One-sample t test

In clinical trial analyses you may want to test the mean for a single population to determine if that value differs from a hypothesized value. For example, let s say that you have the lab test value LDL and you want to know if the change-from-baseline value is significantly different from zero. There are several ways to perform this test in SAS. If you assume the change from baseline for LDL, ldl change, is normally distributed, you can run a one-sample t-test in SAS like this ... 

The example we jnst looked at is called one-sample t-test. It compares the mean of analytical resnlts with a stated valne. This is a typical analytical question. The problem may be two-tailed as in onr example, where it doesn t matter, if the analytical valne is biased to the one or the other direction. Or the question conld be one-tailed, e.g. if we want to know whether the copper content analysed in an alloy is below the specificatioa... 

In this test the calculations are not done with the data itself, but with the differences between the two methods/ laboratories. These differences are tested for a significant difference from zero with a one-sample t-test. 

A one-sample t-test is applied on the differences to decide whether the mean difference is significantly different from zero... 

The paired t-test also known as the one-sample t-test was also developed by Cosset. This test is primarily used for the analysis of data arising from within-patient designs, although we also see it applied when comparing a baseline value with a final value within the same treatment group. 

The one-sample t test can be used to test for systematic errors in the analytical method for a standard material with a knownconcentration po (Ho = p = Po vs Hi = p Po), or to verify if the changes in the elaboration process of a certain product affect the previous concentration po of a compound (Ho = p = Po vs Hi = p > Po) (Massart et al. 1990 Miller and Miller 2000 Martfn-Alvarez 2000, 2006). Table 13.1 shows the results of the one-sample t test... 

Table 13.1 Results of the one-sample t test for 15 replicate values from a new analytical method for a standard material with known concentration of 0.34 pg (Massart et al. 1990)...

Test significance of resnlt by means of a one-sample t test against an expected random average of five correct choices. 

Next, concentrate on the attractiveness of the odors If equally attractive, the animals would spend a proportion of 0.5 on each side. In a one-sample t test, compare the measured proportion of time against that mean of 0.5. 

X 0.005). We, instead, accept the alternative hypothesis that the QC specimen appears to have been prepared to contain a drug concentration different than 200ng/ml. This is an example of a one-sample t-test. 

The use of this method, the one-sample t test, is appropriate when ... 

The one-sample t test will be used to test the null hypothesis. As there are 10 observations and assuming the change scores (the random variable of interest) are normally distributed, the test statistic will follow a t distribution with 9 df. A table of critical values for the t distribution (Appendix 2) will inform us that the two-sided critical region is defined as t < -2.26 and t > 2.26 - that is, under the null hypothesis, the probability of observing a t value < -2.26 is 0.025 and the probability of observing a t value > 2.26 is 0.025. 

The one-sample t test is being used for a two-sided test of the null hypothesis, Hq. g = 0. For each of the following scenarios, define the rejection region for the test ... 

Independent (two) sample t tests, paired-sample t tests, one sample t tests One-Way ANOVA... 

T-Test n Also known as the Student s T-Testis a hypothesis test as to the validity of the sample that was taken from a population with mean, po of a normally distributed random variable, X, (the one-sample t-test), the equivalence of the means of two samples (the two-sample t-test), or the equivalence of the means of the same measurement made under different conditions on the same sample, where each unit is measured under both conditions (the paired sample t-test). 

For the one-sample t-test the null hypothesis is that the mean, p, of X for the population from which the sample was selected is equal to po The test is performed by choosing a significance level, ot, and calculating using the t-distribution the critical values on both tails needed to give a critical region whose volume is equal to a. This is the two-sided test version of the one-sample t-test. The use of slightly different null hypotheses of p > po or p < Po leads to one-sided test versions of the one-sample t-test. 

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