15 basic statistical analyses pt 2

anova assumptions

1. independence of observations

2. normality: both samples are approximately normally distributed

3. homogeneity of variances: both samples show similar variance

4. random sampling: samples were obtained through some form of random sampling methodology

anova response variable

measurements obtained from each sample unit

anova predictor variable

level of each factor

single factor anova

compare means between levels of a single factor

two factor anova

• compare means between levels of two factors

• evaluate interactions between factors

multi factor anova

• compare means between levels of 3 or more factors

• evaluate interactions between factors

anova null hypothesis

no difference in means

anova alternative hypothesis

difference in means unequal

anova test statistic

• f statistic

• this is a function of your data and the basis for obtaining a p value

anova p value

• the probability your test statistic is greater than a critical value under repeated sampling

• small = reject H_O

anova critical values

• use f distribution

  • between group dr

  • within group df

  • alpha a

• compare f observed to f critical

  • F_o > F_c then reject null

  • F_o < F_c then accept the null

general linear model

• generalized form of anova includes ancova and can be built to include more complex designs

• covariates, stratified blocks, nested/hierarchical measurements, repeated measures, and factor interactions

• general form examples

  • response = covariate + main effect + covariate * main effect + error

  • response = covariate + block + main effect 1 + main effect 2 + main effect 1 * main effect 2 + error

basic anova or regression model

response = main effect + error

anova or regression w covariates

response = covariate 1 + covariate 2 + main effect + error

parametric tests

• the most robust and powerful, generally preferred when testing for differences

non-parametric tests

designed to function when parametric assumptions are violated

correlation

• exploratory, examines covariation

• x-y scatterplot

• NOT a clear cause and effect

• test statistic = r, describes the degree of co-variation

• r ranges from -1 to 1

• report r, n, p-value

correlation assumptions

• both variables measured on interval or ratio measurement levels

• linear relationship exists between the two variables

• both populations are normally distributed

• data sets are paired

• no outliers or extreme points

linear regression

• used when we have a continuous response variable and we have a continuous predictor variable

• used to estimate the slope and intercept of the line that best fits the data

y = mx + b

linear model equation

simple linear regression

• single response and predictor variable

multiple linear regression

• single response and multiple predictor variables

• use when you wish to simultaneously examine the influence of multiple predictors on your response variable

linear regression null hypothesis

• no slope

• interpretation: if m = 0, we conclude that there is no influence of the predictor variable on the response variable

linear regression alternative hypothesis

difference in means unequal

linear regression test statistic

• f statistic for the equation and % variance explained

• t statistic for the slope and intercept parameters

linear regression p value

• the probability your test statistic is greater than a critical value under repeated sampling

• small p values mean you reject H₀

linear regression assumption

• a linear relationship exists between x and y

• independence, there is no temporal autocorrelation (no correlation among residuals)

• homoscedasticity, residuals have constant variance at all levels of x

• normality, residuals are normally distributed