• A method to test assumptions about a population parameter
• Two types of hypotheses:
  • Null Hypothesis (H0): No effect or difference
  • Alternative Hypothesis (H1): Some effect or difference
• When testing, you can test one-tailed or two-tailed.

• One-tailed test example: Blood pressure medication efficacy.
  • \(H_0: \mu_1 = \mu_2\)
  • \(H_1: \mu_1 < \mu_2\)
  • To reject \(H_0\), we need p-value \(<\alpha\).
• Two-tailed test example: Height comparison between sexes.
  • \(H_0: \mu_1 = \mu_2\)
  • \(H_1: \mu_1 \neq \mu_2\)
  • To reject \(H_0\), we need p-value \(< \frac{\alpha}{2}\).

1. State the hypotheses
2. Choose a significance level (α) such as 0.1, 0.05, or 0.01 depending on confidence levels
   • A common value is 0.05, meaning there’s a 5% chance of rejecting the null hypothesis when it’s actually true
3. Select a test statistic
   • T-test when comparing means of 1-2 groups with normal, continuous data
   • Chi-square test for categorical data
   • ANOVA for comparison of means of 3 or more groups
4. Compute the p-value
5. Compare p-value with α and make a decision

• Question: Do setosa and versicolor have different sepal lengths?
• Hypotheses:
  • \(H_0: \mu_{setosa} = \mu_{versicolor}\)
  • \(H_1: \mu_{setosa} \neq \mu_{versicolor}\)

Based of this ggplot, let’s focus on setosa and versicolor

data(iris)
setosa_sepal <- iris$Sepal.Length[iris$Species == "setosa"]
versicolor_sepal <- iris$Sepal.Length[iris$Species == "versicolor"]
t.test(setosa_sepal, versicolor_sepal, var.equal = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  setosa_sepal and versicolor_sepal
## t = -10.521, df = 86.538, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1.1057074 -0.7542926
## sample estimates:
## mean of x mean of y 
##     5.006     5.936

• Through the t-test we have our p-value < 2.2e-16
• p-value < 2.2e-16 < \(\frac{\alpha}{2}\), given \(\alpha\) = .05
  • Thus we reject the \(H_0\) and can say with 95% confidence that setosa and versicolor have different sepal lengths.

• Hypothesis testing helps make data-driven decisions.
• p-value determines statistical significance.
• Visualization aids interpretation.
• YOU GOT THIS!