Evaluating Main Effect

Political Orientation and Taste Study

  • The study includes two variables: political orientation (ConLib) and taste condition (Conditioned).
  • ConLib was not statistically significant, but Conditioned was significant as a main effect.
  • The analysis will focus on following up on the Conditioned variable only.
  • Mean squares error will be used for the error term in planned comparisons.
  • Corrected total sums of squares will be used to calculate eta squared.

Main Effect of Taste

  • The effect of liberal versus conservative (political orientation) was not significant.
  • The means for liberals and conservatives showed no statistically meaningful differences in moral judgments.
  • The main effects were observed in the bitter versus water versus sweet taste conditions.
  • The hypothesis was that the bitter condition would lead to more extreme moral judgments.

Pairwise and Complex Comparisons

  • The approach involves first comparing water and sweet conditions.
  • If no significant difference is found, these two conditions will be combined and compared to the bitter condition.
  • The means for water and sweet conditions are nearly identical.
  • An F ratio and p-value will still be computed and reported even if the effect isn't significant.

Pairwise Comparison: Water vs. Sweet

  • Compute psi, which is the difference between the means of water and sweet conditions.
  • psi = 0.0097 (high precision due to slight differences in means)
  • Calculate the sums of squares for the comparison using the formula:
    SS_{comparison} = \frac{N \times psi^2}{Contrast\ Sum\ of\ Squares}
  • N is the sample size associated with the means being compared (N = 40 in this case).
  • Because it is a single degree of freedom comparison, the sums of squares value is also the mean squares value. MS = SS

F Ratio

  • Compute the F ratio using the formula:
    F = \frac{MS{comparison}}{MS{error}}
  • The error term (mean squares error) is taken directly from the SPSS output.
  • The result was not statistically significant.
  • Differences observed are likely due to sampling error.

Effect Size: Eta Squared

  • Compute eta squared as a measure of effect size:
    η^2 = \frac{SS{effect}}{SS{total}}
  • Use the corrected total sums of squares from the SPSS output.
  • In this case, eta squared is 0, indicating no effect.

Complex Comparison: Bitter vs. Combination of Water and Sweet

  • Compute psi using contrast weights.
  • Contrast weights used: 2 (bitter), -1 (water), -1 (sweet).
  • The formula is: \text{psi} = c1 \times \text{mean}1 + c2 \times \text{mean}2 + c3 \times \text{mean}3 where c_i are the contrast weights.
  • Means are obtained from the SPSS output.

Sums of Squares

  • Calculate the sums of squares using the appropriate formula.

  • The resulting sums of squares value is also the mean squares value (single degree of freedom comparison).

    F Ratio for the Complex Comparison

  • Calculate the F ratio using the formula:

    F = \frac{MS{comparison}}{MS{error}}

  • The calculated F ratio exceeds the critical value (3.92).

  • The bitter condition is significantly different from the combination of water and sweet conditions.

Effect Size: Eta Squared for the Complex Comparison

  • Compute eta squared to determine the proportion of variance accounted for.

    η^2 = \frac{SS{effect}}{SS{total}}

  • Eta squared = 0.3031, indicating that approximately 30% of the variation in moral judgment is accounted for by the difference between bitter and the combined water/sweet conditions. This indicates a fairly strong effect.