Again, the χ2 test of independence is used to test whether the distribution of the outcome variable is similar across the comparison groups. Here we rejected H0 and concluded that the distribution of exercise is not independent of living arrangement, or that there is a relationship between living arrangement and exercise. The test provides an overall assessment of statistical significance. When the null hypothesis is rejected, it is important to review the sample data to understand the nature of the relationship. Consider again the sample data.
Photo provided by Flickr
On the other hand, the null hypothesis is straightforward -- what is the probability that our treated and untreated samples are from the same population (that the treatment or predictor has no effect)? There is only one set of statistical probabilities -- calculation of chance effects. Instead of directly testing H, we test H. If we can reject H, (and factors are under control), we can accept H. To put it another way, the fate of the research hypothesis depends upon what happens to H.
Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72
Photo provided by Flickr
The p-value is p = 0.019. This is below the .05 standard, so the result is statistically significant. This means we decide in favor of the alternative hypothesis. We're deciding that the population mean is not 72.
Thus computing a p-value requires a null hypothesis, ..
Example 11: Suppose your null hypothesis is “the average package containsthe stated net weight,” your alternative is “the averagepackage contains less than the stated net weight,” and yoursignificance level α is 0.05.
comparator distribution specified in the null hypothesis is a ..
You therefore fail to reject H0 (and don’tmention H1 ).The sample you have could have come about by randomselection if H0 is true, but it could also have come about byrandom selection if H0 is false. In other words, you don’tknow whether H0 is actually true, or it’s false but thesample data just happened to fall not too far from H0.
so we do not reject the null hypothesis.
If your p-value is less than your significance level,you have shown that your sample resultswere unlikely to arise by chance if H0 is true. The data arestatistically significant.You therefore reject H0 and accept H1.
Null Hypothesis Definition | Investopedia
Entire books are devoted to the statistical method known as . This section will contain only three paragraphs. This is in part because of the view of some statisticians that ANOVA techniques are somewhat dated or at least redundant with other methods such as (see ). In addition, a casual perusal of the worm literature will uncover relatively scant use of this method. Traditionally, an ANOVA answers the following question: are any of the mean values within a dataset likely to be derived from populations that are truly different? Correspondingly, the null hypothesis for an ANOVA is that all of the samples are derived from populations, whose means are identical and that any difference in their means are due to chance sampling. Thus, an ANOVA will implicitly compare all possible pairwise combinations of samples to each other in its search for differences. Notably, in the case of a positive finding, an ANOVA will not directly indicate which of the populations are different from each other. An ANOVA tells us only that at least one sample is likely to be derived from a population that is different from at least one other population.