Statistics Notes

T Distributions 2/15

  • allows to estimate statistics to a population using samples

  • Degrees of Freedom (df)

    • concept in stats that determines the distribution is appropriate for sample data

    • tells you which t distribution to use

  • df=N-1 (Degrees of Freedom for T Distribution/T Test)

    • df means degrees of freedom

    • N means number of samples

    • if a sample contains 12 numbers, df=11

T Distribution Table

  • first column shows degrees of freedom

  • always use .05 unless told otherwise

  • always use two tailed test

  • go back to smallest, closest degree of freedom is not on chart

One-Sample Designs (CH.9) 2/20

  • Null Hypothesis Significance Testing (NHST)

  • is mean of the sample different or equal to the standard

  • effect size index

    • tells us how big of an impact does the difference have

    • d= (xbar - mew 0)/ (s hat)

      • xbar is sample mean

      • mew 0 is standard

      • shat is estimate of the population, standard deviation based on sample

    • Cohen’s D

  • Organize data, solve, interpret

  • one sample t test to determine statistical significance

    • organize data

      • xbar, mew zero, shat, cohens d, n

    • calculate degree of freedom

      • df = n-1

    • calculate effect size

    • establish our NHST logic

      • alternative hypothesis (hypothesis of difference)

      • null hypothesis (hypothesis of equality)

        • only test the null

    • establish significance level (alpha level) always use 0.05

      • probability of having type one error

        • type 1 error

          • finding results when there are none, you will have an error type 1

        • type 2 errors

          • finding nothing when are true, you will have an error type 2

        • eliminate both error types

    • find standard error of the mean (s sub xbar)

      • s sub xbar = shat / sqr root of N

    • find t value

      • one sample t test formula (page 187)

    • go to t distribution chart (table d, appendix c, pg 388)

    • compare critical t with found t

      • critical value in chart

      • found t value math one

        • if found t value > than critical t = we reject the null