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Null hypothesis testing (often described just as '''hypothesis testing''' is very commonly used in epidemiological investigations, and may be used in both analytic studies (for example, assessing whether disease experience differs between different exposure groups), and in descriptive studies (for example, if assessing whether disease experience differs from some suspected value). As in most studies, only a sample of individuals is taken, it is not possible to definitively state whether or not there is a difference between the two exposure groups. Hypothesis tests provide a method of assessing the '''strength of evidence''' in favour or against a true difference in the underlying population. However, despite their widespread use, the results of hypothesis tests are often misinterpreted.<br>
Null hypothesis testing (often described just as '''hypothesis testing''' is very commonly used in epidemiological investigations, and may be used in both analytic studies (for example, assessing whether disease experience differs between different exposure groups), and in descriptive studies (for example, if assessing whether disease experience differs from some suspected value). For the purposes of this page, the use of hypothesis testing in analytic studies will be focussed on. As in most studies, only a sample of individuals is taken, it is not possible to definitively state whether or not there is a difference between the two exposure groups. Hypothesis tests provide a method of assessing the '''strength of evidence''' in favour or against a true difference in the underlying population. However, despite their widespread use, the results of hypothesis tests are often misinterpreted.<br>
==Concept behind null hypothesis testing==
==Concept behind null hypothesis testing==
Hypothesis tests provide a systematic, objective method of data analysis, but do not actually answer the main question of interest (which is commonly along the lines of 'is there a difference in disease experience between individuals with exposure x and individuals without exposure x?'). Rather, hypothesis tests answer the question ''''if there is no difference in disease experience''' between individuals with or without exposure x, what is the probability of obtaining the current data (or data more 'extreme' than this)?' As such, hypothesis tests do not inform us whether or not there is a difference, but instead they offer us varying degrees of '''evidence''' in support of or against a situation where there is no difference in the population under investigation. This situation of 'no difference' is known as the 'null hypothesis', and should be stated whenever a null hypothesis test is performed.<br>
Hypothesis tests provide a systematic, objective method of data analysis, but do not actually answer the main question of interest (which is commonly along the lines of 'is there a difference in disease experience between individuals with exposure x and individuals without exposure x?'). Rather, hypothesis tests answer the question ''''if there is no difference in disease experience''' between individuals with or without exposure x, what is the probability of obtaining the current data (or data more 'extreme' than this)?' As such, hypothesis tests do not inform us whether or not there is a difference, but instead they offer us varying degrees of '''evidence''' in support of or against a situation where there is no difference in the population under investigation. This situation of 'no difference' is known as the 'null hypothesis'(defined as H<sub>0</sub>). Along with this null hypothesis, an '''alternative hypothesis''' (H<sub>1</sub>) should be stated, which will relate to the statement made if 'sufficient' evidence against H<sub>0</sub> is found. An example of a null and an alternative hypothesis is: H<sub>0</sub>:there is no association between the prevalence of disease and exposure to factor x; H<sub>1</sub>: there is an association between the prevalence of disease and exposure to factor x. However, in some occasions, the null and alternative hypotheses may have a direction - for example: H<sub>0</sub>: the prevalence of disease amongst animals exposed to factor x is not higher than amongst animals not exposed to factor x; H<sub>1</sub>: the prevalence of disease amongst animals exposed to factor x is higher than amongst animals not exposed to factor x. The differences in these relate to whether a [[Hypothesis testing#One-tailed and two-tailed tests|one-tailed or a two-tailed test]] will be used.<br>
Null hypothesis testing relies on the fact that the likely values obtained in a sample taken from a population in which the null hypothesis is true (i.e. there is no difference in disease experience between groups) can be predicted. That is, although it is most likely that a sample from this population will also show no difference, it is not impossible that, through chance, a sample will contain more diseased animals in the 'exposed' group than in the 'unexposed' group, for example. Through knowledge of the number of animals sampled and the prevalence of disease in the population, the probability of getting any particular pattern of data from this sample can be ascertained. This probability is known as the '''p-value''', and is the main outcome of interest from a hypothesis test. A p-value of 1.00 would suggest that if there was no difference in disease experience according to exposure in the population and repeated samples were taken from this population and performed hypothesis tests on these, all of these samples would be expected to show this pattern (or 'more extreme' - i.e. show more of a difference). However, a p-value of 0.001 would suggest that there is only a 0.1% chance of seeing these data (or more extreme) if there was no true difference in the population. Note that although 0.001 is a very low p-value, it cannot be used to ''prove'' that the null hypothesis is false, or that the 'alternative hypothesis' (of their being a difference) is true - it can only be stated that it gives 'strong evidence against the null hypothesis'.
Null hypothesis testing relies on the fact that the likely values obtained in a sample taken from a population in which the null hypothesis is true (i.e. there is no difference in disease experience between groups) can be predicted. That is, although it is most likely that a sample from this population will also show no difference, it is not impossible that, through chance, a sample will contain more diseased animals in the 'exposed' group than in the 'unexposed' group, for example. Through knowledge of the number of animals sampled and the prevalence of disease in the population, the probability of getting any particular pattern of data from this sample can be ascertained. This probability is known as the '''p-value''', and is the main outcome of interest from a hypothesis test. A p-value of 1.00 would suggest that if there was no difference in disease experience according to exposure in the population and repeated samples were taken from this population and performed hypothesis tests on these, all of these samples would be expected to show this pattern (or 'more extreme' - i.e. show more of a difference). However, a p-value of 0.001 would suggest that there is only a 0.1% chance of seeing these data (or more extreme) if there was no true difference in the population. Note that although 0.001 is a very low p-value, it cannot be used to ''prove'' that the null hypothesis is false, or that the alternative hypothesis is true - it can only be stated that it gives 'strong evidence against the null hypothesis'.
===Significance levels===
===Significance levels===
===One-tailed and two-tailed tests===
===One-tailed and two-tailed tests===
Another issue to consider when conducting a hypothesis test is whether a one-tailed or a two-tailed is required. The decision of which to use will depend upon the null and alternative hypotheses stated. A two-tailed test will allow the detection of a difference in either direction (for example, either a lower prevalence of disease in the exposed group or a lower prevalence of disease in the unexposed group). One-tailed tests are used when the null and alternative hypotheses have a direction, and will only detect a difference if it is in that particular direction.<br>
For example, consider a clinical trial of a drug which is thought to reduce the risk of death. However, it may be found that the drug actually ''increases'' the risk of death. If H<sub>0</sub> was defined as 'there is no difference in risk of death according to treatment status', then H<sub>1</sub> would be 'there is a difference in risk of death according to treatment status', and a two-tailed test would be performed. This hypothesis test would be expected to find evidence against the null hypothesis (the direction of which would be quantified through a measure of effect such as the risk ratio). However, if the investigators were convinced that the drug would not increase the risk of death, then H<sub>0</sub> may be stated as 'the risk of death is not reduced amongst treated animals', in which case H<sub>1</sub> would be 'the risk of death is reduced amongst treated animals'. In this case, a one-tailed hypothesis test would be performed, which would fail to find evidence against the null hypothesis (since the null is in fact correct). For this reason, two-tailed tests are used in the vast majority of cases.
[[Category:Veterinary Epidemiology - Statistical Methods|E]]
[[Category:Veterinary Epidemiology - Statistical Methods|E]]