PSY 210 Exam #3

A procedure used to evaluate the differences between two or moretreatments (groups) – a t-test compares only two groups.

• Assuming there are 3 groups – more μ values if there are more groups
• H₀: μ₁ = μ₂ = μ₃
• H₁: not H₀

When there is more than 2 sample means it is impossible to computemean differences (therefore need to use “variance”)

Variance is simply a method for measuring how big the differences arefor a set of numbers (variance = differences)

• (1) Not all the scores are the same – there is variability (variance)
• (2) There are 3 types of variability –
• (a) total
• (b) between-treatments
• (c) within-treatments

• (1) The deviation of each score from the Grand Mean (viz. the average of all the scores)
• (2) This variability can be partitioned or divided into 2 parts:
• (a) the amount that score deviates from its group mean
• (i.e., within-treatment variation)
• (b) the amount that score’s group mean differs from the grand mean
• (i.e., between-treatment variation)

• (1) Measures the differences between sample means
• (2) What causes those differences between means?
• (a) Treatment Effects: Systematic differences between groups due to the effect of the IV
• (b) Chance or Experimental Error
• (3) Sources of chance or experimental error
• (a) Individual Differences (e.g., sleep, past drug use, IQ, etc.)
• (b) Measurement Error (e.g., not calibrating a machine, misreading a dial, etc.)

Systematic differences between groups due to the effect of the IV

If all Ss were the same (no experimental error), all the subjects who received thesame treatment (e.g., 10 mg of a drug) would have the same score on the DV

The variability of subjects in the same condition gives us an estimate ofchance or experimental error. As such, within-treatments variability is solelycaused by chance or experimental error.

To test for treatment effects (did the IV impact the DV). The F-ratio allows youto accomplish this goal.

• You form a ratio in which
• [“conceptual formula”]

• 
• This equals 1

• bigger and bigger (making the overall fraction large).
• If the fraction (i.e.,value of this test statistic) gets large enough, we will feel that we haveadequate evidence to Reject H_o and conclude that we have treatment effects

• k = the number of treatment conditions (groups)
• n = the number of scores in each treatment
• N = the total number of scores in the entire study
• T = the total for each treatment condition (ΣX) [needed for formulas so memorize]
• G ("Grand Total") = the sum of all the scores in the study G = ΣT [needed for formulas so memorize]

• (add up all SS values for each group)
• 

• (1) df_Total = N – 1
• (2) df_{Within-treatments} = N – k
• (3) df_{Between-treatments} = k – 1

Need to convert Sums of Squares (SS) into Variance estimates [i.e., Mean Square (MS)values] to use them in Analysis of Variance

MS or Variance = SS/df

• (1) MS_{Between-treatments} = SS_{Between-treatments} / df_{Between-treatments}
• (2) MS_{Within-treatments} = SS_{Within-treatments} / df_{Within-treatments}

F = MS_{Between-treatments} / MS_{Within-treatments}

• (1) F-values will always be positive (there is never a negative variance)
• (2) When H₀ is true, F is close to 1.00. As such, the distribution piles up around 1.00.

Purpose: Used to obtain critical value for boundary of your Critical Region

• * Research Question: Are these drugs equally effective as pain relievers?*
• DV: # of seconds that a painful stimulus is endured

• (A) Step #1 – State the hypotheses
• (1) H₀: μ₁ = μ₂ = μ₃ = μ₄
• (2) H₁: not H₀

• (B) Step #2 – Set the criteria for a decision
• (1) α = .05

• (C)Step #3 Determine and draw boundary of the critical region(from Table B.4)
• ** Draw graph with the critical regionsPage #5

• (D) Step #4 – Collect data and compute sample statistics
• (1) Part 1 = calculate SS values
• (2) Part 2 = calculate MS values
• (3) Part 3 = calculate F statistic
• (4) Part 4 = complete the ANOVA Summary Table
• (E) Step #5 – Make a decision
• (1) Draw obtained score (“test statistic”) on the graph
• (2) Decision Rule:
• (a) If obtained value is in the critical region, you “Reject H₀”
• (b) If obtained value is not in the critical region, you “Fail to Reject H0”
• (3) Decision = Reject H₀ (conclude that these drugs effective are not equally effective as painrelievers -- that is there are differences among the 4 groups)

Note: Still need to do post-hocs to determine “what differs from what”

• (A) Independent scores
• (B) Normality (the populations from which the samples are selected must be normal)
• (C) Homogeneity of Variance (the populations from which the