Flashcards in Quiz 3 Deck (104):
1
Subjects x A null hypotheses and conclusions
Ho: u(sub t1) = u(sub t2) = u (sub t3) = u (sub t4) = u (sub t5)
-There is no statistically significant difference among population means of the fire trials with regard to the number of words correctly recalled.
Conclusion for Trials (only IV): There is a statistically significant difference among the five trials with regard to the number of words correctly recalled.
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Subjects x A x B null hypotheses conclusions
1. u (sub sat) = u (sub sun)
-There is no statistically significant difference between the population means of saturday and sunday with regard to the number of hours of tv watched.
2. u (sub AM = u (sub PM)
-There is no statistically significant difference between the population means of AM and PM with regard to the number of hours of tv watched.
3. There is no statistically significant day x time interaction in the population.
Conclusion: Needed for “day”, “time”, and “day x time”
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Subjects/A x B) null hypotheses and conclusions
1. u (sub R) = u (sub DC) = u (sub BF)
-There are no statistically significant difference among the population means in regard to their ….
2. u (sub BP) = u (sub NBP)
-Similar to first one
3. There is no bug problem x pesticide interaction in the population
-Conclusion: Needed for “problems”, “pesticide”, and “prob x pest”
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What are carry over effects (Logical Assumptions)
1. General Carry Over Effects: general changes in the organism (fatigue, boredom, maturation, adaptation)
2. Specific Carry Over Effects: effect of treatment 1 is followed by treatment 2 is different than the effect of treatment 2 followed by treatment 1
-Think of dilated pupils example (different if bright to dim light vs. dim to bright light)
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How do you get rid of carry over effects?
1. Pre experimental practice
2. Space out trials
3. Randomize order of treatments
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What is a correlation?
-Linear relationship between two variables
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What is the conclusion for p (rho) = 0?
Same as it was for F-test.
There is a statistically significant negative correlation between anger and self-esteem scores such that the higher the anger score, the lower is the self-esteem score.
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What are the characteristics for Fisher’s z’ transformation?
1. Distributes approximately normal
2. Standard error of z’ = 1/square root of N-3
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When can you infer causality in a correlation?
1. If x causes y, then y cannot cause x
2. If x causes y, then no third variable can cause either x or y
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What are the assumptions to correlation?
1. Normality in the arrays
2. Homogeneity of variance in the arrays (homoscedasticity)
3. Linearity
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What happens when the assumptions to correlation are violated?
Still pretty robust
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What happens when you restrict the range in a correlation?
-When you restrict range in a linear relationship, you underestimate what the true population correlation is
-When you restrict the curvilinear relationship, you overestimate what the true population correlation is
-*NEVER say there is no relationship, because it could be curvilinear
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What is linear regression? Formula?
-Where you predict Y from X
-”regression” means prediction
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What is multiple regression?
-Multiple predictors predicting y
-R= multiple correlation (0 → +1) (never negative)
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What are the limits to multiple correlation?
-Def: R; the strength of relationship between the dependent variable or criterion (Y variable) and the predictors (or the X variables)
-Limits: There are no negative values, unlike r, and as the number of predictors increase, then the value of R will go up, and this number will increase by chance alone, so you want a few independent predictors in order to optimize value of R -- lots of sample size and few excellent predictors that are uncorrelated with each other
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How do you test the difference between two independent correlations?
1. Ho: rho sub1 = rho sub2
Pg. 184(stats book)
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What is a point-biserial correlation?
-When one of the variables is a true dichotomy and the other is continuous
-Correlation in which one variable is a true dichotomy and the other continuous
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What is a biserial correlation?
-When the dichotomous variable is artificial (e.g., tall-short, pass-fail, old-young) and the other variable is continuous
-Correlation in which there’s one artificial dichotomy and the other is continuous
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Rules for determining the type of design?
1. Is there only 1 score per subject?
a. Yes: independent groups design (one, two, or three-way)
b. No: repeated measures (go on to question 2)
2. Does every subject participate in every group AND every condition?
a. Yes: Subject x A or Subjects x A x B
b. No: (i.e., there is a grouping factor) Subjects/A x B (mixed design)
Helpful Tips:
-How many IVs are there?
-Draw diagram of design
-Read carefully! Be cognizant of words like “each,” “or,” “and,” “either.”
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Coefficient of Determination
-r^2
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Array
-All y values for a given x
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Error terms for Subject x A x B
1. For effects not involving “subjects,” use the subjects x that effect interaction sa the error term
2. For effects involving “”subjects,” use the largest order interaction as the error term
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What are the conclusions (one-way)?
-Ex:
-H(sub o): There is no statistically significant difference between the population means of males and females with regard to their GPAs.
-H(sub o): u(sub m) = u(sub f)
-With null hypothesis, you always state that there is no statistically significant difference.
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What are the characteristics of Orthogonal Comparisons?
1. A priori hypotheses
2. ∑a(sub i) = 0 (valid comparison)
∑a(sub i)b(sub i) = 0 (independence)
3. Each comparison is on 1 degree of freedom
4. You get as many comparisons as g-1 degrees of freedom
5. Most powerful test of the three
6. Significance level = alpha
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What are the characteristics of Bonferroni?
1. A priori hypotheses
2. ∑a(sub i) = 0 (valid comparison)
Don’t need independence, so ∑a(sub i)b(sub i) does not have to equal 0
3. Each comparison is on 1 degree of freedom
4. You get as many comparisons as you want, but you lose power with each subsequent comparison
5. Moderate power of the three
6. Significance level = alpha/c (c is the number of comparisons)
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What are characteristics of Scheffe?
1. A posteriori or post hoc hypotheses
2. ∑a(sub i) = 0 (valid comparison)
Don’t need independence, so ∑a(sub i)b(sub i)does not have to equal 0
3. Each comparison is on the among degrees of freedom
4. You can make as many comparisons as you want
5. Lowest power of the three tests
6. Significance level = alpha
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What are experimentwise errors?
-Probability of making at least 1 Type I Error over the entire experiment (set of comparisons)
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What are per comparison errors?
-Per Comparison Error: Probability of making a Type I Error for each individual comparison
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What are the problems with multiple t-tests?
-Not okay for multiple t-tests because these are NOT independent and you’ve got an inflated Type I error rate
-You may find differences that may not even be there
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What are the null hypotheses (two-way)?
-Ex:
1. H(sub o): There is no statistically significant difference between the population means of the massed practice and distributed practice groups with regard to stats test scores
-H(sub o): u(sub m) = u(sub d)
2. H(sub o): There is no statistically significant difference between the population means of the in-class and online teaching methods with regard to stats test scores.
-H(sub o): u(sub IC) = u(sub ON)
3. H(sub o): There is no teaching method x (by) study habit interaction in the population.
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What is a main effect?
-The overall difference among the levels of the independent variable tested
-Average of the simple effects
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How many main effects in a specific design?
-The number of main effects is the number of independent variables that you have
-You have as many main effects as IVs
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What is a simple effect?
-The effect of an independent variable at a single level of the other independent variable
-Lack of parallelism (do not cross)
-LOOK ON PAGE 11 OF NOTES
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How many simple effects in a two-way design?
-The additive rather than the multiplicative
-Ex: 2x2 = 4
-Ex: 2x4 = 6
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What is an interaction?
-The lack of parallelism in the simple effect
OR
-The effect of an independent variable differs depending upon the levels of the other IV
-If asked to define this, we have to define “simple effect” too
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How do you plot an interaction? Graph form and in words.
1. Choose an IV to place on the x-axis
2. Values of the cell means go on the y-axis
3. Plot a single curve for each level of the other IV
-MAKE HAND-WRITTEN NOTE CARD (Page 11)
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What are range tests?
-All pairwise comparisons between means
1. Tukey A
2. Student Newman-Kewls
3. Tukey B
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What is the studentized range distribution?
-A sampling distribution of a t-test run between the largest and smallest means from a set of k means
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How do you perform the Tukey A test?
1. Order the means from smallest to largest
2. Compute q for each comparison
3. df(sub # of means, df error)
Compare each q with the critical values of q on the number of means and df error
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How do you perform the SNK test?
1. Order the means from smallest to largest
2. Compute q for each comparison
3. df(sub # of ordered means, df error)
Compare each q with the critical values of q based on the number of ordered means (or number of steps) and df error
*More power
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How do you perform the Tukey B test?
1. Order the means from smallest to largest
2. Compute q for each comparison
3. Average the critical values of the Tukey A and SNK for each comparison
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How do you perform the Fisher-Hayter test?
1. Order the means from smallest to largest
2. Compute the q for each comparison
3. df(sub # of means-1, df error)
Use the number of means - 1 and the df error to obtain the critical value of q
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What was the rationale behind Duncan’s multiple range test and what are its problems?
-Rationale:
-Focused on trying to obtain greatest power possible
1. Experimentwise error rate similar to the orthogonal comparisons 1-(1-alpha)^g-1 -- “protection level”
2. Step-down procedure similar to SNK
3. Derives out his own critical value tables
-Problems:
-No independence
-Kind of like doing t-tests, so error rates go through the roof
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The relationship between q and t?
-HAND-WRITTEN NOTE CARD (PAGE 13)
-Gosset and help forgot “2” when computing, which is why we have “t” and “q”
q(sub 2, infinity) = 2.77 (.05); 3.64 (.01) t(sub infinity) = 1.96 (.05); 2.576 (.01)
q=t x(times) square root of 2 t=q/2
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Problem with unequal n with a one-way ANOVA?
-No problems mathematically, but you lose power.
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What are the characteristics (coefficients) for orthogonal comparisons with unequal n?
- ∑n(sub i)a(sub i) = 0 (valid comparison)
- ∑n(sub i)a(sub i)b(sub i) = 0 (independence)
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What are the problems with unequal n in a two-way design?
-Destroy factorial nature of the design, and it lacks robustness
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What is a factorial design?
-Design in which each level of each independent variable occurs equally often with each level of every other independent variable
-Must have equal n
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How do you get rid of unequal n?
1. Randomly discard data
2. Yates Substitution Formula
3. Least Squares Solution
-Mathematically ideal
-SAS
4. Unweighted Means Solution
-Used on SPSS
1. SSeffect → use cell means
2. SSwithin → use new data
*LOOK ON PAGE 2
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What is the harmonic mean and why do you use it?
-Average the reciprocals and take the reciprocal of that average
-HAND-WRITTEN NOTE CARD HAS FORMULA
-Used when dealing with unequal n
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What is complete confounding?
-A design in which you do not know where the difference lies
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What are the null hypotheses (three-way)?
Ex:
1. H(sub o): There is no statistically significant difference between the population means of males and females in regard to Machiavellian personality scores.
-H(sub o): u(sub m)=u(sub f)
2. There is no statistically significant difference between the population means of Political Science majors and Psychology majors in regard to Machiavellian personality scores.
-H(sub o): u (sub psy) = u (sub pol)
3. There is no statistically significant difference between the population means of graduates and undergraduates in regard to Machiavellian personality scores.
-H(sub o): u (sub U) = u (sub UG)
4. H(sub o): There is no sex by major interaction in the population.
5. H(sub o): There is no sex by class interaction in the population.
6. H(sub o): There is no major by class interaction in the population.
7. H(sub o): There is no sex by major by class interaction in the population.
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State Central Limit Theorem
-CLT
-Given a population with infinite mean u (mew) and finite variance O^2 (sigma squared), the sampling distribution of the mean approaches a normal distribution with mean u and variance O^2/N, as N, the sampling size, increases
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Statistic
-Quantity calculated from a sample
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Population
-Set of all objects that we’re interested in researching
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Parameter
-Quantity calculated from a population
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Significance
-Unlikely to have occurred by chance alone
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Sample
-Subset of a population
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Random Sample
-Each member of a population has equal likelihood of being chosen
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X-bar
_
X
-Sample mean
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S^2
-Sample variance
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S
-Sample standard deviation
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U (mew)
-Population mean
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O^2 (sigma squared)
-Population variance
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O (sigma)
-Population standard deviation
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Descriptive Statistics
-Numbers that summarize or describing data
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Inferential Statistics
-More in terms of hypothesis testing
-Allow us to test hypotheses about the differences between groups on the variable being measured
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Measures of Central Tendency
-Mean: arithmetic average
-Median: middlemost score
-Mode: most frequently occurring score
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Measures of Dispersion
-Range
-Standard Deviation
-Variance
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Range
-Largest score - Smallest score
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Frequency Distributions
-Leptokurtosis
-Platykurtosis
-Normality
-Skew
-Kurtosis
-Bimodal
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Kurtosis
-The peakedness or flatness around the mode of a frequency distribution
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Leptokurtosis
-More scores in the tails and fewer scores in the middle as compared to the corresponding normal distribution
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Platykurtosis
-Fewer scores in the tails and more scores in the middle as compared to the corresponding normal distribution
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Normality (Normal Distribution)
-The left and right sides look alike (if you split the graph down the middle)
-a.k.a. Bell curve or Gaussian distribution
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Skew
-Refers to the amount of asymmetry of the distribution
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Positively Skewed
-Vast majority of the data is on the left (or low side) of the tail
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Negatively Skewed
-Vast majority of the data is on the right (or high side) and the tail is pointing to the left
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Frequency Polygon
-Shows the distribution of subjects scoring among various intervals
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Histogram
-A graphical representation of the data using bars
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Bar Chart
-When the x-axis is categorical in nature
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Bimodal Distributions
-Most common distribution found in psychology
-Two humps
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Sampling Distribution
-A distribution under repeated sampling and equal-sized samples of any statistic
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Z-Scores
-Statistic that allows us to determine how far we are away from the mean
-a.k.a. Standard scores
-Determine how far away scores are from the mean in standard deviational units
-May be both descriptive and inferential
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Characteristics of standard normal distribution
-Has a mean (or u) of 0
-Has standard deviation (or o (theta)) of 1
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Confidence Interval
-A 95%, 99% (or some stated) probability that the interval falls around (or about) the parameter
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df
-Degree of freedom (independent piece of information)
-Can change, but for confidence interval, it will be N-1
-If N>/= 100, use infinity
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T-Distribution
-William Gosset
-Is leptokurtic, and as you increase the sample size, it becomes normal, such that t(sub infinity)=z
-Kate Moss
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Standard Error
-Standard deviation of a sampling distribution
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Hypothesis
-Educated guess about which group will be significantly higher on a measure or if there will be a positive or negative relationship between two measurements
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Independent Variable
-A variable that is manipulated by the experimenter
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Dependent Variable
-A variable that is measured
-A score
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Null Hypothesis
-Ho (that’s a sub o)
-”Null” means “no”
-No difference in rates, scores, etc.
-No statistically significant difference between or among population means on a particular measurement
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Type I Error
-Probability of rejecting the null hypothesis when in fact it’s true
95
Type II Error
-Inability of detecting a difference if in fact one exists
-Insensitivity of experiment
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Power
-Ability to detect a difference if in fact one exists
-Sensitivity of the experiments
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Determinants of Alpha
-(fishy looking thing)
-1. Experimenter
-2. Journal Editors
-We usually set our alpha = .05
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Determinants of Power
-Power and B go opposite
-Look in notes
-1. N goes up, Power goes up, B goes down
-2. O^2 goes up, Power goes down, B goes up
-3. Skew goes up, Power goes down, B goes up
-4. Outliers go up, Power goes down, B goes up
-5. Difference between group means go up, Power goes up, B goes down
-6. Alpha goes up, Power goes up, B goes down
-7. One vs. Two-Tailed Tests: 1 tail (more power); 2 tail (less power)
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Heuristic Formula of F (in words)
# of folks in a group x(times) variance among group members/ average variance within groups
100
Is the F-Ratio that you compute larger than the critical value in the table? (Conclusion).
-If yes, statistically significant. Group A is significantly higher than Group B on the dv.
-p < .05; p< .01
-If no, not statistically significant (nonsignificant). There is no statistically significant difference between Group A and Group B on the dv.
-p > .05; n.s.
101
Assumptions of ANOVA. Why Fisher made them?
-1. Normality in the Population
-a. That’s how Fisher derived out the critical values of F
-b. From CLT, the sampling distribution of the mean approaches normality as N increases
-Kolmogorov-Smirnov
-Shapiro-Wilk’s W=1.0
2. Homogeneity (homoscedasticity) of Variance in the Population
O(sub 1)^2 = O(sub 2)^2 = O(sub 3)^2
-Why? Fisher averaged “like commodities” (sample within variation) to obtain his best estimate of O^2 from O^2/N
102
What happens when you violate the assumptions?
-1. Robust = when you violate the assumption, the Type I error rate doesn’t change appreciably from the normal level. (stated)
-2. Liberal = when you violate the assumption, the Type I error rate is higher than the nominal level
-We don’t like these tests
3. Conservative = when you violate the assumption, Type I error rate is lower than the stated level
-When you violate these assumptions? It is still robust
103
Characteristics of F
-1. F distribution is positively skewed
-2. X-bar(sub F) = df(sub w)/df(sub w) -2
-3. F (sub infinity), infinity = always 1.00
-Any ration below 1.00 will be nonsignificant
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