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Formally we reject the null hypothesis.

Example: We compare the observed mean birth weight with the hypothesized values of 18 grams.

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Null and Alternative Hypotheses for a Mean

The test is called the χ2 test of independence and the null hypothesis is that there is no difference in the distribution of responses to the outcome across comparison groups. This is often stated as follows: The outcome variable and the grouping variable (e.g., the comparison treatments or comparison groups) are independent (hence the name of the test). Independence here implies homogeneity in the distribution of the outcome among comparison groups.

Null hypothesis: μ = 72  Alternative hypothesis: μ ≠72

In the olden days, when people looked up P values in printed tables, they would report the results of a statistical test as "PPP>0.10", etc. Nowadays, almost all computer statistics programs give the exact P value resulting from a statistical test, such as P=0.029, and that's what you should report in your publications. You will conclude that the results are either significant or they're not significant; they either reject the null hypothesis (if P is below your pre-determined significance level) or don't reject the null hypothesis (if P is above your significance level). But other people will want to know if your results are "strongly" significant (P much less than 0.05), which will give them more confidence in your results than if they were "barely" significant (P=0.043, for example). In addition, other researchers will need the exact P value if they want to combine your results with others into a .

Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

How to Set Up a Hypothesis Test: Null versus Alternative

Generally, when comparing or contrasting groups (samples), the null hypothesis is that the difference between means (averages) = 0. For categorical data shown on a contingency table, the null hypothesis is that any differences between the observed frequencies (counts in categories) and expected frequencies are due to chance.

One of the main goals of statistical hypothesis testing is to estimate the P value, which is the probability of obtaining the observed results, or something more extreme, if the null hypothesis were true. If the observed results are unlikely under the null hypothesis, your reject the null hypothesis. Alternatives to this "frequentist" approach to statistics include Bayesian statistics and estimation of effect sizes and confidence intervals.

Null hypothesis statistical significance testing

The Z formula is:    Note that the population mean is 18 under the null hypothesis, and the standard error is 1, as we just calculated.

One considerable limitation of hypothesis testing is described above: namely, hypothesis tests do not relate to the main question of interest (whether or not there is a true difference in the population), and only provide degrees of evidence in favour or against there being no true difference. Another limitation is that there will always be a difference of some magnitude between the two groups, even if this is of no relevance. Consider a cohort study where 1 million nondiseased individuals are followed up to see whether or not exposure to substance x is associated with disease. It may be that in this whole population of 1 million animals, 10.0% of exposed individuals develop the disease and that 9.9% of unexposed individuals develop the disease. Of course, this difference is not of any biological relevance, and yet there is a difference there (as this is a whole population rather than a sample, we would not conduct a hypothesis test). As the size of any sample increases, the ability to detect a true difference increases. As there will be a 'true difference' (however small) in most populations, this means that hypothesis tests on large sample sizes will tend to give low p-values (indeed, some statisticians view hypothesis testing as a method of determining whether or not the sample size is sufficient to detect a difference). This problem can be reduced by ensuring that the appropriate measure of effect is always presented along with the hypothesis test p-value. In the example above, the incidence risk of disease amongst exposed individuals was 0.100, and that amongst unexposed was 0.099, giving a risk ratio of 0.100/0.099 = 1.01. Therefore, regardless of the result of hypothesis testing, there is very little association between exposure and disease in this case.

Although the approach described above (of varying degrees of evidence against the null hypothesis) is the most statistically correct interpretation of p-values, it is often not practical to apply this in epidemiological analysis. For example, an investigator may want to identify a number of exposures which appear to be associated with the outcome in order to investigate these further - the approach described above would not allow this (as it will never lead to an association being proven. As such, many studies will use significance levels as a method of interpretation of p-values as 'significant' or 'not significant'. Commonly, a p-value of 0.05 or less is used to denote a 'significant' association. This means that if the there is a 5% chance or less of observing the data in question (or more extreme) if the null hypothesis is true, then the association will be denoted as 'significant'. Of course, there remains a 5% chance that there is no true difference in the population, and this can be a problem when testing large numbers of exposures (as shown in the cartoon ). Because of this, great care should be taken whenever using significance levels to interpret hypothesis tests, and the actual p-value should always be presented.

The Z formula is:    Note that the population mean is 460 under the null hypothesis, and the standard error is 15.6, as we just calculated.
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  • Learn About Null Hypothesis and Alternative Hypothesis

    In the second step of the procedure we identify the kind of data that is expected if the null hypothesis is true.

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Null and Alternative Hypothesis | Real Statistics Using …

How do you know which hypothesis to put in H0 and which one to put in Ha? Typically, the null hypothesis says that nothing new is happening; the previous result is the same now as it was before, or the groups have the same average (their difference is equal to zero). In general, you assume that people’s claims are true until proven otherwise. So the question becomes: Can you prove otherwise? In other words, can you show sufficient evidence to reject H0?

Suppose we perform a statistical test of the null hypothesis ..

Finally, say you work for the company marketing the pie, and you think the pie can be made in less than five minutes (and could be marketed by the company as such). The less-than alternative is the one you want, and your two hypotheses would be


If you only want to see whether the time turns out to be greater than what the company claims (that is, whether the company is falsely advertising its quick prep time), you use the greater-than alternative, and your two hypotheses are

If you have a null hypothesis symbol is h is used

For example, if you want to test whether a company is correct in claiming its pie takes five minutes to make and it doesn’t matter whether the actual average time is more or less than that, you use the not-equal-to alternative. Your hypotheses for that test would be

Research paper | Null Hypothesis | Statistical Significance

Which alternative hypothesis you choose in setting up your hypothesis test depends on what you’re interested in concluding, should you have enough evidence to refute the null hypothesis (the claim). The alternative hypothesis should be decided upon before collecting or looking at any data, so as not to influence the results.

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