Significance probability value

Test at the 5 per cent probability value if the new method mean is significantly different from the standard reference mean. 

For similar reasons, the statement If the Durbin-Watson test demonstrates a correlation, then the relationship between the two assays is not linear is not exactly correct, either. Under some circumstances, a linear correlation can also give rise to a statistically significant value of DW. In fact, for any statistic, it is always possible to construct a data set that gives a high-probability value for the statistic, yet the data clearly and obviously fail to meet the pertinent criteria (again, Anscombe is a good example of this for a few common statistics). So what should we do Well, different statistics show different sensitivities to particular departures from the ideal, and this is where DW comes in. 

Conventionally a p (probability) value of < 0.05 is taken to mean statistical significance. This means that if p = 0.05 then the observed difference could occur by chance on 1 in 20 (5%) of occasions. In effect, this means a 5% chance of a false-positive result. 

This value ranges from 0 to 1. The probability that a given number of actives or greater, that is, the cumulative significant probability, is then simply the complement ... 

In an alternative approach, critical values of Spearman s rank correlation coefficient, tabulated as a function of observation size and significance probability [32], are employed. The 5% critical value is 0.738 when N = 8, hence rs = 0.369 is not significant (not even at the 10% level, with critical value 0.643). 

The statistical test procedures that we use unfortunately are not perfect and from time to time we will be fooled by the data and draw incorrect conclusions. For example, we know that 17 heads and 3 tails can (and will) occur with 20 flips of a fair coin (the probability from Chapter 3 is 0.0011) however, that outcome would give a significant p-value and we would conclude incorrectly that the coin was not fair. Conversely we could construct a coin that was biased 60 per cent/40 per cent in favour of heads and in 20 flips see say 13 heads and 7 tails. That outcome would lead to a non-significant p-value (p = 0.224) and we would fail to pick up the bias. These two potential mistakes are termed type I and type II errors. 

Significance of the data was evaluated by analysis of variance with appropriate contrasts, and least square difference techniques. A probability value of less than 0.05 was judged to be statistically significant. 

The t-test analysis computes for each gene the probability that the difference between the mean fluorescence intensities of the test and reference samples is falsely called significant (p-value), by theoretical t-distribution or permutation test. 

Table IV shows the overall analysis of variance (ANOVA) and lists some miscellaneous statistics. The ANOVA table breaks down the total sum of squares for the response variable into the portion attributable to the model, Equation 3, and the portion the model does not account for, which is attributed to error. The mean square for error is an estimate of the variance of the residuals — differences between observed values of suspensibility and those predicted by the empirical equation. The F-value provides a method for testing how well the model as a whole — after adjusting for the mean — accounts for the variation in suspensibility. A small value for the significance probability, labelled PR> F and 0.0006 in this case, indicates that the correlation is significant. The R2 (correlation coefficient) value of 0.90S5 indicates that Equation 3 accounts for 91% of the experimental variation in suspensibility. The coefficient of variation (C.V.) is a measure of the amount variation in suspensibility. It is equal to the standard deviation of the response variable (STD DEV) expressed as a percentage of the mean of the response response variable (SUSP MEAN). Since the coefficient of variation is unitless, it is often preferred for estimating the goodness of fit.

---