Unformatted text preview: Looking ahead... Week Looking ahead... Week of 3/24 Lab #7 Week of 3/31 Lab #8 Week of 4/7 Lab #9 Week of 4/14 Game Show in Labs
If there is room, you're more than welcome to you' sit-in on other labs for review! sit Quiz of 4/21 Lab #10 4/23 Last class (end of material) 4/28 ONLY Final rounds for Game Show contestants & Review 5/5 at Noon: Final Exam (location TBD) #4 4/16 Introduction to Where we've been... Describing Predicting Testing Analysis of Variance & graphically depicting data relationships among variables: correlation, regression hypotheses about means: 1 Sample Z-test (is the sample mean = to the population mean?) ZBinomial (are our observed frequencies = expected?) Chi-Sq (are our observed frequencies = expected? is there an Chiassociation between two categorical variables?) t-tests (are two means = ?)
"Certainty is the mother of quiet and repose, and uncertainty the cause of variance and contentions" contentions" -Edward Coke
One sample Dependent groups/Paired samples (w/n subjects) Independent groups (b/n subjects) 1 ANOVA Testing ANOVA preview Introduction mean differences observed between two or more means.
Can look at one factor that has more than two levels. One of the major advantages over using a t-test tAnother advantage is using a smaller number of statistical tests to analyze your data. to ANOVA logic One-way Between Subjects ANOVA (2 + Onegroups, means on one measure: do the groups differ?) One-way Repeated measures ANOVA (one Onegroup, 2+ measurements such as testtestretest, do the means across measurements change/differ?) Factorial ANOVA: (2+ groups, 2+ measurements) ANOVA: Basic Logic ANOVA ANOVA Basic Logic Although = Analysis of Variance Analysis = dividing into smaller parts The formula analyzes variability within and
between the groups. ANOVA uses variances in the computation, the purpose is to evaluate differences in means between treatment. computational purposes, cannot compute a mean difference of more than 2 means.
Concept of mean difference becomes difficult to define and impossible to calculate when there are more than 2 means. For obtained difference between 2 sample means variance (differences) between sample means t =F = standard error (difference expected w/no tx effect variance (differences) expected effect) 2 ANOVA: General Example
Placebo Placebo Drug A Drug B GRAND Mean ANOVA: Basic Logic ANOVA = Analysis of Variance Analysis = dividing into smaller parts The formula analyzes variability within and
between the groups. Mean2 Mean1 Mean3 variance (differences) between sample means treatment effect + differences due to chance (error) F= F= variance (differences) to chancew/no tx effect differences due expected (error) ANOVA Logic
treatment effect + differences due to chance (error) F= differences due to chance (error) Null ANOVA: Basic Logic
hypothesis: All groups are randomly drawn from identical populations (means are equal)
H 0 : 1 = 2 = 3 = ...k Research Sources of variability for the F-ratio F If there are no treatment effects, what would we expect F to ~ equal? hypothesis: Groups are drawn from populations w/ different means (means are not equal) H 0 : 1 2 3 ... k 3 ANOVA: Basic Logic Basic ANOVA: Basic Logic If logic = we will get two estimates of the population variance using two different methods and see if they agree
If H0 is true, they should agree If H0 is false, they will not agree null hypothesis is true, there are two equally good ways of estimating the population variance:
Within-groups estimate: Based on variation of Withinthe scores within each group Between-groups estimate: Based on the Betweenvariation of the means of the groups ANOVA: Basic Logic
Variation: Ho true: w/n estimate reflects: btwn estimate reflects: Ho false: w/n estimate reflects: btwn estimate reflects:
F= ANOVA: General Example
Placebo Placebo Drug A Drug B Sampling Error Tx effects X X X X GRAND Mean Mean2 X Mean1 Mean3 treatment effect + differences due to chance (error) differences due to chance (error) 4 ANOVA: Basic Logic Therefore... Therefore... ANOVA: Basic Logic If Ho is true:
The two estimates (within-treatment variance and (withinbetween-treatment variance) are equal betweenAnd the ratio of Between/Within should be about 1 If Ho is false:
Between Ratio group estimate will be larger of Between/Within > 1 Chance= Individual differences, experimental error... F distribution Example to explain the Theory... F= variance (differences) between sample means variance (differences) expected w/no tx effect 5 Ferreira, Does an Energy Drink Modify the Effects of Alcohol in a Maximal Effort Test?
et al., 2004
Alcoholism: Clinical and Experimental Research, 28(9) Jagerbomb Study The main purpose of this study was to verify the effects of alcohol and alcohol combined with energy drink, on the performance of volunteers in a maximal effort test (cycle ergometer) and also on physiological indicators Physiological indicators oxygen Methods 120 uptake, ventilatory threshold, respiratory exchange rate, heart rate, and blood pressure, glucose, lactate, insulin, cortisol, ACTH, dopamine, noradrenaline, and adrenaline blood alcohol levels participants were randomized to conditions:* control (water), alcohol (1.0 g/kg) energy drink (3.57 ml/kg Red Bull) Bull and alcohol energy drink The effort test began 60 min after drug or control ingestion, and the dependent variables were measured until 60 min after the test. *details have been altered to suit demonstration 6 Methods
a standardized meal of 1000 calories was served (1 Big Mac, 1 Mac medium portion of fried potatoes, and a 500 ml soft drink). ANOVA Logic All Participants in Study Control (water) Alcohol Red Bull Alcohol & RedBull ANOVA Logic ANOVA Logic
All Participants in Study M, s2, s All Participants in Study Control (water) M, s2, s Control (water) Alcohol Red Bull Alcohol & RedBull Alcohol M, s2, s Red Bull M, s2, s Alcohol & RedBull M, s2, s 7 ANOVA Logic IF ANOVA Logic If the null hypothesis is true, and there are no differences between the conditions (water, alcohol, red bull, jagerbomb) on number of minutes on exercise machine... machine...
The extent of variation between groups should be equal to the extent of variation within groups ALL of our variance is sampling error/error variance the research hypothesis is true, and condition (treatment) DOES have an effect on performance... performance...
The extent of variation between groups will be greater than the extent of variation within groups Between group variance will be due to BOTH sampling error AND treatment effects ANOVA... Introduction One-way One- to ANOVA logic Between Subjects ANOVA (2 + groups, means on one measure: do the groups differ?) One-way Repeated measures ANOVA (one Onegroup, 2+ measurements such as testtestretest, do the means across measurements change/differ?) Factorial ANOVA: (2+ groups, 2+ measurements) 8 ...
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This note was uploaded on 04/07/2008 for the course PSY 031 taught by Professor Dicorcia during the Spring '08 term at Tufts.
- Spring '08