Q. Which statistical test to use?

1. Differences of Groups

t-Test: looks at differences between two groups on some variable of interest

ex: Do males and females differ in how long they spend shopping in a given month?

Chi-square: compares observed frequencies to expected frequencies

ex: Is the ratio of male voters to female voters 1:1?

ANOVA: tests the significance of group differences between two or more groups (only determines if there is a difference between groups, but does not tell which is different)

ex: Do SAT scores differ for low-, middle-, and high-income students?

ANCOVA: same as ANOVA, but adds control of one or more covariates

ex: Do SAT scores differ for low-, middle-, and high-income students after controlling for single/dual parenting?

MANOVA: same as ANOVA, but can study two or more related dependent variables while controlling for the correlation between the dependent variables

ex: Does ethnicity affect reading achievement, math achievement, and overall scholastic achievement among 6 graders? 

MANCOVA: same as MANOVA, but adds control of one or more covariates

ex: Does ethnicity affect reading achievement, math achievement, and overall scholastic achievement among 6 graders after controlling for social class?

2. Relationships

Correlation: tests whether two variables covary (does not distinguish between independent and dependent variables)

ex: How strongly are the amount of damage to a house on fire and number of firefighters at the fire correlated? In what direction are they correlated?

Linear Regression: tests whether see whether variation in an independent variable causes some of the variation in a dependent variable

ex: Does variation in temperature cause variation in chirping speed in crickets?

Multiple Regression: an extension of simple linear regression, used with several independent variables and one dependent variable

Note: the dependent variable must be continuous

ex: IVs drug use, alcohol use, child abuse DV. suicidal tendencies

Path Analysis: looks at direct and indirect effects of predictor variables, and used for relationships/causality

ex: Child abuse causes drug use which leads to suicidal tendencies.

3. Group Membership

Logistic Regression: estimates the odds probability of the dependent variable occurring as the values of the independent variables change

Note: the dependent variable must be binary

ex: What are the odds of a suicide occurring at various levels of alcohol use?

4. Goodness-of-Fit

Exact Test: test fit of observed frequencies to expected frequencies, use for small sample sizes (less than 1000)

ex: count the number of red, pink and white flowers in a genetic cross, test fit to expected 1:2:1 ratio, total sample <1000

Chi-square Test: test fit of observed frequencies to expected frequencies, use for large sample sizes (greater than 1000)

ex: count the number of red, pink and white flowers in a genetic cross, test fit to expected 1:2:1 ratio, total sample >1000

G-Test: test fit of observed frequencies to expected frequencies, used for large sample sizes (greater than 1000)

ex: count the number of red, pink and white flowers in a genetic cross, test fit to expected 1:2:1 ratio, total sample >1000

Repeated G-Test: test fit of observed frequencies to expected frequencies in multiple experiments

ex: count the number of red, pink and white flowers in a genetic cross, test fit to expected 1:2:1 ratio, do multiple crosses

Note: This document comes from California State University website and handbook of biological statistics.