# Levels of confidence and statistical significance relationship

### Statistical significance - Wikipedia

In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis. More precisely, a study's defined significance level, α, is the probability of the . Using Bayesian statistics can improve confidence levels but also requires making additional assumptions, and. May 8, The specification of the level of significance also fixes the probability that The confidence interval is a range of values calculated by statistical. Apr 2, Previously, I used graphs to show what statistical significance really In this case, the confidence level is not the probability that a specific.

If it is wrong, however, then the one-tailed test has no power.

Stringent significance thresholds in specific fields[ edit ] Main articles: Limitations[ edit ] Researchers focusing solely on whether their results are statistically significant might report findings that are not substantive [43] and not replicable. A study that is found to be statistically significant may not necessarily be practically significant.

## Statistical significance

Effect size Effect size is a measure of a study's practical significance. To gauge the research significance of their result, researchers are encouraged to always report an effect size along with p-values.

An effect size measure quantifies the strength of an effect, such as the distance between two means in units of standard deviation cf. Cohen's dthe correlation coefficient between two variables or its squareand other measures.

Reproducibility A statistically significant result may not be easy to reproduce. Each failed attempt to reproduce a result increases the likelihood that the result was a false positive. If the consequences of a type I error are serious or expensive, then a very small significance level is appropriate.

Example 1 Two drugs are being compared for effectiveness in treating the same condition. Drug 1 is very affordable, but Drug 2 is extremely expensive.

### Type I and II Errors

The null hypothesis is "both drugs are equally effective," and the alternate is "Drug 2 is more effective than Drug 1. That would be undesirable from the patient's perspective, so a small significance level is warranted. If the consequences of a Type I error are not very serious and especially if a Type II error has serious consequencesthen a larger significance level is appropriate. Two drugs are known to be equally effective for a certain condition. They are also each equally affordable. However, there is some suspicion that Drug 2 causes a serious side-effect in some patients, whereas Drug 1 has been used for decades with no reports of the side effect.

The null hypothesis is "the incidence of the side effect in both drugs is the same", and the alternate is "the incidence of the side effect in Drug 2 is greater than that in Drug 1. So setting a large significance level is appropriate.

**confidence and significance level**

See Sample size calculations to plan an experiment, GraphPad. Sometimes there may be serious consequences of each alternative, so some compromises or weighing priorities may be necessary.

The trial analogy illustrates this well: Which is better or worse, imprisoning an innocent person or letting a guilty person go free? Trying to avoid the issue by always choosing the same significance level is itself a value judgment. Sometimes different stakeholders have different interests that compete e. Similar considerations hold for setting confidence levels for confidence intervals.