• Hypothesis testing is a fundamental concept in statistics.
• It allows us to make inferences about populations based on sample data.
• This presentation will focus on coding aspects of hypothesis testing in R.

• The null hypothesis, \(H_0\), typically represents the status quo or no effect.
• The alternative hypothesis, \(H_1\), represents the claim we want to test

\[ \begin{align*} H_0 &: \mu_{\text{Control}} = \mu_{\text{Treatment}} \\ H_1 &: \mu_{\text{Control}} < \mu_{\text{Treatment}} \end{align*} \]

• To test our hypotheses, we calculate a test statistic and assess its significance.
• The test statistic helps us determine the likelihood of observing the observed difference in effectiveness under the null hypothesis.

\[ \text{Test Statistic: } t = \frac{\bar{x}_{\text{Treatment}} - \bar{x}_{\text{Control}}}{s/\sqrt{n}} \]

\[ \text{p-value: } p = P(T \geq t | H_0) \]

• Let’s consider a fictional drug efficacy study.
• The null hypothesis states that there is no difference in effectiveness between the control and treatment groups.
• The alternative hypothesis suggests that the treatment group shows greater effectiveness than the control group.

  Treatment_Group Response_Variable
1         Control          51.26659
2         Control          49.85727
3         Control          49.78565
4       Treatment          61.84301
5         Control          48.87115
6       Treatment          62.58235

Calculate test statistic and p-value

    Welch Two Sample t-test

data:  Response_Variable by Treatment_Group
t = -5.0405, df = 86.129, p-value = 2.537e-06
alternative hypothesis: true difference in means between group Control and group Treatment is not equal to 0
95 percent confidence interval:
 -6.968314 -3.026524
sample estimates:
  mean in group Control mean in group Treatment 
               49.73238                54.72980 

Hypothesis testing is crucial in drug efficacy studies, helping us determine if new treatments offer significant improvements. By formulating clear hypotheses and rigorously analyzing data, we ensure informed decisions in medical practice. We should continue advancing medical science for better patient outcomes through evidence-based research.