Statistics and Quantitative Methods
Statistics and Quantitative Methods tests descriptive statistics, probability, sampling, estimation, hypothesis testing, regression, time series, index numbers and decision analysis.
Core rules
- Mean, median and mode measure central tendency; standard deviation measures dispersion.
- A sampling distribution of the mean has standard error σ/√n.
- A hypothesis test compares the test statistic with a critical value; the p-value is the probability of a result at least as extreme under the null.
- Correlation measures association, not causation.
- In simple linear regression, y = a + bx; b is the slope and a the intercept.
Worked example
A sample of 25 items has mean 52 and standard deviation 10. Test H0: μ = 50 against H1: μ ≠ 50 at 5%. t = (52 − 50)/(10/√25) = 2/2 = 1.00. With df = 24, the two-tailed critical value is about 2.064. Since 1.00 < 2.064, do not reject H0. There is no significant evidence of a difference at the 5% level.
Traps
Do not use the z critical value when the population standard deviation is unknown and n is small. Check whether the test is one- or two-tailed. A high R² does not prove causation. Do not confuse the standard deviation with the standard error.