## Example 11.3. Hypotheses with One Sample of One Measurement Variable

Photo provided by Flickr

### Example of a complex multiple independent variable hypothesis:

Testing for statistical significance is often performed on measures of effect to evaluate the likelihood that the effect observed differs from the null hypothesis (i.e., no effect). While many studies, particularly in other areas of biomedical research, may express significance by p-values, epidemiological studies typically present confidence intervals (CI) (also called confidence limits). A 95% confidence interval, for example, is a range of values for the effect measure that includes the estimated measure obtained from the study data and that which has 95% probability of including the true value. Values outside the interval are deemed to be unlikely to include the true measure of effect. If the CI for a rate ratio includes unity, then there is no statistically significant difference between the groups being compared.

Photo provided by Flickr

### Example 11.5. Hypotheses with Two Samples of One Measurement Variable

Taking this as a benchmark, further developments in the area of statistical modelling have taken two main directions: models for repeated categorical measures and models which extend the Generalized Linear Models (Generalized Additive Models). In both instances, the aims are focused on increasing the flexibility of the statistical tools in order to cope with more complex problems arising from reality. Repeated measures models are needed in many occupational studies where the units of analysis are at the sub-individual level. For example:

Photo provided by Flickr

Our common practice, however, was to consider all alternative conjectures, including other medical problems including the impaired function of upper motor neurones, lower motor neurones, as well as the neuromuscular junction. Again, we deduced outcome statements from the above hypotheses. For example, if any solvent reported to produce polyneuropathy (e.g., n-hexane, methyl butylketone, acrylamide) were the cause, it would also impair the nerve conduction velocity (NCV); if it were other medical problems involving upper motor neurones, there would be signs of impaired consciousness and/or involuntary movement.

Photo provided by Flickr

## Types of Hypotheses Directional Hypotheses ..

When we pose a research question, we want to know whether the outcome is due to the treatment (independent variable) or due to chance (in which case our treatment is probably not effective). For example, the claim that tutoring improves math performance generally does not predict exactly how much improvement. Each level of improvement has a different probability associated with it, and it would take a long time and a great deal of effort to specify the probability of each of the possible outcomes that would support our research hypothesis.

## you just went for directional ..

The alternative hypothesis can be__directional__ or __non-directional__.“Eating oatmeal lowers cholesterol” is a directional hypothesis; “Amountof sleep affects test scores” is non-directional.

## directional research hypothesis

A significance test examines whether the null hypothesis provides a plausible explanation of the data. The *null hypothesis* itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or differences between means or proportions or correlations or odds ratios or any other numerical summary of the population. The *alternative hypothesis* is typically the research hypothesis of interest. Here are some examples.

## The second type of hypothesis is a directional hypothesis

For example, if a calculated test statistic exceeds the critical value for a significance level of 0.05 then this means that values of the test statistic as large as, or larger than calculated from the data would occur by chance less than 5 times in 100 if the null hypothesis was indeed correct.

## non-directional: In mathematics ..

For example, when an alternative hypothesis predicts that the mean of one sample would be greater (but not less) than another, then a directional alternative would be used.