Symbols, Meanings & Formulas

Adapted from

Name Symbol
Population Sample
Sample Size $N$ $n$
Mean $\mu$ ("mu") $\bar{x}$ ("x-bar")
Standard Deviation $\sigma$ (lower case "sigma") $s$
Variance $\sigma^2$ (lower case "sigma" squared) $s^2$
Proportion $\pi$ $p$
Correlation Coefficient $\rho$ (lower case "rho") $r$

Name Symbol Concept
Summation $\Sigma$ (upper case "sigma")
Null Hypothesis $H_0$ prediction of no difference $\rightarrow \bar{x} = \mu$
Alternate Hypothesis $H_1$ prediction of a difference $\rightarrow \bar{x} \neq \mu$
Power $1 - \beta$ tba
Type 1 Error $\alpha$ (lower case "alpha") tba
Type 2 Error $\beta$ (lower case "beta") tba

one sample z-test

  • population variance known
  • critical values always +/- 1.96
  • one sample t-test

  • population variance unknown
  • critical values depend on the degrees of freedom (df = n - 1)
    1. state hypotheses
    2. determine critical values
    3. calculate estimated standard error of the mean
    4. calculate observed t-score
    5. compare observed t-score to critical values
    6. obtain p-value
    7. conclude whether to reject the null, or fail to reject the null. however, there is still the possibility of an error - type 1 and type 2 errors will be covered next.

    non-directional (two-tailed) vs. directional (one-tailed) tests

    non-directional (two-tailed)
  • alpha (.05) split equally between two tails
  • critical values are larger
  • directional (one-tailed)
  • alpha (.05) is all in one tail
  • critical values larger
  • more 'powerful' test
  • further steps for z-tests & t-tests

    1. confidence intervals
    2. checking for errors