F tests

• F test = variation of scores between groups/variation of scores within groups
• F test is also known as ANOVA
• F test is an inferential statistic that uses the F distribution for determining if there’s a significant difference among group scores.
• One-way ANOVA have 1 IV
• two-way ANOVA have 2 IV
• three-way ANOVA have 3 IV
• Factorial ANOVAs are ANOVAs with at least 2 IV
• Between subjects design: Each group experiences one condition only (each participant gets either drug A or drug B but not both)
• Within subjects design: Each group experiences all conditions (each participant gets both drugs)
• One-way between-subjects ANOVA are ANOVAs with 1 IV where participants are assigned to only 1 of multiple conditions
• One-way within-subjects ANOVA are ANOVAs with 1 IV where participants are assigned to all conditions
• If p value from SPSS output is less than .05, reject H null
• Numerator DF concern the variation of scores between groups
• Denominator DF concern variation of scores within groups
• Numerator DF for one-way between-subjects ANOVA?

  g-1 (g = number of groups)
• Denominator DF for one-way between-subjects ANOVA?

  Error DF = g(n-1) n = subjects/group
• Numerator DF for one-way within-subjects ANOVA?

  g-1 (g = number of groups/time period)
• Denominator DF for one-way within-subjects ANOVA?

  Error DF = n-1 x g-1, n = # of subjects
• What is the numerator DF of a one-way between-subjects ANOVA with 3 groups?

  (g-1) => (3-1) = 2
• What is the denominator DF of a one-way between-subjects ANOVA with 3 groups and 10 participants per group?

  g(n-1) => 3(10-1) = 27
• What is the numerator DF for a one-way within-subjects ANOVA with 3 groups per time period?

  (g-1) => (3-1) = 2
• What is the denominator DF of a one-way within-subjects ANOVA with 15 participants measured across 3 time periods?

  (n-1)x(g-1) => (15-1)x(3-1) = 28
• What is the denominator DF for a one-way within-subjects ANOVA with 30 participants measured across 3 time periods?

  (n-1)x(g-1) => (30-1)x(3-1) = 58
• One-way between-subjects ANOVA example: Suppose you examine 30 participants for a difference in anxiety among people with 3 different types of pets. What is the IV, DV, how many groups, how many participants, and how many participants per group?


  IV: Pet type DV: Anxiety

  Number of groups: 3 (one for each type of pet)

  Number of participants: N = 30

  Number of participants per group: n = 10
• Write these between-subjects results in APA format: Pet type DF = 2, Error DF = 27, F = 4.033, Sig = .029?

  F(2, 27) = 4.03, p = .03
• One-way within-subjects ANOVA example: Suppose you examine for a difference in anxiety among 3 time periods in 1 group of 15 participants. Suppose anxiety is measured once before therapy and twice (at different) after therapy What is the IV, DV, how many groups and participants?


  IV: Therapy

  DV = Anxiety

  3 groups

  N = 15
• Write these within-subjects results in APA format: Sphericity Assumed DF = 2, Error DF = 28, F = 4.632, Sig = .018?


  F(2, 28) = 4.63, p = .02
• Two-way between-subjects ANOVA example: Test the effect of 2 drugs (drug A and B) and 2 doses (high and low dose) on symptoms. What are the IV, DV, and how are participants assigned to conditions?


  IV: Drug (A or B) and Dose (high or low dose) DV: Symptoms

  Participants receive 1 of 4 conditions (A low, A high, B low, B high), 2 x 2 factorial ANOVA (each IV has 2 groups)
• Factorial ANOVAs: examine multiple IVs at once and the interaction of the IVs
• two-way between-subjects ANOVA example: Examine a difference in anxiety level as a function of disorder type (OCD, generalized anxiety) and pet type (dog, cat, owl). 30 participants (N = 30), disorder type n = 15, pet type n = 10, 2 x 3 factorial ANOVA. 1 IV has 2 groups, 1 IV has 3 levels.
• Anxiety Disorder Type: F(1,24)=10.82, p=.003. Reject H null?

  Yes
• Pet Type: F(2,24)=4.91, p=.02. Reject H null?

  Yes
• Anxiety Disorder Type by Pet Type Interaction: F(2,24)=.52, p=.60. Reject H null?

  No
• Two-way within-subjects ANOVA example: Test the effect of 2 drugs (drug A and B), and 2 doses (low and high dose) on symptoms. What is the IV, DV, how are participants assigned to conditions?


  IV: Drug (A and B), Dose (low and high dose) DV: Symptoms Participants are assigned to all 4 conditions (A low, A high, B low, B high)
• Main effect is the effect of one IV averaged across the levels of the other IVs
• Main effect tests if there is a difference between drug A and drug B
• Main effect tests if there is a difference between doses (low and high dose)
• The number of main effects equals the number of IVs
• Interactions test whether the relationship between two variables depends on another variable.
• Simple effect is the effect of one IV at one level of another IV