Independent samples t-test

Independent samples t-tests were conducted to determine whether there was a... 

Individual quiz questions were looked at in detail in semester 2, 2005 to determine whether there were differences in performance between the P and N groups for particular questions. After conducting a series of independent samples t-tests, no significant differences were found between the P and N groups. 

In semester 2, 2005, independent samples t-tests confirmed that NESB students in the P group performed significantly better than students in the N group for El 8 = -2.350, p = 0.021, es = 0.45). This was the only significant difference found when investigating language background. 

In semester 1, 2008, the quiz marks of all students in a course who completed either all P or all N online modules were summed to produce a total mark for the common modules that students in all courses completed. A further total tnark 1901, included the marks for E12 that only the Cheml901 students completed, while total mark 1001 and total mark 1101 included the marks for Wl that only the CHEMlOOl and ChemllOl students completed. Independent samples t-tests were conducted to determine whether there was a difference in academic performance between students who completed the P or N versions of the online chemistry modules. The results are summarized in Table 1. 

Independent samples t-tests were conducted to determine whether there was a difference in academic performance of BC smdents who completed the P or N versions of the stoichiometry online chemistry module. No significant difference in quiz performance was found (Z, = -1.40, p = 0.206). 

As for the large group, independent samples t-tests were conducted to determine whether there were differences in quiz performance between students in the small group who completed the P or N version for the modules. No significant differences were found for E18 (Z = -1.393, p = 0.173) or E21 (Z j = 0.000, p = 1.000). Furthermore, independent samples t-tests also showed that there were no differences in performance of students in the P and N groups for the additional retention (Z = 1.173, p = 0.249) and transfer (z = 0.793, p = 0.434) tests. 

In what follows we shall assume that the sample size is going to be determined as a function of the other factors. We shall take the example of a two-arm parallel-group trial comparing an active treatment with a placebo for which the outcome measure of interest is continuous and will be assumed to be Normally distributed. It is assumed that analysis will take place using a frequentist approach and via the two independent-samples t-test. A formula for sample size determination will be presented. No attempt will be made to derive it. Instead we shall show that it behaves in an intuitively reasonable manner. 

Moreover, independent-samples t tests indicated that the foreign pilots had higher scores on flight workloads as compared to those of Taiwanese (t = -3.87, p <. 001). In contrast, Taiwanese pilots demonstrated more stress on interpersonal relationships (t = 6.02, p <. 001) than foreign pilots (Fignre 6.2). 

Independent-samples t tests suggested that local and foreign pilots displayed different reactions on all of these measures while experiencing a stressful situation (all p values were less than. 001) (Figure 6.3). Obviously, Taiwanese pilots tended to have stronger reactions than foreign pilots. However, both Taiwanese and foreign pilots demonstrated seriously poor concentration when they were in a stressful condition (mean = 3.50, SD =. 68). 

Moreover, descriptive statistics demonstrated that these civil pilots had the highest mean scores on job ability (mean = 4.05, SD =. 54), and the lowest mean scores on achievement at work (mean = 3.21, SD =.76). Independent-samples t tests showed that Taiwanese and foreign pilots both believed that they were very professional (job abihty) and had very good relationships with their co-woikers (good peer relationship). However, it was of interest to note that Taiwanese pilots even felt better about achievement at woik (t = 6.50, p <. 001) and good peer relationship (t = 3.66, p <. 001) than did foreign pilots. TTiese results were shown in Figure 6.5. 

Interval Independent sample t-test Paired sample t-test... 

Independent sample t-test Wilcoxon Rank Sum Test Wald-Wolfowitz runs test Kolmogorov-Smimov two sample test Paired sample t-test Wilcoxon Signed Rank Test... 

The mean time over the four trials was calculated, while the standard deviation (SD) of each participant was used as the variability indicator. Lower mean SD values indicated less variability between trials. Independent samples t-test and Pearson product moment correlation were used to compare group score and identify relationships, respectively. Significance level was set at p<.05. 

Independent samples t-test was carried out to determine the significant differences in dieletric constant, loss factor and loss tangent across the groups. 

Survey analysis was conducted after site visits. Data were first cleaned to remove invahd data entries and missing data. Descriptive analysis computed item means and standard deviations by gender and ethnicity for the sample. In addition, independent sample t-tests and chi-square tests by gender and ethnicity were conducted. These tests determined the extent to which men and women as well as White, Black, and Hispanic students differed from each other in their survey responses. We conducted separate descriptive statistics both for lower division (freshman and sophomore) and upper division (junior and senior) students. This distinction is important because we expect perceptions among these students to differ. Freshmen take a wide variety of courses, most from outside the engineering college, while seniors take courses primarily from a specific department. Moreover, seniors have more experience with the department than freshmen are likely to have and as a result their perceptions may be more accurate or reUable. Additional analyses estab-hshed the reliability and vahdity of individual survey items. Further analyses including factor analysis are explained in more detail in chapter five. 

In clinical trial analyses you may want to test the means of two independent populations to determine if they are significantly different. 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 after treatment between active chug and placebo. If you assume the change from baseline for LDL, ldl change, is normally distributed, you can run a two-sample t-test in SAS like this ... 

If we don t have one stated value, but two independent sets of data (e.g. two analytical results from different laboratories or methods) we have to use the two-sample t-test, because we have to consider the dispersion of both data sets. In the same way as above we have to look carefully, what our question is it may be two-tailed (are the results significantly different ) or one-tailed (is the result from method A significantly lower than that from method B )... 

More generally the test statistic is constructed as the signal/noise (signal-to-noise) ratio or something akin to this. We will develop this methodology in relation the comparison of two independent means for a between-patient design. The resulting test is known as the unpaired t-test or the two-sample t-test. 

Which statistical test was to be used for the comparison of the treatment groups in terms of the primary endpoint do you think This is a comparison between two independent groups in a parallel group trial and the primary endpoint is continuous so the sample size calculation will undoubtedly have been based on the two-sample t-test (although this is not specified). 

When comparing the means from two independent sampies we use the unpaired or two-sample t-test. If the numj)er of observations, means and standard deviations in the respective samples are nl, 1, si and n2, s2, then ... 

The sample mean is a poor measure of central tendency when the distribution is heavily skewed. Despite our best efforts at designing well-controlled clinical trials, the data that are generated do not always compare with the (deliberately chosen) tidy examples featured in this book. When we wish to make an inference about the difference in typical values among two or more independent populations, but the distributions of the random variables or outcomes are not reasonably symmetric, nonparametric methods are more appropriate. Unlike parametric methods such as the two-sample t test, nonparametric methods do not require any assumption about the shape of a distribution for them to be used in a valid manner. As the next analysis method illustrates, nonparametric methods do not rely directly on the value of the random variable. Rather, they make use of the rank order of the value of the random variable. 

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

One such method of determining significance is to perform a paired t-test, also known as a two-sample t-test. This test assumes that the data are independent and normally distributed. The value for t is the difference in means divided hy the square root of the sum of the square of the standard deviation of the first set divided by the number of tests and the sum of the square of the standard deviation of the first set divided by the number of tests. In the example. 

For the two-sample t-test the null hypothesis is that the mean of the population from which first sample was selected, Pj, and the mean of the population from which the second sample was selected, p, are equal. The test is performed by selecting a significance level, a, and calculating using the t-distribution random variable, T, with values, t, given by (assuming the two samples are independent and the two population distributions have the same variance) ... 

Statistical Methods. Means of treatment groups for plasma retention of BSP, plasma osmolality, total plasma protein concentration and urine flow rates were compared by students t test for independent sample means (17). Plasma enzyme activity data were converted to a quantal form and analyzed by the Fischer Exact Probability Test (18). Values greater than 2 standard deviations (P < 0.05) from the control value were chosen to indicate a positive response in treated fish. 

One uses ANOVA when comparing differences between three or more means. For two samples, the one-way ANOVA is the equivalent of the two-sample (unpaired) t test. The basic assumptions are (a) within each sample, the values are independent and identically normally distributed (i. e., they have the same mean and variance) (b) samples are independent of each other (c) the different samples are all assumed to come from populations having the same variance, thereby allowing for a pooled estimate of the variance and (d) for a multiple comparisons test of the sample means to be meaningful, the populations are viewed as fixed, meaning that the populations in the experiment include all those of interest. 

Having calculated the level of significance can be obtained from appropriate tables. The Wilcoxon signed rank test is the non-parametric equivalent of the paired t-test. The Kruskal-Wallis test is another rank sums test that is used to test the null hypothesis that k independent samples come from identical populations against the alternative that the means of the populations are unequal. It provides a non-parametric alternative to the one-way analysis of variance. 

If the volume values from treatment and control probes come, for example, from the same patient or, as in DICE experiments, from the same gel, then there is a dependency between the resulting values. Hence, the t-test for paired samples, which has even a higher statistical power than the t-test for independent samples, can be used here. The term power is explained below. For the paired t-test the difference d between the treatment and control value is used. 

Two independent methods of analysis have been used to analyse a sample of unknown composition. Is the difference between the two results significant and thus indicative of an error in one method Examine data for unreliable results. Establish that both sets have similar precisions by F-test. Apply T- test (equation (2.10))... 

If you can assume that your data are normally distributed, the main test for comparing two means from independent samples is Student s f-test (see Boxes 41.1 and 41.2, and Table 41.2). This assumes that the variances of the data sets are homogeneous. Tests based on the t-distribution are also available for comparing paired data or for comparing a sample mean with a chosen value. 

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