Final Exam

What are the four steps of the Monte Carlos Stimulation?

1. Define a domain of possible values 2. Generate random numbers within that domain from a probability distribution 3. Perform a computation using the random numbers 4. Combine the results across many repetitions

Randomness is…

unpredictable

Parameter of interest

population interest we want to infer about

Null Hypothesis

default assumption. no effect or no difference H0

Alternative Hypothesis

testing for an effect or relationship. H1

P-value

the probability of obtaining test results at least as extreme as the observed results

Type 1 Error

null is incorrectly rejected

Type II Error

null is incorrectly accepted

Significance level

predetermined threshold used to assess the strength of evidence against the null hypothesis in hypothesis testing

Confidence levels

the degree of certainty or assurance that a researcher has in the results of a statistical analysis

Confidence Interval of the mean is…

CI = point estimate ± critical value ∗ standard error

Effect Sizes

the magnitude of difference or relationship between variables

Statistical Power

the probability of correctly rejecting null hypothesis or to detect an effect

How to use statistical power

1. to determine appropriate sample sizes

2. optimize study designs

Contingency Table

displays frequencies and examines the relationship between categorical value

chi-squared

checks for association between actual counts and what we’d expect to see if the variables were independent

correlation coefficient

(-1 to 1), close to 1 = strong positive linear relationship, 0 = no linear relationship, -1 = strong negative linear relationship

effect of outliers

distorted relationship. Affects the strength of the data and its direction

impact of model performance

skews estimate. reduces reliability

Addressing outlier points

graphs will visually identify them

linear regression

models relationships between a dependent variable and 1 or more IV using linear equation

General Linear Model

helps understand how different things affect something else. (Analysis of ANOVA)

Cross Validation

estimates a models perspective performance on new data set

sign test

compares data points to see if one tends to be consistently higher than the other, whilst not considering exact values

T-tests

compares mean to a hypothesized value to determine if there's a significant difference