1 Why do we care about probability?
Statistical Methods for Life Sciences
1.1 Do studies give different results?
Two research groups independently sample individuals from a group of PhD students taking “Statistical Methods for Life Science” course, and measure their heights.
They ended up with sample means of 172 and 175 cm respectively.
Could this difference arise simply because they sampled different individuals?
Let’s discuss:
- What information would help you answer?
- Would a difference of 3 cm be surprising if individual heights varied very little? What if they varied a lot?
- Would your answer change if each group studied 5 individuals rather than 100?
- If we repeated this study many times, would we always get the same sample mean?
- What exactly is the population we want to learn about?
- How were the students selected? Could selection systematically favour taller or shorter people?
- Were heights measured in the same way in both groups?
- How could we describe which sample means are common and which are unusual?
Key message
Different samples from the same population can give different results. Probability models help us describe how much sampling variation to expect and which results would be unusual under our assumptions.
When discussing the question above, some of the following terms may come to mind:
- Population, sample, sample size
- Biological variability, variance, standard deviation (SD)
- Sampling variability, statistic
- Random variable, event, sampling distribution
- Standard error (SE) and precision
- Selection bias, measurement error
- Probability model and assumptions
Let’s explore how these concepts connect and how probability helps us understand variation in our results.