A 90% confidence interval means that if we were to repeat the experiment many times, 90% of the intervals we calculate would contain the true population parameter.
Understanding Confidence Intervals
A confidence interval is a range of values that is likely to contain the true value of a population parameter. It is calculated from sample data and provides a measure of uncertainty about the estimate.
- Population Parameter: This is the true value of a characteristic within the entire population you are studying. For example, the average height of all women in the United States.
- Sample Data: This is the data collected from a subset of the population. For example, the average height of 100 randomly selected women in the United States.
- Confidence Level: This is the probability that the confidence interval will contain the true population parameter. A 90% confidence level means that there is a 90% chance that the interval will contain the true value.
Interpreting a 90% Confidence Interval
Let's say you are studying the average weight of adult males in a particular city. You collect a sample of 100 men and calculate a 90% confidence interval for the average weight to be (175 pounds, 185 pounds).
This means that:
- You are 90% confident that the true average weight of all adult males in the city falls between 175 and 185 pounds.
- If you were to repeat the study many times, 90% of the calculated confidence intervals would contain the true average weight.
- There is a 10% chance that the true average weight is outside the interval.
Practical Insights
- Confidence intervals are not absolute: They only provide a range of plausible values, not a guarantee.
- Higher confidence levels lead to wider intervals: A 99% confidence interval will be wider than a 90% confidence interval because it needs to capture a higher percentage of possible values.
- Confidence intervals are useful for comparing different groups: You can use confidence intervals to see if there is a significant difference between the average weight of men and women in the city, for example.
Example
Imagine you are a researcher studying the effectiveness of a new medication. You conduct a clinical trial and calculate a 90% confidence interval for the difference in average blood pressure between the treatment group and the control group. The interval is (-5 mmHg, 2 mmHg).
This means:
- You are 90% confident that the true difference in average blood pressure between the treatment and control groups is between -5 mmHg and 2 mmHg.
- This suggests that the medication may have a small effect on blood pressure, but the effect is not statistically significant.
Conclusion
A 90% confidence interval indicates that we are 90% confident that the true population parameter lies within the calculated range. It provides a useful tool for estimating population parameters and assessing the uncertainty of our estimates.
