4/22/2010. Test 3 Review ANOVA
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1 Test 3 Review ANOVA 1
2 School recruiter wants to examine if there are difference between students at different class ranks in their reported intensity of school spirit. What is the factor? How many levels does it have? Null hypothesis: Research hypothesis: 2
3 Null hypothesis: school spirit does not differ among the class ranks Mean Fresh = Mean Soph = Mean Junior = Mean Senior Research hypothesis: at least one mean school spirit differs among class rank Mean Fresh Mean Soph Mean Junior Mean Senior 3
4 More than 2 groups Same outcome measure =ANOVA F = MS between MS within MS between = SS between /df between MS within = SS within /df within SS between = 36 SS within = 50 N = 40 4
5 F = MS between MS within MS between = SS between /df between Df between = k-1 (k=# of groups) = 4-1 =3 36/3 = 12 MS within = SS within / df within Df within = N-k (N=sample size) = 40-4 =36 50/36 = 1.39 F = MS between MS within =12/1.39 =
6 At F(3, 36), critical value at p <.05 is 2.88 At p <.01 = > 2.88 So it does exceed the critical value If over the critical value, reject the null 6
7 There was at least one significant difference in school spirit among class rank levels, F(3,36) 36) = 8.43, p <.01. 7
8 Type III Sum Source of Squares df Mean Square F Sig. Corrected Model (a) Intercept cond Error Total Corrected Total Source Type III Sum of Squares df Mean Square F Sig. Corrected Model (a) Intercept gender video gender * video Error Total Corrected Total
9 Correlation A study of the relationship between consumption of high fructose corn syrup and weight gain in one month Participants Intake (g) Weight (lbs)
10 Null hypothesis: no relationship between intake of corn syrup and weight gain in a month Ρ intake*weight = 0 (okay to use r instead of rho) Research hypothesis: relationship between intake of corn syrup and weight gain in a month R intake*weight 0 10
11 Relationship between 2 continuous measures e at o s p bet ee co t uous easu es = Correlation coefficient 11
12 r xy = xy n ΣXY - ΣX ΣY [n ΣX 2 (ΣX) 2 ][n ΣY 2 -(ΣY) 2 ] r xy = correlation coefficient between x & y n = size of sample X = score on X variable Y = score on Y variable Part. X (Intake) SUM Y (Weight) X 2 Y 2 XY 12
13 Part. X (Intake) Y (Weight) X 2 Y 2 XY SUM Part. X (Intake) Y (Weight) X 2 Y 2 XY SUM
14 r xy = xy n ΣXY - ΣX ΣY [n ΣX 2 (ΣX) 2 ][n ΣY 2 -(ΣY) 2 ] = 6(870)- (310)(9) [6(23150) (310) 2 ][6(39)- (9) 2 ] = [ ] / sr [( )(234-81) =2430/sr(42800)(153) = 2430/sr =2430/ =.95 14
15 df = n 2 = 6 2 = 4 At df = 4, critical value at p <.05 is.81, at p <.01 is >.81 &.92 So it does exceed the critical value If over the critical value, reject the null 15
16 There was a significant positive correlation between intake of high fructose corn syrup and weight gain during a month, r(4) =.95, p <.01. r =.95 16
17 r =.95 r 2 =.90 90% of variance in weight gain is explained by variance in how much corn syrup was consumed during the month How much was not explained? Regression 17
18 A study of the relationship between consumption of soda and weight gain two months later 18
19 Null hypothesis: no relationship between soda consumption and weight gain b = 0 Research hypothesis: relationship between soda consumption and weight gain b 0 19
20 Continuous measurements One measurement e e theoretically et or empirically precedes the other = Linear regression b = ΣXY (ΣXΣY / n) b ( / ) ΣX 2 [(ΣX) 2 / n] 20
21 Part. X (Intake) SUM Y (Weight) X 2 Y 2 XY Part. X (Intake) Y (Weight) X 2 Y 2 XY SUM
22 b = ΣXY (ΣXΣY / n) ΣX 2 [(ΣX) 2 / n] =[870 (310*9/6)] / [310 2 /6] = ( ) / ( ) =405/ =.06 Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) Intake
23 The output indicates that β =.95 exceeds the test statistic at p <.01 So it does exceed the critical value If over the critical value, reject the null 23
24 Consumption of soda significantly predicted weight gain, β =.95, t = 8.43, p <.01, such that more soda consumption predicted d greater weight gain Could further say that: for every additional gram of soda consumed, participants gained an additional.06 pounds. Chi-square 24
25 Do more students prefer their statistics course or pottery making? 25
26 Null hypothesis: there is no difference in the proportion p of students who prefer statistics versus pottery making P Stats = P Pottery Research hypothesis: there is a difference in the proportion of students who prefer statistics versus pottery making P Stats P Pottery 26
27 Frequency of 2 categories =chi-square x 2 = Σ (O-E) 2 X 2 = chi square O = observed frequency E = expected frequency E 27
28 O E (O-E) (O-E) 2 (O-E) 2 /E Statistics Pottery Total
29 df = r-1 (r=# of rows) = 2-1 = 1 At df = 1, critical value at p <.05 is 3.84, at p <.01 is > 3.84 & 6.64 So it does exceed the critical value If over the critical value, reject the null 29
30 Significantly more participants reported a preference for Statistics (80%) versus Pottery Making (20%), Χ 2 (1) = 18.00, p <
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