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Review t-tests. Single-sample t-test (df = N – 1) Independent samples t-test (df = (n 1 – 1)+(n 2 – 1) ) Related or paired-samples t-test (df = N – 1). ANOVA formulas. One-way ANOVA df total = N – 1 df between = k – 1 df within =  (n – 1) or N – k. Repeated-measures ANOVA

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review t tests
Review t-tests
  • Single-sample t-test (df = N – 1)
  • Independent samples t-test (df = (n1 – 1)+(n2 – 1) )
  • Related or paired-samples t-test (df = N – 1)
anova formulas
ANOVA formulas

One-way ANOVA

dftotal = N – 1

dfbetween = k – 1

dfwithin = (n – 1) or N – k

Repeated-measures ANOVA

dftotal = N – 1

dfbetween = k – 1

dfwithin = N – k

dfbetween subjects = n – 1

dferror = dfwithin – dfbetween subjects

One-way ANOVA Repeated-measures ANOVA

Two-way ANOVA

dftotal = N – 1

dfbetween = k – 1 (or # cells -1)

dfwithin = N – k (or  (n-1) )

dfA = k – 1 (# rows – 1 for factor A)

dfB = k – 1 (# columns – 1 for factor B)

dfAxB = dfbetween – dfA - dfB

effect size analyses
Effect size analyses
    • Variance accounted for (r2)
      • Small >.01
      • Medium >.09
      • Large > .25
  • Paired samples t-test
    • CI = MD ± t*(sMD)
    • Cohen’s d
    • Variance accounted for (r2)
    • ANOVA: effect size = eta2
  • z-test
    • CI = M +/- z*(σM)
  • One-sample t-test
    • CI = M +/- t*(sM)
  • Independent t-test
    • CI = M1 – M2 +/- t*(sM1-M2)
    • Cohen’s d
      • Small >.2
      • Medium >.5
      • Large > .8
other formulas
Other formulas
  • Goodness of fit chi-square
  • Frequency table of data
    • Observed frequencies (fo)
  • Compare to null hypothesis
    • Expected frequencies (fe)
  • Expected frequency
    • fe = pn
  • Chi-square equation
  • df = C – 1, where C = # of categories
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