Regression, Chi Square, and Two-Way ANOVA Flashcards
What is the two factor ANOVA and when do we use it?
- Two factor ANOVAs have two independent variables
- Both independent and quasi-independent variables ma be employed as factors in a two-factor ANOVA
- Allows us to examine three types of mean differences within one analysis (Main effect of A, main effect of B, interaction of AB)
Main effects vs interactions
- Main effects describe the mean differences among thelevels of one factor (The main effect of each factor is evaluated independently of the other factor)
- Interactions indicate when mean differences between individual treatment conditions, or cells, are different from what would be predicted from the main effects of the factors (The unique effect of two factors working together… when the wo factors are not independent. The effect of one factor depends on the other)
Understand within treatments and between treatments SS
- within treatmens SS is the sum of SS inside each condition
- Between is the SS total-SS within
Mean squares formulas
- MS= SS/df
df formulas ANOVA two-factor
- df between= k-1 (k=# of cells)
- df within=sum of df in each cell (df cell=n-1)
How do you report results of a two-factor ANOVA (including p-value)
- F(df cell, df within)=4.00 p> or <= .05
Multiple regression
- produes an equation that uses ore than one variable to predict y
- ex. freind drinking (X) and parent drinking (X2) predict individual drinking (Y)
- Equation still minimizes the squared distances between y and y
- It’s idenfifying the regression plane instead of the regression line to do this
What are the strengths of Regression
- Determines the equation for the straight line that best fits a specific set of data (not just how well the line fits)
- Allows predictive power
- Is used to predict the value of a DV based on the value of at least one IV
- Is used to explain the impact of changes in an IV on the DV
What are the linear regression assumptions
- The underlying relationship between the x and y variables is linear
- Residuals are independent
- The residuals are normally distributed
- The residuals have constant variance at every value of x
Regression Hypotheses
-H0: the slope of the regression line is equal to 0
H1: the slope of the regression line (b or beta) is not equal to 0
Parametric vs nonparametric tests
- parametric tests evaluate hypotheses about population parameters, rely on assumptions about the data being examined
- nonparametric tests evaluate hypotheses without using population parameters, make few if any assumptions about population distribution
For nonparmetric tests the data are frequencies rather than numerical scores, allows to examine associations between nominal and ordinal data
Chi-square tests for goodness of fit
- uses frequency data from a sample to test hypotheses about proportons in a population
- each individual in the sample is classified into one category on the scale of measurement
- The data, called observed frequencies, simply count how many individuals from the sample
Chi-Squre goodness of fit test hypotheses
- H0 specifies the proportion of the population that should be in eac category
- use H0 to compute expeted frequencies that describe how the sample would appear if it were in perfect agreement with the null
- Expected frequency=fe=pn (p=proportion in the population)(n=sample size)
How is chi goodness similar to one-sample t-test
- testing observed values against a hypothesized value
- Useful when we have a meaninful value to test against
Chi-Square test for independence
- used to test hypotheses about the relationship between two variables in a population
- For example: is an individual’s score on Y independent of his/her score on V
- Similar to independent measures or correlation
