Create Presentation
Download Presentation

Download Presentation
## ANOVA Analysis of Variance

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**The Plan for Today**• Basics of parametric statistics • ANOVA – Analysis of Variance • T-Test and ANOVA in SPSS • Lunch • T-test in SPSS • ANOVA in SPSS**What kind of data canwe analyse usingparametricstatistics?**• The arithmetic mean can only be derived from interval or ratio measurements. • Interval data – equal intervals on a scale; intervals between different points on a scale represent the difference between all points on the scale. • Ratio Data – has the same property as interval data, however the ratios must make mutually sense. Example 40 degrees is not twice as hot as 20 degrees; reason the celsius scale does not have an absolute zero.**Whencanweuseparametricstatistics?**• Assumption 1: Homogeneity of variance – means should be equally accurate. • Assumption 2: In repeated measure designs: Sphericity assumption. • Assumption 3: Normal Distribution**Parametric statistics**• Assumption 1:Homogeneity of variance • The spread of scores in each sample should be roughly similar • Tested using Levene´s test • Assumption 2:The sphericityassumption • Tested using Mauchly´s test • Basically the same thing:homogeneity of variance**When is a distribution far enough from normal to become a**problem? • Assumption 3: Normal Distribution. • In SPSS this can be checked by using: • Kolmogorov-Smirnov test • Shapiro-Wilkes test • These compare a sample set of scores to a normally distributed set of scores with the same mean and standard deviation. • If (p> 0.05) The distribution is not significantly different from a normal distribution • If (p< 0.05) The distribution is significantly different from a normal distribution**Analysis of Variance**• Difference between t-test and ANOVA: • t-test is used to analyze the difference between TWO levels of an independent variable. • ANOVA is used to analyze the difference between MULTIPLE levels of an independent variable.**Analysis of Variance**• Independent variable = apple • Dependent variables could be: sweetness, decay time etc. t-test ANOVA …or more**Analysis of Variance**• The ANOVA tests for an overall effect, not the specific differences between groups. • To find the specific differences use either planned comparisons or post hoc test. • Planned comparisons are used when a preceding assumptions about the results exists. • Post Hoc analysis is done subsequent to data collection and inspection.**Analysis of Variance**• A Post Hoc Analysis is somewhat the same as doing a lot of t-tests with a low significance cut-of point, the Type I error is controlled at 5%. • Type I error: Fisher’s criterion states that there is a o.o5 probability that any significance is due to diversity in samples rather than the experimental manipulation – the α-level. • Using a Bonferroni correction adjusts the α-level according to number of tests done (2 test = o.5/2 = 0.025. 5 test= 0.5/5= 0.01). Basically the more tests you do the lower the cut of point.**The logic of an ANOVA**• Variation in a set of scores comes from two sources: • Random variation from the subjects themselves (due to individual variations in motivation, aptitude, etc.) • Systematic variation produced by the experimental manipulation.**F-ratio**• ANOVA compares the amount of systematic variation to the amount of random variation, to produce an F-ratio: systematic variation F = random variation (‘error’)**F-ratio**• Large value of F: a lot of the overall variation in scores is due to the experimental manipulation, rather than to random variation between subjects. • Small value of F: the variation in scores produced by the experimental manipulation is small, compared to random variation between subjects.**Calculations I**• In practice, ANOVA is based on the variance of the scores. The variance is the standard deviation squared: variance**Calculations II**• We want to take into account the number of subjects and number of groups. Therefore, we use only the top line of the variance formula (the "Sum of Squares", or "SS"): • We divide this by the appropriate "degrees of freedom" (usually the number of groups or subjects minus 1). sum of squares**Three types of SS (sum of squares)**• Between groups SSM: a measure of the amount of variation between the groups. (This is due to our experimental manipulation).**Three types of SS (sum of squares)**• Within GroupsR: a measure of the amount of variation within the groups. (This cannot be due to our experimental manipulation, because we did the same thing to everyone within each group).**Three types of SS (sum of squares)**• Total sum of squares:a measure of the total amount of variation amongst all the scores. (Total SS) = (Between-groups SS) + (Within-groups SS)**Significance of F-Ratio**• The bigger the F-ratio, the less likely it is to have arisen merely by chance. • Use the between-groups and within-groups d.f. to find the critical value of F. • Your F is significant if it is equal to or larger than the critical value in the table.**Here, look up the critical F-value for 3 and 16 d.f.**Columns correspond to between-groups d.f.; rows correspond to within-groups d.f. Here, go along 3 and down 16: critical F is at the intersection. Our obtained F, 25.13, is bigger than 3.24; it is therefore significant at p<.05. (Actually it’s bigger than 9.01, the critical value for a p of 0.001).**Overview**• One –Way ANOVA • Independent • Repeated Measures • Two-way ANOVA • Independent • Mixed • Repeated Measures • N-way ANOVA**One-Way Independent ANOVA**• One-Way: ONE INDEPENDENT VARIABLE • Independent: 1 participant = 1 piece of data. Independent variable: Yoga Pose,3 levels Dependent variables: Heart rate, oxygen saturation**One-Way Dependent ANOVA**• One-Way: ONE INDEPENDENT VARIABLE • Dependent : 1 participant = Multiple pieces of data. Independent variable:Cake,3 levels Dependent variables: Blood sugar, pH-balance**Two-Way Independent ANOVA**• Two-Way : TWO INDEPENDENT VARIABLES • Independent : 1 participant = 1 piece of data. Independent variables: Age, Music Style >40 <40 Indie-Rock Classic Pop**Two-Way Mixed ANOVA**• Two-Way : TWO INDEPENDENT VARIABLES • Mixed: • Variable 1: Independent (Controller) • Variable 2: Repeated measures (Space Ship)**Two-Way Dependent ANOVA**• Two-Way: TWO INDEPENDENT VARIABLES • Dependent : 1 participant = Multiple pieces of data. Independent variables: Exercise, Temperature 30 ° 20 ° 25 °**SPPS**SPSS**Click ‘Options…’**Then Click Boxes: Descriptive; Homogeneity of variance test; Means plot**Things to remember**• One-way independent-measures ANOVA enables comparisons between 3 or more groups that represent different levels of one independent variable. • A parametric test, so the data must be interval or ratio scores; be normally distributed; and show homogeneity of variance. • ANOVA avoids increasing the risk of a Type 1 error.