252, and three had dilated pupils. This dose Induced no tachycardia or hyperthermia. Of seven men given 2.7 pg/kg, five had decreased performance in the Number Facility Ttest of more chan 25%, three had dilated pupils, two had heart rates greater than 100 beats/mln, and one had a blood pressure above 140/90. There were no cases of hyperthermia (the report did not state the environmental conditions of the study). The mean heart rate after the larger dose was about 92 beats/min, whereas that after the smaller dose was about 79 beats/min. 

Spreadsheet Summary In the first exercise in Chapter 3 of Applications of Microsoft Excel in Analytical Chemistry, we use Excel to perform the t test for comparing two means assuming equal variances of the two data sets. We first manually calculate the value of t and compare it with the critical value obtained from Excel s function TINV(). We obtain the probability from Excel s TDIST() function. Then, we use Excel s built-in function TTEST() for the same test. Finally, we employ Excel s Analysis ToolPak to automate the t test with equal variances. 

There are times when the required assumptions for ANOVA, a parametric test, are not met. One example would be if the underlying distributions are non-normal. In these cases, nonparametric tests are very useful and informative. For example, we saw in Section 11.3 that a nonparametric analog to the two-sample ttest, Wilcoxon s rank sum test, makes use of the ranks of observations rather than the scores themselves. When a one-factor ANOVA is not appropriate in a particular case a corresponding nonparametric approach called the Kruskal-Wallis test can be used. This test is a hypothesis test of the location of (more than) two distributions. 

TTEST Calculates the probability associated with Student s t test VAR Calculates the variance of a series of numbers... 

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