research analysis quiz 4

frequency expected vs observed expected

Observed frequency is the number of times a particular event is occurring actually when an experiment is conducted in the real world. While the expected frequency is the number of times a particular event is expected to occur or claimed to occur.

test linear relationships between two continuous variables

test correlations - Pearson’s r

what will provide equation for line that best fits data

regression analysis

regression line equation for multiple linear regression

sum of squares

between the predicted value and the mean of the dependent variable

measures the deviation of data points away from the mean value

model sum of squares (SSR or explained sum of squares)

variation in the dependent variable explained by model

residual sum of squares (SSE or sum of squared errors)

variation not explained by model

model much bigger than residual

model effectively captures the variation in the data and errors (residual) relatively small

Covariance

joint variability, how much scores vary

partial correlation

a measure of the strength and direction of a linear relationship between two continuous variables whilst controlling for the effect of one or more other continuous variables

missing data what to do

easy list wise deletion or pair wise deletion

list wise deletion

delete all data in a row a whole observation

why do we standardize things?

can’t just use covariance because it is dependent on units of measurement which is difficult to interpret

test hypothesis between categorical variables

non parametric test

how to calculate power?

 the probability of observing a statistically significant result at level alpha (α) if a true effect of a certain magnitude is present.

increased effect size and larger sample sizes lead to higher ____

How does power relate to type 1 & type 2 errors

setting a lower significance level decreases a type 1 error risk, but increases a type II errors risk

increasing ___ decreases a type II error risk, but increases a type 1 error risk

Binary outcome

Logistic regression

Interpret standardized beta coefficient from multiple linear regression model

• if beta coefficient for predictor variable is .58, how to interpret - for every one unit change in x there is a .58 standard deviation increase in outcome

• indicates the effect of a predictor variable on the dependent variable when both variables are measured in standard deviation units

testing data vs training data

see how well it predicts outcome in next group

logistic regression - see low base rate so model predicts no, model is bias just 1 or 0, bias is overfitted

confusion matrix

ODDS ratio interpret

standardized to 1 - .45 oz ration - 55% decrease odds. 1.55 - 55% greater odds - percentage or times more likely - 3.1 3x more likely

multiple linear regression

continuous outcome(height age salary) with two or more variables

multiple independent variables determine the outcome of a single dependent variable

why would we use logistic regression and when?

trying to predict binary outcome (yes or no) with two or more predictors

when you want to predict a categorical outcome, specifically a binary (yes/no, success/failure) or multinomial (multiple categories) outcome, and you have one or more independent variables that you believe might influence the outcome

b knot

dummy coding (categorical variable into predictor model) how many groups you need to create

k-1

r square means what for multiple regression?

a statistical measure in a regression model that determines the proportion of variance in the dependent variable that can be explained by the independent variable

how does r square relate to Pearson’s r correlation ?

coefficient of determination r2 is the square of the Pearson correlation coefficient

correlation

pearsons r

when the relationship is linear and both variables are quantitative and normally distributed and have no outliers

chi square

to analyze categorical data and determine if there’s a statistically significant relationship between two or more variables

to compare observed results with expected results

x²

to analyze categorical variables, particularly when examining relationships between nominal variables (where order doesn't matter)

can binary outcome but one predictor is categorical

2 categorical variable