BIOL 300 Final Memorize

what are 24 tests covered in BIOL 300

1. binomial test

2. x² goodness of fit test

3. x² goodness of fit using a poisson distribution

4. x² contingency test

5. fisher’s exact test

6. one-sample t-test

7. paired t-test

8. two-sample t-test

9. single factor ANOVA

10. correlation

11. linear regression

12. welch’s t-test

13. shapiro-wilk test

14. mann-whitney u test

15. levene’s test

16. tukey-kramer test

17. kruskal-wallis test

18. spearman’s (rank) correlation

19. logistic regression

20. ANCOVA

21. Multifactor ANOVA

22. Simulation

23. Randomization

24. Bootstrapping

which 10 tests do you need to know how to do by hand?

1. binomial test

2. x² goodness of fit test

3. x² goodness of fit test using a poisson distribution

4. x² contingency test

5. one-sample t-test

6. paired t-test

7. two-sample t-test

8. single factor ANOVA

9. correlation

10. linear regression

which tests can you perform when one variable is involved?

1. binomial test

2. x² goodness of fit test (proportional model)

3. x² goodness of fit test (poisson distribution)

4. one sample t-test

5. shapiro-wilk test

which tests can you perform when two variables are involved?

1. x² contingency test

2. fisher’s exact test

3. paired t-tets

4. two-sample t-test

5. welch’s t-test

6. mann-whitney u test

7. ANOVA

8. Kruskal-Wallis test

9. Tukey-Kramer test

10. regression

11. logistic regression

12. correlation

13. spearman’s rank correlation

which tests can you perform when three variables are involved?

1. multi-factor ANOVA

2. ANCOVA

which tests can you pick from if you are analyzing 1 categorical variable + how do you decide which one to use for which case?

1. binomial test

2. x² GOF with proportional model

which tests can you pick from if you are analyzing 1 numerical variable + how do you decide which one to use for which case?

1. x² GOF with poission distribution

2. one-sample t-test

3. shapiro-wilk test

which tests can you pick from if you are analyzing 2 categorical variables + how do you decide which one to use for which case?

1. x² contingency test

2. fisher’s exact test

which tests can you pick from if you are analyzing 1 categorical explanatory variable and 1 numerical response variable + how do you decide which one to use for which case?

1. paired t-test

2. two-sample t-test

3. welch’s t-test

4. mann-whitney u test

5. ANOVA

6. Tukey - Kramer test

which tests can you pick from if you are analyzing 2 numerical variables + how do you decide which one to use for which case?

1. regression

2. correlation

3. spearman’s rank correlation

which test should you pick from if you are analyzing 1 numerical explanatory variable and 1 categorical response variable (binary)

logistic regression

which test should you pick from if you are analyzing 2 categorical explanatory variables and 1 numerical response variable

multi-factor ANOVA

which test should you pick if you are analyzing 1 categorical explanatory variable, 1 numerical explanatory variable and 1 numerical response variable

ANCOVA

brief description of the binomial test; null, test statistic, df (if applicable), assumptions (if applicable), extra notes

uses data to test wether a population proportion p matches a null expectation for the proportion

1. null: the relative frequency of successes in the population is p0

2. test statistic: P-hat or X (number of successes of N trials)

*note: works if categorical variable only has two outcomes (eg. “success” or “failure”)

brief description of the x² GOF test; null, test statistic, df (if applicable), assumptions (if applicable), extra notes

the x² GOF test compares counts to a categorical or discrete numerical probability distribution

1. null: the data comes from a specified probability distribution (proportional, poisson)

2. test statistic: x²

3. df: (# of categories) - (# parameters estimated from data) - 1

4. assumptions: no more than 20% of categories with expected < 5; no category with expected < 1; random sampling

brief description of the x² contingency test; null, test statistic, df (if applicable), assumptions (if applicable), extra notes

tests the association of two or more categorical variables

1. null: the variables are independent

2. test statistic: x²

3. degrees of freedom (#columns - 1) * (#rows - 1)

4. assumptions: no more than 20% of categories with expected <5; no category with expected < 1; random sampling

brief description of the one-sample t-test; null, test statistic, df (if applicable), assumptions (if applicable), extra notes

the one-sample t-test compares a sample mean to a population mean proposed in a null hypothesis

1. null: population mean = null mean

2. df: n - 1

3. test statistic:

4. assumptions: variable is normally distributed; random sampling

brief description of the paired t-test; null, test statistic, df (if applicable), assumptions (if applicable), extra notes

the paired t-test compares the mean of the differences between two treatments to a value given in the null hypothesis

1. null:

2. test statistic:

3. degrees of freedom: number of pairs - 1

4. assumptions: differences are normally distributed; random sampling

brief description of the two-sample t-test null, test statistic, df (if applicable), assumptions (if applicable), extra notes

the two-sample t-test compares the differences in the means of two treatments to a value given in the null hypothesis

1. null:

2. test statistic:

3. df: n

4. assumptions: both populations have normal distributions; equal population variances; random

brief description of the ANOVA: null, test statistic, df (if applicable), assumptions (if applicable), extra notes

the analysis of variance (ANOVA) tests differences among means of multiple groups

1. null:

2. test statistic:

3. df:

4. assumptions: all populations have normal distributions; equal population variances; random sampling

brief description of the correlation test: null, test statistic, df (if applicable), assumptions (if applicable), extra notes

brief description of the regression: null, test statistic, df (if applicable), assumptions (if applicable), extra notes

brief description of the fisher’s exact test: null, test statistic, df (if applicable), assumptions (if applicable), extra notes

brief description of the welch’s approximate t-test: null, test statistic, df (if applicable), assumptions (if applicable), extra notes

brief description of the levene’s test: null, test statistic, df (if applicable), assumptions (if applicable), extra notes

brief description of the shapiro-wilk test

brief description of the mann-whitney u test: null, test statistic, df (if applicable), assumptions (if applicable), extra notes

brief description of the kruskal-wallis test: null, test statistic, df (if applicable), assumptions (if applicable), extra notes

brief description of the tukey-kramer test

brief description of the spearman’s rank correlation

brief description of the logistic regression

brief description of the multi-factor ANOVA

brief description of the ANCOVA

what are the computationally intensive methods?

1. simulation - creates new data from a theory

• generates artificial data based on a known theoretical model or set of parameters to study the behavior of a system or estimate probabilities

• eg. random number generation

• used to calculate probabilities for complex scenarios where you know the “rules” of the world but not the outcome

2. permutation (randomization) - shuffles existing data with replacement

• a statistical significance test that builds a null distribution by repeatedly reshuffling the observed data’s labels without replacement

• breaks the relationship between variables by shuffling group assignments (eg. swapping who got the drug and the placebo)

• used for hypothesis testing (calculating a p-value) to see if an observed difference is due to chance

3. bootstrapping - recycles existing data with replacement

• a resampling technique that estimates the sampling distribution of a statistic by drawing repeated samples from the original dataset with replacement

• treating the sample as if it were the population and drawing from it over and over to see how much the statistic varies

• used for creating confidence intervals and estimating standard error

what are the steps for statistical testing

1. clearly state:

• null and alternative hypotheses

• name of test

2. calculate and show the test statistic

3. indicate alpha and when appropriate df and the critical value of the test statistic

4. give the p-value as precisely as you can (either from tables or from other info - eg. calculated directly in binomial test, or using software like R)

5. interpret results in words

how to obtain a proportion confidence interval

how to obtain a mean of a normally distributed variable confidence interval

how to obtain a difference in means confidence intervals

how to obtain a regression slope confidence interval

population variance vs sample variance formula

coefficient of variation formula

power formula

law of total probability

general multiplication rule

addition rule

sample proportion formula

formula for N choose X

How to calculate expected values for x²

z-score formula

formula for t in a correlation test

t = r/SEr

formula for MS

formula for SStotal