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Two-sample f-tests

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. [Pg.257]

Statistical hypothesis testing requires the formulation of a so-called null hypothesis H0 that should be tested, and an alternative hypothesis H which expresses the alternative. In most cases there are several alternatives, but the alternative to test has to be fixed. For example, if two distributions have to be tested for equality of the means, the alternative could be unequal means, or that one mean is smaller/larger than the other one. For simplicity we will only state the null hypothesis in this overview below but not the alternative hypothesis. For the example of testing for equality of the means of two random samples xl and x2 the R command for the two-sample f-test is... [Pg.36]

Coming back to the example of the two-sample f-test and R, all results can be saved in an R object, for instance, named result from which particular results can be extracted as follows ... [Pg.36]

Some tests that are widely used in univariate statistics are listed here together with hints for their use within R and the necessary requirements, but without any mathematical treatment. In multivariate statistics these tests are rarely applied to single variables but often to latent variables for instance, a discriminant variable can be defined via a two-sample f-test. [Pg.37]

The first experimental design we are going to consider involves the measurement of the same end-point in two groups of people, rats, tablets (or whatever). We calculate the mean value of the end-point in each group and then want to test whether there is convincing evidence of a difference between the two mean values. The procedure we use is a two-sample f-test, the term two-sample reflecting the fact that we are comparing two distinct samples of individuals. [Pg.68]

Table 6.2 Generic output from a two-sample f-test comparing theophylline clearances in rifampicin treated and control subjects... Table 6.2 Generic output from a two-sample f-test comparing theophylline clearances in rifampicin treated and control subjects...
Figure 6.5 General interpretation of the results of a two-sample f-test... Figure 6.5 General interpretation of the results of a two-sample f-test...
The two-sample f-test takes account of the apparent size of the experimental effect, the SDs of the samples and the sample sizes. It then combines all of these to determine whether the data are statistically significant. [Pg.78]

The two-sample f-test is robust, i.e. it will still function reasonably well with samples that are somewhat non-normally distributed. However, where data is severely nonnormal, even this test will start to produce inappropriate conclusions. In that case, either transform the data to normality or use a non-parametric test. [Pg.80]

We have met our first hypothesis test .The two-sample f-test is used to determine whether two samples have produced convincingly different mean values or whether the difference is small enough to be explained away as random sampling error. The data in each sample are assumed to be from populations that followed normal distributions and had equal SDs. [Pg.80]

The design of all experiments should involve a rational calculation of how large the samples need to be. For an experiment that will be analysed by a two-sample f-test, the main influences upon necessary sample size are ... [Pg.101]

Figure 6.9 showed the interplay between various factors in the outcome of a two-sample f-test. Two of these factors were the extent of the difference observed and the sample sizes. It is perfectly possible for a study to produce a statistically significant outcome even where the difference is very small, so long as the sample size is correspondingly large. In principal, there is no lower limit to the size of experimental effect that could be detected, if we were prepared to perform a big enough experiment. However, this can cause problems, as the next example demonstrates. [Pg.104]

This is summarised in Figure 12.3. The logic is very similar to that for the two-sample f-test, with one crucial difference. For a two-sample f-test, the variability that has to be considered is that among the two sets of weighings (the first two columns of data in Table 12.1). With a paired f-test, what matters is the variability among the individual weight changes (final column of Table 12.1). Therefore, with a paired f-test, the initial... [Pg.138]

General statistical methods such as sample size estimation, determination of practical significance and one-sided testing can be applied to the paired f-test in the same manner that we have already seen for the two-sample f-test. [Pg.144]

With f-tests, we can compare two sets of data. There are other experimental designs which will require a comparison of more than two sets of data and that is when we need an analysis of variance (AoV or ANOVA). Traditional statistics books always get their knickers in a frightful twist trying to explain ANOVAs. It is difficult to imagine why, because they are actually quite minor extensions of the two-sample f-test. [Pg.146]

Figure 13.1 shows that the application of a one-way ANOVA to this data is only a minor extension of what we already did with the rifampicin/theophylline clearances and a two-sample f-test. [Pg.148]

With most statistics packages, data that are to be subjected to a one-way analysis of variance are entered into two columns in a similar way to that seen with a two-sample f-test (Section 6.8). One column contains a series of codes indicating what catalyst was used and the other column contains the corresponding experimental results. In the first five rows, the results are labelled as being due to the use of platinum (Pt), the next five are due to palladium (Pd) and so on. The general appearance will be as in Table 13.2. [Pg.150]

The requirements are similar to those for the two-sample f-test. Each set of data should be drawn from a normally distributed population and they should all have the... [Pg.155]

If we were just to ignore this non-normality and perform a two-sample f-test on the raw data, the results would include a P value of 0.115, indicating a lack of statistical significance. However, we would be very unwise simply to accept this negative result, given that the test used is not appropriate for highly skewed data. [Pg.224]

We can try to find a mathematical transformation of the data that shows a better approximation to a normal distribution. With positive skew, either a square-root or a log transform may be useful. With this data, the square-root transform is insufficiently powerful and the data remain distinctly skewed. The results of the more powerful log transform are presented in Table 17.1 and Figure 17.2(b). The latter shows that the distribution for the smokers data is now much more symmetrical. The effect on the non-smokers data is not shown but is also satisfactory. We would then perform a standard two sample f-test, but apply it to the last two columns in Table 17.1. Generic output is shown in Table 17.2. [Pg.226]

Table 17.2 Generic output for a two-sample f-test comparing the logs of the amounts of toxic metabolite produced by smokers and non-smokers (last two columns of Table 17.1)... Table 17.2 Generic output for a two-sample f-test comparing the logs of the amounts of toxic metabolite produced by smokers and non-smokers (last two columns of Table 17.1)...
Instead of transforming the data to normality, we could employ one of a range of procedures referred to as non-parametric tests . These partially duplicate the functionality of tests we have already met, but use a method of calculation that does not depend upon a normal distribution. The non-parametric test that is generally substituted for the two sample f-test goes by a variety of names, but is most commonly called the Mann-Whitney test. [Pg.228]

The Wilcoxon rank-sum test is a nonparametric test for assessing whether two samples of measurements come from the same distribution. That is, as an alternative to the two-sample f-test, this test can be used to discover differentially expressed candidates under two conditions. For example, again consider the measurements of the probe set used for the two-sample t-test. The gene expression values are 12.79, 12.53, and 12.46 for the naive condition and 11.12, 10.77, and 11.38 for the 48-h activated condition. Measurement 12.79 has rank 6, measurement 12.53 has 5, and measurement 12.46 has rank 4. The rank sum of the naive condition is 6 -I- 5 -I-4=15. Then after the sum is subtracted by ni(ni-I-l)/2 = 3 x 4/2 = 6, the Wilcoxon rank-sum test statistic becomes 9. Considering all of the combinations of the three measurements, we can compute the probability that the rank sum happens more extremely than 9. The probability becomes its p-value. This is the most extreme among the 20 combinations thus the p-value is 2 x Pr( W > 9) = 2 x = 0.1 for the two-sided test. It is hard to say that the probe set is differentially expressed since the p-value 0.1 > 0.05. This test is also called the Mann - Whitney- Wilcoxon test because this test was proposed initially by Wilcoxon for equal sample sizes and extended to arbitrary sample sizes by Mann and Whitney. As a nonparametric alternative to the paired t-test for the two related samples, the Wilcoxon signed-rank test can be used. The statistic is computed by ordering absolute values of differences of paired samples. For example, consider a peptide in the platelet study data. Their differences for each... [Pg.75]


See other pages where Two-sample f-tests is mentioned: [Pg.110]    [Pg.215]    [Pg.70]    [Pg.72]    [Pg.73]    [Pg.80]    [Pg.108]    [Pg.116]    [Pg.122]    [Pg.125]    [Pg.144]    [Pg.148]    [Pg.228]    [Pg.303]    [Pg.295]   
See also in sourсe #XX -- [ Pg.257 ]




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F-test

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Sampling testing

Test sample

Two-sample

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