Research Class 8 Part 1

what does bi-variate mean?

bi = two, variate = variable

variance is the standard deviation squared, and we only use this in ___, not in real life applications

equations

___ are only for intervals and ratio level variables

central tendency and variability

nominal and ordinal are not very ___ variables

strong

measures of central tendency and variability ___ be done on nominal and ordinal values

for e.g. colours which is nominal (red, yellow, blue)

cannot

we are often interested in nursing research how variables are ___ to each other

related

___ allow us to explore how two variables are related to each other

bivariate statistics

contingency tables are for ___ or (e.g. gender) ordinal data (smoking status for e.g)

nominal

contingency table allows us to ___ one level to another

compare

contingency tables are ___ frequency distributions in which the frequencies of two variables are cross-tabulated

two dimensional

____ example looking at genders of cats and dogs

dogs cat

male 42 10

female 9 39

total 51 49

contingency table

columns go down, rows go ___

across

the dependent variable are in the ___

rows

the independent variable is in the ___

columns

how the ___ is worded will imply what the independent and dependent variables are

research question

what is each box of data in a contingency table called

cell

N means ___, N1 (with subscript of 1) means a subset of that total sample

for e.g.

N = total sample

n1 = dogs

n2 = cats

total sample

when you have decided from the RQ which is the DV vs IV, then you know which to put in the ___ and which to put in the row

column

the contingency table format therefore makes it ___ to understand the research question clearly

easier

some research questions could investigate either relationship when ___

reversed

what does the contingency table do?

gives you frequency counts and precents of scores (for nominal or ordinal data) for two variables

suppose you are not interested in the proportions between 2 variables (contingency tables for nominal or ordinal data), but you are interested in the relationship between two variables that are ___ levels of measure (i.e continuous variables)

interval or ratio

___ is a statistical technique that is used to measure and describe a relationship between 2 variables

correlation

there is no attempt to ___ the variables with correlation, the researcher observes what is occurring naturally

control or manipulate

correlation means ___ or the degree that two variables go together

co-relation

___ correlation means the two variables go together in a straight line (not all are linear)

linear

the ____ is a number that summarizes the direction and degree (closeness) of linear relations between two variables

correlation coefficient (r)

for bivariate data, “r” statistically quantifies the ___ and direction of the relationship

strength

when should correlation be used? refer back to the 3 basic questions…

1. what kind of data is used (usually numeric/continuous, ratio/interval)

2. what kind of relationship is of interest (direction and strength)

3. how many groups are involved (usually one sample, with 2 or more variables)

scores (X and Y) are represented in a table or on a ___ (X values on horizontal axis of a graph, and Y values on vertical axis)

scatter plot

X is the ___ variable

independent

Y is the ___ variable

dependent

___ helps us to visualize whats going on between 2 variables

scatter plots

the direction of the relationship can either be positive or ___ as indicated by correlation

negative

positive means 2 variables change in the ___ direction

same

negative means the 2 variables change in ___ directions

opposite

the ___ of the relationship is another characteristic

form

the ___ being 0 means there is no relationship (non-linear), and r = 1 means there is a strong linear relationship

r value

however ___ relationship does not mean there is actually NO relationship, once you put it on the scatter plot, you may see a pattern even if the r value is zero

non linear

the degree or ___ of the relationship, i.e. how strong is the relationship, is another characteristic to look at

magnitude

the degree is how well the data ___ the specific form (e.g. a linear correlation measures how well the data points fit on a straight line)

fits

___ correlation is always +1 or -1, this indicates a perfect fit

perfect

a correlation of ___ means no fit at all

0

numerical values between ___ reflect the degree to which there is a consistent, predictable relationship between the 2 variables

+1 and -1

there are several forms of correlation coefficients, ___ is the most common version

Pearson product-moment correlation coefficient

the Pearson product-moment correlation coefficient measures the ___ and the direction of the linear relationship between 2 variables

degree

why use the pearson r?

• it helps with prediction (one variable can predict the other)

• it helps to assess validity and reliability of instruments

• it helps verify theories

the Pearson r is used for ___ and ratio levels of measurement

interval

for two variables, X and Y, it is assumed that there is a ___ between X and Y (assumptions for pearsons r)

linear relationship

X and Y are assumed to be both ___ variables (pearson R)

continuous

X and Y must be ___ of each other and X (pearson R assumption)

independent

X and Y have roughly equal ___ (homoscedasticity), which is another pearson R assumption

variability

___ means the variables stay consistent across the variables as X changes

homoscedasticity

any violation of these assumptions can produce ___ results

inaccurate

correlations mean variables are related but does not ___ why

explain

___ can have a strong effect on the value of a correlation

outliers

correlations should not be interpreted as ___ (the correlation is squared to measure the proportion of variability)

proportions

the closer r is to +1, the ___ the relationship

stronger

0.00-0.25 is little relationship, 0.90-1.00 is very ___ relationship

high

you look at the ___ to determine if there is statistical significance

this is the amount of risk you want to take that you are wrong

p value

you only want to take a 5% chance, meaning you are ___ confident that the results are accurate

95%th

therefore, you want a ___ of 0.05 or less, for the test to be statistically significant

p value

correlation (r value) can be 0.875, but then the p value is 0.052, which is 5.2%. therefore, this is unacceptable, this is not statistically significant. this could be due to __ sample size

small

negative (inverse) but strong relationship can have an r value of…

-0.9

no correlation r value can be…
(dots are scattered everywhere)

0.1

a non-linear relationship can have an r value of…
(dots do have a V shape pattern)

0.01

r value of 0.7 is a high or strong relationship.

coefficient of determination is r squared, which is (0.7×0.7 = 0.49) what does this mean

49% of the variance of one variable is explained by the other

recall that you can make a contingency table to demonstrate ___ in bivariate nominal ordinal data

proportions

what is a regression line

the graphing of a relationship between two variables

the regression line defines the precise, one to one relationship between each X value and its ___ Y value

corresponding

line makes the ___ easier to see

relationship

the regression line identifies the ___ (central tendency) of the relationship

center

the line can be used for ___

prediction

regression line reflects the best guess as to what the score on the Y variable would be predicted by a score on the X variable, also called the ___

best fit line

the regression line represents the best ___ line, predicting Y (outcome) from X (predictor)

prediction

the least squares solution is the predicted Y and is called the…

Y hat

the distance between this predicted Y value and the actual Y value in the data is determined by ___

distance

___ is the prediction we are making for each value

Y hat

the ___ is the distance between predicted Y and actual Y

prediction error