A review of inference concepts in .NET Encoder PDF-417 2d barcode in .NET A review of inference concepts

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A review of inference concepts generate, create pdf417 none on .net projects MS Word In the absence of syst Visual Studio .NET PDF 417 ematic differences between the sample means, the two mean squares will have the same expected value, and their ratio (the F-statistic) will be near 1. Systematic differences between the sample means will add extra variation into the treatment mean square, with no effect on the residual mean square, resulting in an expected F -statistic that is larger than 1.

In the output above, the F -statistic is 0.33, on 3 and 8 degrees of freedom, with p = 0.33.

There is no convincing indication that there are indeed differences among the treatment means. Interest then turns to teasing out the nature of those differences. The one-way analysis of variance formally tests whether the variation among the means is greater than what might occur simply because of the natural variation within each group.

This comparison is based on the F-statistic, which is given in the output column headed F value. An F-statistic that is much larger than 1 points to the conclusion that the means are different. The p-value is designed to assist this judgment.

Figure 4.6 is one of a number of graphical presentation possibilities for a one-way layout. Others are (1) a side-by-side comparison of the histograms but there are too few values for that; (2) density plots again there are too few values; and (3) a comparison of the boxplots this works quite well with 12 values for each treatment.

. 4.4.1 Multiple comparisons In Figure 4.6 we gave .net vs 2010 PDF-417 2d barcode two yardsticks the LSD and the HSD against which to compare differences between means.

Because neither of these suggested a difference between treatments, the choice between them was not of great consequence. Also, there were just three treatment levels, so that the difference between the LSD and the HSD is not large. The 5% HSD is designed so that, under the null model (no difference between treatments), the maximum difference will be greater than the HSD in 5% of experiments.

In other words, the 5% relates to an experiment-wise error rate, de ned as just described. The HSD is an appropriate yardstick against which to compare treatment differences if the demand is for a 5% or other speci ed probability of nding a difference between the largest and smallest means when there was no difference in the populations from which they were drawn. Contrast this with the 5% least signi cant difference (LSD).

This is designed, if used without a preliminary F -test, to give a 5% comparison-wise error rate. A reasonable practical strategy is to do a preliminary analysis of variance F -test. If that suggests differences between the means, then it is of interest to use both yardsticks in comparing them.

The LSD gives an anti-conservative yardstick, i.e., one that, in the absence of the preliminary F -test, would be somewhat biased towards nding differences.

Tukey s HSD gives a stricter conservative yardstick, i.e., one that is somewhat biased against nding differences.

Ignoring changes in degrees of freedom and possible associated changes in the standard error, the HSD will increase as the number of treatment groups that are to be compared increases.. Microarray data severe multiplicity Multiple tests are a s PDF-417 2d barcode for .NET erious issue in the analysis of microarray data, where an individual slide (or sometimes, as for Plate 2, half-slide) may yield information on some thousands. 4.4 One-way unstructured comparisons of genes. Each slide ( visual .net PDF-417 2d barcode or, here, half-slide) is commonly used to compare, for each of a large number of genes, the gene expression in two samples of genetic material.

The experiment that led to Plate 2 was designed to investigate changes in gene expression between the pre-settlement free-swimming stage of coral, and the post-settlement stage. For 3042 genes (one for each of 3042 spots), which showed an increase in gene expression and which a decrease Note that each panel in Plate 2 has 3072 spots; this includes 30 blanks. Where there was an increase, the spot should be fairly consistently blue, or bluish, over all six panels.

Where there was a decrease, the spot should be fairly consistently yellow, or yellowish. Here, all that will be attempted is to give broad indications of the experimental procedure, and subsequent processing, that led to the plots shown in Plate 2. The slides are rst printed with probes, with one probe per spot.

Each probe is designed to check for evidence of the expression of one gene. The two samples are separately labeled so that when later a spot lights up under a scanner, it will be possible to check for differences in the signal intensity. After labeling the separate samples, mixing them, and wiping the mixture over the slide or half-slide, and various laboratory processing steps, a scanner was used to determine, for each spot, the intensities generated from the two samples.

Various corrections are then necessary, leading nally to the calculation of logarithms of intensity ratios. Essentially, it is logarithms of intensity ratios that are shown in Plate 2. For these data there are, potentially, 3042 t-statistics.

This is small, by the standards of microarray experiments. There are severe problems of multiplicity to address. Details of a defensible approach to analyzing the data shown in Plate 2 will be posted on the web site for the book.

For further information on the analysis of microarray data, see Smyth (2004). For background on the coral data, see Grasso et al. (2008).

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