Statistical Thinking

Key Components of Statistical Investigation are:

Planning the study: Start by asking testable questions and deciding how to collect data. For example, how long was the study period of the coffee study?

Examining the data: What are appropriate ways to examine the data? For example, in the coffee study, did the proportions differ when we compared the smokers to the non-smokers?

Inferring from the data: What are valid statistical methods for drawing inferences “beyond” the data you collected? In the coffee study, is the 10%–15% reduction in risk of death something that could have happened just by chance?

Drawing conclusions: Based on what you learned from your data, what conclusions can you draw? Can you draw a cause-and-effect conclusion about your treatments? (Are scientists now saying that the coffee drinking is the cause of the decreased risk of death?)

Distribution

Analyzing the pattern of variation

P-value

tells you how often a random process would give a result at least as extreme as what was found in the actual study, assuming there was nothing other than random chance at play.

Cut-off value

A result is statistically significant if it is unlikely to arise by chance alone.

What happens if the p-value is less than the cut-off value?

The hypothesis of random chance was at play is rejected.

Random sampling

Using a probability-based method to select a subset of individuals for the sample from the population

Margin of error

The expected amount of random variation in a statistic; often defined for 95% confidence level.

Random Assigning

Using a probability-based method to divide a sample into treatment groups.