Statistical Significance: Analyzing Data To Determine Real Effects And Reject Null Hypotheses

Determining Significance

1) Determine desired long-run rate of false-positive (Type I) errors (⍺) –> change to 0.0052) Take an estimate of effect (e.g., a mean difference) and uncertainty, and convert them into a test statistic 3) Compare test statistic to critical value associated with level of ⍺4)Reject H0 if calculated test statistic exceeds critical value

In statistics, determining significance refers to the process of analyzing data to determine if the results are likely to have occurred by chance or if there is a real effect. Significance testing is an essential part of statistical analysis, and it is used to make decisions about whether to accept or reject a null hypothesis.

Null hypothesis testing involves setting up a null hypothesis and an alternative hypothesis. The null hypothesis assumes that there is no difference or relationship between groups or variables, while the alternative hypothesis suggests that there is a difference or relationship.

To determine significance, we use statistical tools, such as p-values, confidence intervals, and effect sizes. These tools help us determine if the results of an experiment or analysis are statistically significant, or if they occurred by chance.

P-values are a measure of the probability of obtaining the observed results if the null hypothesis were true. The smaller the p-value, the less likely it is that the results occurred by chance. Typically, a p-value of less than 0.05 is considered statistically significant, which means that there is less than a 5% chance that the results occurred by chance.

Confidence intervals are a range of values around a sample estimate, such as a mean or a proportion. We can use confidence intervals to estimate the range within which the true population value is likely to fall with a certain degree of confidence. For example, a 95% confidence interval indicates that we are 95% confident that the true population value falls within the calculated interval.

Effect size is a measure of the magnitude of the difference or relationship between groups or variables. It is the difference between the means divided by the standard deviation. A large effect size indicates a strong relationship or significant difference between groups.

In summary, determining significance involves analyzing data using statistical tools to determine if the results are likely due to chance or if there is a real effect. P-values, confidence intervals, and effect sizes are common statistical tools used to determine significance.

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