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## Six Easy Steps for an ANOVA

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**Six Easy Steps for an ANOVA**• 1) State the hypothesis • 2) Find the F-critical value • 3) Calculate the F-value • 4) Decision • 5) Create the summary table • 6) Put answer into words**Example**• Want to examine the effects of feedback on self-esteem. Three different conditions -- each have five subjects • 1) Positive feedback • 2) Negative feedback • 3) Control • Afterward all complete a measure of self-esteem that can range from 0 to 10.**Example:**• Question: Is the type of feedback a person receives significantly (.05) related their self-esteem?**Step 1: State the Hypothesis**• H1: The three population means are not all equal • H0: pos = neg =cont**Step 2: Find F-Critical**• Step 2.1 • Need to first find dfbetween and dfwithin • Dfbetween = k - 1 (k = number of groups) • dfwithin = N - k (N = total number of observations) • dftotal = N - 1 • Check yourself • dftotal = Dfbetween + dfwithin**Step 2: Find F-Critical**• Step 2.1 • Need to first find dfbetween and dfwithin • Dfbetween = 2 (k = number of groups) • dfwithin = 12 (N = total number of observations) • dftotal = 14 • Check yourself • 14 = 2 + 12**Step 2: Find F-Critical**• Step 2.2 • Look up F-critical using table F on pages 370 - 373. • F (2,12) = 3.88**Step 3: Calculate the F-value**• Has 4 Sub-Steps • 3.1) Calculate the needed ingredients • 3.2) Calculate the SS • 3.3) Calculate the MS • 3.4) Calculate the F-value**Step 3.1: Ingredients**• X • X2 • Tj2 • N • n**X**X = 85 Xp = 40 Xn = 25 Xc = 20**X2**X = 85 X2 = 555 Xp = 40 Xn = 25 Xc = 20 X2n = 135 X2c = 90 X2p = 330**T2 = (X)2 for each group**X = 85 X2 = 555 Xp = 40 Xn = 25 Xc = 20 X2n = 135 X2c = 90 X2p = 330 T2n = 625 T2c = 400 T2p = 1600**Tj2**X = 85 X2 = 555 Tj2= 2625 Xp = 40 Xn = 25 Xc = 20 X2n = 135 X2c = 90 X2p = 330 T2n = 625 T2c = 400 T2p = 1600**N**X = 85 X2 = 555 Tj2= 2625 N = 15 Xp = 40 Xn = 25 Xc = 20 X2n = 135 X2c = 90 X2p = 330 T2n = 625 T2c = 400 T2p = 1600**n**X = 85 X2 = 555 Tj2= 2625 N = 15 n = 5 Xp = 40 Xn = 25 Xc = 20 X2n = 135 X2c = 90 X2p = 330 T2n = 625 T2c = 400 T2p = 1600**X = 85**X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SStotal**X = 85**X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SStotal 85 73.33 555 15**X = 85**X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SSWithin**X = 85**X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SSWithin 2625 30 555 5**X = 85**X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SSBetween**X = 85**X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SSBetween 43.33 2625 85 5 15**Step 3.2: Calculate SS**• Check! • SStotal = SSBetween + SSWithin**Step 3.2: Calculate SS**• Check! • 73.33 = 43.33 + 30**Step 3.3: Calculate MS**43.33 21.67 2**Step 3.3: Calculate MS**30 2.5 12**Step 3.4: Calculate the F value**21.67 8.67 2.5**Step 4: Decision**• If F value > than F critical • Reject H0, and accept H1 • If F value < or = to F critical • Fail to reject H0**Step 4: Decision**• If F value > than F critical • Reject H0, and accept H1 • If F value < or = to F critical • Fail to reject H0 F value = 8.67 F crit = 3.88**Step 6: Put answer into words**• Question: Is the type of feedback a person receives significantly (.05) related their self-esteem? • H1: The three population means are not all equal • The type of feedback a person receives is related to their self-esteem**Practice**• You are interested in comparing the performance of three models of cars. Random samples of five owners of each car were used. These owners were asked how many times their car had undergone major repairs in the last 2 years.**Practice**• Is there a significant (.05) relationship between the model of car and repair records?**Step 1: State the Hypothesis**• H1: The three population means are not all equal • H0: V = F =G**Step 2: Find F-Critical**• Step 2.1 • Need to first find dfbetween and dfwithin • Dfbetween = 2 (k = number of groups) • dfwithin = 12 (N = total number of observations) • dftotal = 14 • Check yourself • 14 = 2 + 12**Step 2: Find F-Critical**• Step 2.2 • Look up F-critical using table F on pages 370 - 373. • F (2,12) = 3.88**Step 3.1: Ingredients**• X = 60 • X2 = 304 • Tj2 = 1400 • N = 15 • n = 5**X = 60**X2 = 304 Tj2= 1400 N = 15 n = 5 Step 3.2: Calculate SS • SStotal**X = 60**X2 = 304 Tj2= 1400 N = 15 n = 5 Step 3.2: Calculate SS • SStotal 60 64 304 15**X = 60**X2 = 304 Tj2= 1400 N = 15 n = 5 Step 3.2: Calculate SS • SSWithin**X = 60**X2 = 304 Tj2= 1400 N = 15 n = 5 Step 3.2: Calculate SS • SSWithin 1400 24 304 5**X = 60**X2 = 304 Tj2= 1400 N = 15 n = 5 Step 3.2: Calculate SS • SSBetween