Overview
This lecture explains how statistics are used in science to interpret data, assess reliability, and determine if differences between groups are significant.
Introduction to Data Interpretation
- Statistics help estimate data reliability and determine differences within or between groups.
- Sample size and group composition can affect interpretation of experimental results.
Key Statistical Measures
- The mean (average) is found by summing data points and dividing by the number of points.
- Two different data sets can have the same mean but different variability.
Variation and Standard Deviation
- Standard deviation measures how much data points vary from the mean.
- A larger standard deviation indicates more variability; a smaller one indicates less.
- In a normal distribution, about two-thirds of data falls within one standard deviation of the mean.
Standard Error and Sample Size
- Standard error estimates how well a sample mean represents the true population mean.
- Larger sample sizes give more confidence in representing the population.
- Standard error = standard deviation ÷ square root of sample size.
Confidence Intervals
- The 95% confidence interval is a range where we are 95% certain the true mean lies.
- Calculated as mean ± 2 × standard error.
- If confidence intervals of groups do not overlap, there is likely a significant difference.
Practical Examples
- Surveys use confidence intervals because not all individuals can be sampled.
- Overlapping confidence intervals between groups mean no significant difference can be confirmed.
- Increasing sample size narrows confidence intervals and can reveal differences.
The p Value
- The p value indicates the probability that observed differences are due to chance.
- A p value ≤ 0.05 suggests a statistically significant difference between groups.
- If p > 0.05, we cannot confidently claim a difference.
Key Terms & Definitions
- Mean — the average of a data set.
- Standard deviation — a measure of variability within a data set.
- Standard error — an estimate of how far the sample mean is from the true population mean.
- 95% confidence interval — the range where the true mean lies with 95% certainty.
- p value — the probability that observed differences occurred by chance (significant if ≤ 0.05).
Action Items / Next Steps
- Review definitions and importance of mean, standard deviation, standard error, confidence interval, and p value.
- Practice interpreting data using these statistics.
- Ask questions if any concepts remain unclear.