Stats Exam #3

inferential statistics

conducted to examine relationships, make predictions, and determine differences among groups in studies

-nature of hypotheses (null and alternate) or research questions

-level of measurement of variables (dependent/research)

-design (independent or paried)

-number of groups studied

key factors for inferential statistics

effectiveness

inferential statistics determines the _____ of an intervention or treatment

independent sample

one subject of a group is unrelated/random to the selection of other subjects or observations

paired sample

subjects or observations selected for data collection are related in some way to the selection of other subjects or observations

regression analysis/linear regression

focused on the prediction of a dependent variable using one or more independent variables

simple regression

one dependent variable and one independent variable

multiple regression

one dependent variables and more than one independent variable (multiple predictors predicting one variable)

quantitative or mixed methods

inferential statistic research is:

Pearson’s r

examines the relationship between two continuous variables which are measured at interval or ratio level; purpose is NOT to determine cause and effect between variables

positive/direct relationship

when one variables increases/decreases as the other variable increases/decreases

negative/inverse relationship

one variable increases as the other decreases

-1.00 or +1.00

indicates the strongest possible relationship; r cannot be greater than

r<0.3

R weak relationship

r=0.3-0.5

R moderate relationship

r>0.5

R strong relationship

n-2

What is the degree of freedom for Pearson’s r?

-table of critical values for r

-level of significance for the study (usually 0.05)

-degrees of freedom

to determine r value you need:

mirror image table of Pearson’s r

where the same labels appear in the same order for both x and y axes

power analysis and to determine sample size and examine power of  the study

What is effect size of r used in

greater

the smaller the effect size the ___ the sample size

smaller

larger effect size requires a ___ sample size

R² (coefficient of determination)

percentage of variance in the dependent variable explained by the independent variable/s (percentage of variance shared between two variables)

r² x 100%

calculation for percentage of variance explained in a relationship

greater

the stronger the r value the ___ the percentage of variance explained

slope/line of regression

the sign of the r value is the same sign as the ____

attributiontional, characteristics of the patient like blood pressure, diagnosis, health status, gender (when normally distributed)

what kind of variables are utilized for Pearson’s r?

-interval or ratio data

-normal distribution of at least one variable

-independence of observations pairs

-homoscedasticity

pearson’s r involves the following assumptions

homoscedasticity

when data is evenly dispersed above and belove regression line; indicated linear relationship; reflects equal variance of both variables (for every value of x the distribution of y values should have equal variability)

y=bx+a

equation for regression line of best fit

dependent variable (outcome)

what does y mean in y=bx+a?

independent variable (predictor)

what does x mean in y=bx+a?

slope of the line (regression coefficient)

what does b mean in y=bx+a?

y intercept (regression constant)

what does a mean in y=bx+a?

slope

expresses the extent to which y changes for every one-unit change in x

line of best fit

purpose is to develop the line to allow the highest degree of prediction possible

method of least squares

procedure for developing line of best fit (minimizes the squared differences between actual and predicted Y values.

-independent variables measured with minimal error

-variables treated as interval or ratio

-dependent variable score are normally distributed

-residuals are not correlated/random

-scores are homoscedastic

-y scores have equal variance at each value of x

assumptions of multiple linear regression:

which independent variables are most correlated with dependent variable

multiple linear regression determines:

need to have strong correlations with dependent variable but weak correlations with other independent variables

what do independent variables need to be effective predictors?

multicollinearity

when independent variables in the multiple linear regression are strongly correlated

R² (coefficient of determination)

one of the outcomes from multiple linear regression; used to calculate percentage of variance predicted by regression formula

ANOVA

What is R² significance tested with?

the regression equation has predicted the variation in the dependent variable and R² is not random

What does a significant F (statistic for ANOVA) indicate?

-normal distribution of dependent variable

-linear relationship between x and y

-independent observations 

-no (or little) multicollinearity

-homoscedasticity 

assumptions for simple linear regression

continuous

For simple linear regression the dependent variable must be ____

the correlation between the actual y values and the predicted y values using the new regression

How is R used in simple linear regression?

the new regression equation more accurately predicts y because the higher the correlation the closer the actual y values are to predicted y values

What does a higher R value indicate for the new regression equation?

0.02

small effect size for R²

0.15

moderate effect size for R²

0.26

large effect size for R²

y-intercept

where the regression line touches the y axis (where it starts)

slope (B)

In multiple linear regression each predictor (IV) has its own ___

multiple linear regression

all the predicted values are tested simultaneously

the independent relationship between one of the predictors and y after controlling for the presence of every other predictor in the model

What does B/beta represent in multiple linear regression?

attributional/characteristics

What kind of variables are in multiple linear regression?

actual y - predicted y 

What is the residual?

residual

how much the data (predicted y) differs from the line of fit (actual y values)

unpatterned

residuals should be ___

heteroscedasticity

occurs when residuals are not evenly scattered around the regression line (there’s a pattern); looks like a cone or triangle

birds nest (no real pattern)

homoscedasticity should look like a ___

predictive power; generalizability

Multicollinearity does not affect ___ ___ but rahter causes problems with _____

amount of variance (R²)

If there is multicollinearity what will be inflated by each variable?

before

performing multiple correlation analyses (examining multicollinearity) has to occur ___ conducting regression analyses

<0.20 or 0.10

Tolerance scores that indicate problem with multicollinearity

5 or 10

Variance inflation factor scores that indicate problem with multicollinearity

dummy coding of nominal variables

when categorical predictors in regression analysis in a coding system are developed to represent group memberships (grouping IVs)

0 and 1

What numbers are used when variable is dichotomous?

2

How many dummy values (groups) are used when there are 3 categories?

3; 1

for more than __ categories the number of values increase; the number of dummy variables is __ less than the number of categories

Independent Samples T-test

parametric statistical technique used to determine significant differences between the average scores obtained from two groups (determines differences between two groups)

larger; greater

the ___ calculated t ratio (absolute value) the ___ the difference between the two groups

(number of subjects in sample 1 + number of subjects in sample 2) -2

degrees of freedom for independent samples t-test

Bonferroni

used when there were multiple t-tests in a study; makes sure that there is not inflated type I error

calculation for Bonferroni

alpha/number of t-tests=new alpha value

-scores are normally distributed

-dependent variable/s are interval or ratio level

-the two groups examined for differences have equal variance achieved by random sample and random group assignment

-scores or observations within each group are independent/not related to the scores in the other group

assumptions for independent samples t-test

results are reliable even if one of the assumptions has been violated

When a t-test is robust (strong)

lacks independent assumptions or have extreme violation of assumption of normality

When a t-test is NOT robust

size, variance, independent

in independent t-test groups do not need to be of equal ___ but rather of equal ___ and must be__

active or attributional

in independent t-tests the independent variable must be

active

independent variable refers to an intervention, treatment, or program; ex: control and treatment grous

attribution

independent variable refers to a characteristic (demographic) of a participant; ex: gender, diagnosis, ethnicity

research designs that may utilize independent t-test

randomized experimental, quasi-experimental, and comparative designs (not grounded theory)

sample size of each group (not total number of participants)

What does n equal in the calculation for independent samples t-test?

Mann-Whitney U

nonparametric alternative to independent samples t-test; differences between two samples when the dependent variable isn’t a normally distribution

Wilcoxon Signed Rank Test

nonparametric alternative to paired/dependent samples t-test; compares 2 sets of data from one group when the dependent variable isn’t normally distributed

Spearman Rank Order Coefficient

nonparametric alternative to pearson’s r; when one or both of the variables being associated are not continuous/normally distributed

Paired/Dependent Samples t-test

calculated to determine differences between two sets of repeated measures data from one group of people (ex:pre-test and post-test); can also be used when the groups are matched to ensure similarities between the two groups (ex: twins, husband and wife)

One-sample crossover design

when one group of participants is exposed to one level of an intervention and then those scores are compared with the same participants’ responses to another level of the intervention resulting in paired scores

-distribution of scores is normal or approximately normal

-dependent variable/s are measured at interval or ratio levels

-repeated measures data are collected from one group of subjects, resulting in paired scores

-differences between the paired scores are independent

assumptions for dependent samples t-test

square root of variance

how do you get standard deviation?

n-1

What is the degrees of freedom for dependent/paired samples t-test?