What is the relationship among the separate F-ratios in a two-factor ANOVA? They may have different df values but they all have the same denominator.

When comparing more than two treatment means we use ANOVA because a t test increases the risk of type 1 error . For example if we wish to compare 4 population means there will be 4C2 = 6 separate pairs and to test the null hypothesis that all four population means are equal would require six two sample t test.

What is the main advantage that ANOVA testing has compared with t testing? It can be used to compare two or more treatments. ANOVA is to be used in a research study using two therapy groups. For each group, scores will be taken before the therapy, right after the therapy, and one year after the therapy.

If the null hypothesis is true, the between treatment variation (numerator) will not exceed the residual or error variation (denominator) and the F statistic will small. If the null hypothesis is false, then the F statistic will be large.

Many practitioners have been trained to see if the P-value is greater or less than 0.05. Technically, P-values of 0.049 and 0.051 would be on opposite sides of statistical significance, when, in fact, they are equivalent, and some have argued against this all or none phenome- non of statistical significance.

In the majority of analyses, an alpha of 0.05 is used as the cutoff for significance. If the p-value is less than 0.05, we reject the null hypothesis that there’s no difference between the means and conclude that a significant difference does exist. Below 0.05, significant. Over 0.05, not significant.

A low P value indicates that the null hypothesis can be rejected and the alternative hypothesis is the most likely. Thus, a p-value of 0.045 might be classified as statistically significant while a p-value of 0.055 might not. However, it is important to keep in mind that the limit 0.05 is not black and white.

The p value adjusts for uncertainty, by telling you how likely is the effect observed in your data if the null hypothesis were true.

In exploratory studies, p-values enable the recognition of any statistically noteworthy findings. Confidence intervals provide information about a range in which the true value lies with a certain degree of probability, as well as about the direction and strength of the demonstrated effect.

A likelihood is a more nuanced starting point than a p-value for showing how the false positive risk varies with the prior probability.

If your test statistic is positive, first find the probability that Z is greater than your test statistic (look up your test statistic on the Z-table, find its corresponding probability, and subtract it from one). Then double this result to get the p-value.

A p-value is the probability that the results from your sample data occurred by chance. P-values are from 0% to 100%. They are usually written as a decimal. For example, a p value of 5% is 0.05.

Consider them simply different ways to quantify the “extremeness” of your results under the null hypothesis. The larger the absolute value of the t-value, the smaller the p-value, and the greater the evidence against the null hypothesis.