Exam 4
What are the possible values for a correlation?
0-1
What is the simplest possible factorial design? What is the factorial notation for this design?
2x2
How many F ratios are obtained for a two-factor ANOVA?
3
If the null hypothesis is true, what is the expected value of F?
F will be close to 1 and can't be negative
What values are possible for an F ratio?
F will be greater than or equal to 0
How is this measure of effect size computed for each main effect and the interaction from a two-way ANOVA?
Factor A: n2 = SSA/SStotal Factor B: n2 = SSB/SStotal A x B: n2 = SSAxB/SStotal
What three omnibus tests are conducted in a two-factor ANOVA?
Main effect Factor A, Main effect Factor B, Main effect Factor (AxB)
What are the characteristics of a factorial design?
More than one independent variable, 2 or more conditions for each independent variable
What abbreviation is used to represent the total number of subjects used in an ANOVA?
N
How are df pithing computed for a one-way ANOVA?
N-k
State the alternative hypothesis for a main effect in a two-factor ANOVA.
One of the means does not equal another
State the alternative hypothesis for an interaction in a two-factor ANOVA.
The effect of one independent variable on a dependent variable depends on the level of the second independent varriable
State the null hypothesis for an interaction in a two-factor ANOVA.
The effect of one independent variable on a dependent variable does not depend on the level of the second independent varriable
Define interaction.
Whenever the mean difference between individual treatment conditions are different from what would be predicted from the overall main effects of the factor
What equation is used to compute the intercept for a regression equation (to predict Y)?
a = ȳ - (bx̅) OR Aa = My - (bMx)
Define cell.
a treatment condition represented in the matrix
State the null hypothesis for a main effect in a two-factor ANOVA.
all the means are equal
What does ANOVA stand for?
analysis of variance
What equation is used to compute the slope in a regression equation (to predict Y)?
b = EXY - (EXEY)/n / (EX2 - (EX)2/n)
How do we decide whether to reject or fail to reject the null hypothesis for an interaction in a two-way ANOVA?
determine the cv in f obtained exceeds cv reject null
How do we decide whether to reject or fail to reject the null hypothesis for a main effect in a two-way ANOVA?
determine the cv with the df if the f obtained exceeds cv reject null
How are df computed for each component of the two-factor ANOVA summary table (dfbetween,, dfA, dfB, dfAxB, dfwithin, and dftotal)?
df between: ab-1, df a: a-1 , df b: b-1, df AxB: (a-1(b-1), df within: N-ab, df total: N-1
How are degrees of freedom computed for the Pearson correlation?
df=(n-2)
How is each F ratio in a two-factor ANOVA computed?
divide each MS between value by MS within
How is MS computed for each component of the two-factor ANOVA summary table?
divide ss by df
Define the term coefficient of determination.
explains how much of the variability of a factor can be caused or explained by its relationship to another factor
How do we determine whether a correlation is statistically significant?
if it exceeds the cv
When is it necessary to use ANOVA rather than a t statistic?
in situations where there are 2 or more means being compared
What symbol represents the number of treatment conditions in a one-way ANOVA?
k
How are df between computed for a one-way ANOVA?
k-1
In what research situation is it appropriate to perform a factorial ANOVA?
more than one Independent variable on a dependent variable
What abbreviation is used to represent the number of subjects within a particular treatment condition?
n
How is this measure of effect size computed for a one-way ANOVA?
n^2= ss between/ss total
What information is conveyed via the sign of a correlation coefficient?
positive = positive correlation Negative= negative correlation
What symbol is used to represent a Pearson product-moment correlation?
r
What equation is used to compute the Pearson correlation?
r = EXY - (EXEY/n) / √(EX2 - (EX)2/n) (EY2 - (EY)2/n)Compare amount of covariability (variation from the relationship between X and Y) to the amount X and Y vary separately
In what research situation is it most appropriate to perform a one-way ANOVA?
testing to see if a variable moves in one direction, when there is one independent variable with 2 or more levels
Define level.
the individual conditions or values that make up a factor
Define alpha inflation
the overall risk of type one error, the more test that higher chance of type 1 error, the ANOVA protects from type one error
What is the purpose of a regression analysis?
the predict the value of one variable given knowledge about another variable
Define factor.
the variable that designates the groups being compared
What is the purpose of a correlational analysis? In what research situation is it appropriate to perform a correlational analysis?
to measure and describe relationships between 2 variables
In what research situation is it appropriate to perform a regression analysis?
when you want to predict a continuous dependent variable from a number of independent variables.
What equation used to predict Y in a regression equation?
ŷ = bx + a (Final Form of a Regression Equation) ŷ = criterion variable, what we are trying to predict b = slope value a = intercept
What are the components of an ANOVA summary table?
MS between/MS within
How are MSbetween and MSwithin computed?
MS between= SS between/ df between
How is an F ratio computed?
MS within= SS between/ df within
What information is conveyed via the absolute value of a correlation coefficient?
Magnitude or strength of the relationship 0= no relationship 1= positive relationship
In what research situation is it most appropriate to perform post hoc multiple comparisons, (such as the Scheffé test or the Bonferonni test)?
When the null hypothesis is rejected for an omnibus test
How do we decide whether to reject the null hypothesis for a single-factor (one-way) ANOVA?
When the F ratio is larger than the critical value
When is it appropriate to compute post hoc test (multiple comparisons)?
When the null hypothesis is not true
In what research situation is it appropriate to perform a within-subjects ANOVA?
When the sample participants receive more than 2 levels of treatment
What are three advantages of a factorial design?
Economy, the design provides more information for the same amount of work Experimental control, results are more generalized Can investigate interactions among independent variables
State the null hypothesis for a single-factor (one-way) ANOVA
All the means are equal to each other
State the alternative hypothesis for a single-factor (one-way) ANOVA
At least one of the means is not the same as the others
How do we obtain the critical value for an F ratio?
Based on between treatment df= K-1,and within treatment df= (N-k), also the alpha level .01 or.05
What does MS represent? (State the term and define it.)
Between treatments the size of the difference between the sample means Within treatments the size difference inside each of the samples
What are the sources of variance for ANOVA? What are the sources of between-group variance? What are the sources of within-group variance?
Between variances, Treatment effect, experimental error, individual differences, Within variances, Experimental error and individual difference
What measure of effect size is used for ANOVA?
Compute the percentage of variance accounted for by the treatment conditions n2 = SSbetween/SStotal
State the null and alternative hypothesis for using the Pearson correlation in hypothesis testing (assume a non-directional/two-tailed hypothesis test).
H0: ρ = 0 (no relationship) H1: ρ =/(does not equal) 0 (relationship)
If the results of a two-factor ANOVA are presented in a graph, what would indicate the presence of an interaction between variables?
If lines cross (are not parallel) or move towards each other = presence of interaction between variablesIf lines are parallel = no presence of interaction between variables
Define main effect.
The mean differences among the levels of one factor
What does omnibus test measure?
The overall ANOVA
How are main effects and interactions related (or unrelated) to one another?
They are not related both are independent and do not correlate with eachother
