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Hypothesis Testing
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Hypothesis testing is a statistical method used to make decisions or draw conclusions about a population based on sample data. It helps determine whether there is enough evidence to support a specific claim or assumption about the data.
In hypothesis testing, two statements are defined. The first is the null hypothesis, which represents the default assumption that there is no effect or no difference. The second is the alternative hypothesis, which represents the claim that there is an effect or a difference.
| Hypothesis | Description |
|---|---|
| Null Hypothesis (H0) | Assumes no effect, no difference, or no relationship |
| Alternative Hypothesis (H1) | Assumes there is an effect, difference, or relationship |
Hypothesis testing involves collecting sample data, calculating a test statistic, and comparing it to a significance level. The significance level, often denoted by alpha, is the probability of rejecting the null hypothesis when it is actually true. A common significance level is 0.05.
The result of a hypothesis test is usually expressed using a p-value. The p-value represents the probability of obtaining the observed results if the null hypothesis is true.
| p-value | Decision |
|---|---|
| p-value ≤ 0.05 | Reject the null hypothesis |
| p-value > 0.05 | Fail to reject the null hypothesis |
In R, hypothesis testing can be performed using built-in functions. One common example is the t-test, which is used to compare means.
# Sample data
group1 <- c(20, 22, 19, 24, 21)
group2 <- c(30, 28, 32, 29, 31)
# Perform t-test
t.test(group1, group2)The output of the t-test includes the p-value, confidence interval, and test statistic. Based on the p-value, a decision is made about whether to reject or fail to reject the null hypothesis.
Hypothesis testing is an essential part of statistical analysis. It allows researchers and analysts to make data-driven decisions, validate assumptions, and draw conclusions about populations based on sample data.
