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Lecture 9

# PYB210 Lecture 9 Notes.docx

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Department
Psychology
Course
PYB210
Professor
Unknown
Semester
Spring

Description
PYB210 Lecture Notes – Week 9 Chapter 8 - Power and Effect Size Overview of Lecture  Effect Size o Eta squared (R ) o Omega squared o PASW/SPSS  Power o Calculation o Sample size o PASW/SPSS Effect Size  A significant F simply tells us that there is a difference between means. It does not tell us how big this difference is or how important this effect is.  An F that is significant at 0.01 does not necessarily imply a bigger or more important effect size than an F significant at 0.05. This is because the significance of F is dependent on the sample size and the number of conditions.  Therefore, we need a statistics which summarizes the strength of the treatment effect: 2 2 o Eta squared (η ) = R o Omega squared (ω ) 2  Both of these indicate the proportion of the total variability in the data accounted for by the effect of the IV. Eta Squared 2 2  Eta squared – or η – treats our ANOVA data as though it came from a correlation st2dy. η is simply the squared correlation coefficient from a regression on this data – a.k.a. it is R .  There is a sum for calculating eta squared which essentially the sum of squares for the treatment variability divided by the sum of squares for the total variability (treatment + error).        These sums of squares totals come from the following table (example below).  The example sum provided above tells us that 65% of the variability comes from the IV. Problems with Eta Squared  The eta squared relies on numerically ordered data to provided a regression from which the η is calculated. In other words, it wrongly assumes that the levels of the IV can be treated as quantitative.  It also wrongly assumes that the regression line will pass through the groups’ means.  Thus, in instances where our independent variable is categorical, there is no logical way to order our levels of the IV into a correlation.  However, SPSS still uses this as its go-to measure of effect size and in most cases it is relatively accurate. Omega Squared  This on the other hand is a better estimate of effect size as it does not have the two problems that eta squared d2es (highlighted previously).  There are two versions of ω . One is for fixed model ANOVAs and the other is for random model ANOVAs.  A fixed model ANOVA is where the particular levels of the IV have been deliberately chosen by the experimenter (e.g. deliberately choosing 4, 8 and 12 hrs sleep deprivation).  A random model ANOVA is where the particular levels of the IV in the experiment have been selected at random from a number of possible levels of the IV.  In PYB210 we always assume that we are using a fixed model ANOVA. 2  The conceptual formula for ω is as follows:  There is also a computational formula which is much larger but easy and could possibly be on the exam! An example of this formula is given below:  Where a = number of levels of IV; F = F ratio for ANOVA; n = number of scores per group.  The above example tells us that the IV accounted for 54.3% of the variability in the data (this is a large effect). Interpreting Effect Size  Once you have obtained either you eta or omega squared you need to interpret it.  Remember that they are both a proportion and can range from 0 (IV had no effect) to 1 (100% variability accounted for by IV).  If the F is < 1 than the proportion will be expressed as a negative number.  Cohen (1988) proposed the following scale for effect size: o 0.01 = small effect o 0.06 = medium effect o > 0.15 = l
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