Question

which of the following are ways statistics are used in scientific analysis? select all that apply. check all that apply p values are used for statistical significance and help determine if results of an experiment are due to chance. correlations are important in determining causation. statistics enable us to prove our hypotheses. confidence intervals allow us to represent the amount of variation in our data set.

Explanation:

• P - values: In hypothesis testing, a \(p\) - value is calculated. If \(p\leq\alpha\) (where \(\alpha\) is the significance level, often \(0.05\)), we reject the null hypothesis. So \(p\) - values help determine if results are likely due to chance or not.
• Correlations: Correlation (\(r\) value between \(- 1\) and \(1\)) measures the strength and direction of a linear relationship between two variables. But correlation does not imply causation. There could be a third - variable (confounding variable) that affects both variables.
• Statistics and hypotheses: Statistics (e.g., hypothesis testing) can provide evidence for or against a hypothesis. But we cannot "prove" a hypothesis in the absolute sense. We can only reject or fail to reject the null hypothesis.
• Confidence intervals: A confidence interval (e.g., \(95\%\) confidence interval) gives a range of values within which the True population parameter is likely to lie. It accounts for sampling variability.

Answer:

• \(P\) values are used for statistical significance and help determine if results of an experiment are due to chance.
• Confidence intervals allow us to represent the amount of variation in our data set.