15 basic statistical analyses pt 1

why statistics

• estimating effect sizes

• hypothesis testing

• wildlife science is an increasingly quantitative discipline

• thinking critically about information

• a basic understanding of statistics will make us better citizens and scientists

summary data

• start with _____

  • descriptive statistics ie means and measures of variance

  • make some plots

  • get a feel for the data

• do before comparative or fancy statistics

difference tests

• are these treatments different

  • t-test

  • analysis of variance

  • analysis of covariance

  • non-parametric equivalents

relational or association tests

• is this response variable related to that predictor variable

  • correlation

  • linear regression

  • non-parametric equivalents

goodness of fit

• how closely does observed data meet expectations

  • chi squared test

chi squared test

• used when you wish to compare observed counts of a phenomenon within a category to expected counts within a category

• often used in habitat selection analyses

chi squared response variable

counts of observations within a category

chi squared predictor variable

different categories

chi squared assumptions

1. both response and predictor variables are categorical

   • AMD vs non-AMD and EPT

   • clear cut vs old growth and high vs low biodiversity

2. all observations are independent

   • value of one obs does not affect the value of another

3. cells in the contingency table are mutually exclusive

   • observations can belong in only one cell, cannot apply to more than one

4. expected value of cells should be 5 or greater in at least 80% of cells, and no cell has an expected value <1

contingency table

tabulations of the number of observations within each category

null hypothesis

observed counts equal expected counts

t test

• used when

  • you want to compare the mean of 1 population with a hypothetical mean

  • you wish to compare the mean of 2 populations

  • you wish to compare means of repeated measurements on the same units

t test response variable

measurements obtained from each distinct population

t test predictor variable

the different populations (treatment)

one sample t test

• compare the mean of one sample to a hypothetical mean

• test effects of mgt on average size of bass in a lake when you have an earlier mean size and a current (post-mgt) sample

two sample t test

• compare the means of samples obtained from two different populations

• species richness upstream and downstream of acid mine drainage

paired t test

• compare the means of repeated measurements on the same sample; equivalent to 1 sample t test

• effect of pollution on fish survival, “before-after”

t test assumptions

• independence of observations

• normality: both samples are approximately normally distributed

• homogeneity of variances: both samples show similar variance

• random sampling: samples were obtained through some form of random sampling methodology

t test null hypothesis

difference in means equal to some value (usually 0)

t test alternative hypothesis

difference in means not equal to some value (alternatively, 1-sided tests allow you to state > or < some value)

t test test statistic

• t statistic

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

t test p value

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

• small = reject H_O

critical values

• for t test use t distribution

  • degrees of freedom

  • alpha a

• compare t observed to t critical

  • t_O > t_c then reject null

  • t_o < t_c then accept the null

analysis of variance

• used when

  • we wish to compare the means of 2 or more populations

  • we wish to evaluate the influence of several factors simultaneously

  • we wish to include blocking variables and/or covariates or use more advanced hierarchical, nested, repeated measures

anova factor

a variable that represents 2 or more mutually exclusive categories

anova factor level

the difference values each factor can obtain