Psych 210 Exam 3

marginal mean

marginal mean

finding the means for each level of the independent variable in a factorial ANOVA

main effects

the impact of each IV on the DV if we ignore the other IV being analyzed

ex: the separate effect of humidity on on comfortability

and the separate effect of room temperature on comfortability

interaction effect

examining the combined effect of both IVs

ex: does the effect of humidity depend on temperature?

an interaction effect is most easily seen in a graph (line or bar)

if you have parallel lines, likely no statistical significance

what is a factorial ANOVA?

so far we’ve just looked at ANOVAs with one independent variable. A factorial ANOVA introduces 2+ independent variables.

—is efficient and can look at interactions between two variables on the dependent variable

two-ways independent ANOVA

two independent variables, different participants in all conditions

variance within a two-way independent ANOVA

within subjects variance is the same, then you divide the between-subjects into Factor A variance, Factor B variance, and interaction variance

grand mean in a factorial ANOVA

the mean of every single data point divided by N (total number of data points in the study)

sum of squares

our measure of variability used in factorial ANOVAs

—SSbetween (var A, var B, interaction)

—SSwithin

—SS total

sum of squares within

do for each individual group in the data set, then add them all together at the end

—each individual score within the group - group mean, squared and added together

sum of squares total

each individual score - the grand mean, added together and squared

sum of squares between groups

—so there’s one for the total, but then there’s three partitions of it

total: group mean- grand mean squared and added together

for a variable: marginal mean #1 - grand mean x group size) squared

interaction: you can find this through algebra

mean squares in a factorial ANOVA (MS)

same basic formula as with the one-way ANOVA, but this time you still have to split it up for the two different variables and the interaction

hypotheses for factorial ANOVA

restate the question as a null and alternative hypothesis

—there will be three research hypotheses, one for each main effect, and one for the interaction

—state the interaction hypothesis in words

cohen’s d

effect size used for t-tests

partial eta squared

effect size used for one-way ANOVAs, but it’s the only one that SPSS uses

eta squared

effect size used for factorial ANOVAs

n squared = SSbetween/SStotal

confidence interval

If you were to take 100 samples, 95% of them would contain the true population mean within their interval (think of the visual she had on the slide)

—range of possible differences between group means in which we feel confident that the actual group mean difference will lie in the larger population

power in statistics

anything to increase the likelihood of rejecting the null hypothesis (possible type I error if increased power by too much)

a priori

way to increase power in statistics

done beforehand, the estimated r value and desired power are calculated (at least 80% for power), and then the sample size is created accordingly

post hoc

way to increase power in statistics

done after running analysis, can identify which groups exactly are different from one another in analysis. for ANOVAs, we use Tukey’s HSD.

increases the chance of rejecting null, because you can more closely look at the significance between different groups

between-subjects design

participants are assigned to one and only one experimental group

within-subjects design

participants are assigned to multiple groups

ie: they can have measures recorded before and after doing something, or similar things to that

Bonferroni Adjustment

dividing the alpha level by the number of statistical comparisons being made, making it smaller, and therefore harder to find statistical significance; this controls the chance of making a Type I error across all statistical tests being conducted

but here we might run into a type II error, where we fail to reject the null when we should’ve

family-wise type I error

likelihood of detecting at least one statistically significant result when conducting multiple statistical tests. It is called “family-wise” because it is the error rate for a series (family) of statistical tests

you can’t just do a bunch of t tests to compare group means— you’ll end up finding a result that’s significant by “sheer luck”

post hoc tests

statistical analysis after the test was run

Pearson’s r

statistic that quantifies the linear relationship between two SCALE variables

most common form of measuring linear correlations

—measurement of the type and strength of a relationship between two variables

linear relations

—straight line relationship

can be positive or negative

measuring the strength with Pearson’s correlation coefficient

curvilinear relationships

results when the relationship between two variables is not a linear relationship

—when the values of the two variables tend to be positively correlated up to a certain value, but then the variables are negatively correlated after that certain variable (Yerkes-Dodson’s Law)

—enjoyment of pizza per every slice

(can also have zero relationship)

(also a caution in interpreting correlations— if you don’t look far out enough, you might misinterpret)

restricted range (cautions in interpreting correlations)

occurs when we do not or cannot measure the entire range of values that a variable (such as height) can take on

the correlation between the two variables is smaller than it likely would be if we could measure all the values of both the variables

spurious correlation

two variables are correlated due to a third, unmeasured variable

—spuriously correlated variables are not causally linked

ex: ice cream sales and drowning deaths

correlation matrix

contains each variable being examined, and their means and SDs (sometimes)

predictor variable

the one that goes on the x axis, the variable that we’re looking at how it predicts the outcome

outcome variable

the one that goes on the y axis

best-fitting line

same as the regression line, straight line that best fits or summarizes the datapoints in a scatterplot

univariate regression

statistical tool in which we use one predictor variable to forecast scores on an outcome variable

multiple regression

statistical tool in which we use two or more predictor variables to forecast scores on an outcome variable

predicted values

y-hat in the regression equations

residuals

the sum of squares residuals

—the smaller the differences, the less prediction error

—residuals are the difference between the regression line and actual values (Y values)

purpose of regression

to describe or visually represent the relationship between X and Y, to predict the value of Y based on X

SStotal

difference between the mean and actual Y values, which our regression line should be more accurate than the SStotal

slope

the change in y variable over the change in the x variable

intercept

the point on the Y axis where X is 0

standardized slope

standardized beta coefficient

—the predicted change in the outcome variable in terms of standard deviations for a 1 standard deviation increase in the predictor variable

—often called a beta or beta weight

—standardized because measured in standard deviation units

—allows us to see the strength of the relationship between predictor and outcome no matter how the variable was measured

R squared

the percentage of variability that the predictor variables account for in the outcome variables

—based on the SS again (SSm)

—is this a good fitting model in terms of generalizing to the population?

SSregression model (or SSm in R squared)

model variability, amount of variance in the outcome variable that is explained by the regression line. (difference in variability between using the regression model and the mean)

adjusted R squared

purpose: adding predictor variables, the R squared value will always increase, can’t decrease

—accounts for the variables that don’t do anything, takes into account the quality of the predictor variables

shared versus unique variance

shared variance is the variance in Y accounted for by the overlap in two predictor variables

unique is the variance in Y attributed to one predictor variable (in multiple regression, I guess you don’t need for univariate)

nonparametric tests

a family of tests with three characteristics:

—no inferences about parameters in the population

—no normal distribution

—nominal or ordinal

chi-squared sampling distribution

skewed to the right

—not normally distributed

—nominal data, the descriptives used are frequencies

—tests hypotheses about the frequency distribution in the population: does our proportion of people across categories match that of the population, etc

chi-square goodness of fit test

is our frequency distribution of a categorical variable different from the population?

—one nominal outcome variable

—if our data is a “good fit” for the population distribution, we will fail to reject the null hypothesis

to reject the null hypothesis, we need a bad fit— meaning that our data is significantly different from that of the population