Review t tests
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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

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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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