Term
| Characteristics of relationship to examine |
|
Definition
Strength - weak to perfect
Direction - positive or negative
Form or Nature - linear, curvilinear, values |
|
|
Term
| Nominal Measurement - bivariate measure's of association |
|
Definition
| Phi, Contingency Coefficient, Cramer's V, Yule's Q |
|
|
Term
| Marginals in a contingency table |
|
Definition
| the totals for each column and row on the right and bottom of the table |
|
|
Term
| Proper form of a Contingency Table |
|
Definition
-Clear Heading
-Clear Categories
-Independent is on top, dependent is on left
-column percentages and at least column marginal frequencies
-Sample size ALWAYS reported |
|
|
Term
| Steps to find relationship using contingency table |
|
Definition
a. Independent variable is at the top of the table to form columns
b. Calculate Column percentages --- must sum to 100% at the bottom
c. Compare across the categories (i.e. columns) of the independent variable
d. No difference = no relationship; diff = a relationship
e. The bigger the difference between the categories of the independent variable, the stronger the relationship |
|
|
Term
| Difference between Descriptive Statistics and Inferential |
|
Definition
a. Descriptive tells us something about our variables (e.g., typical value, amount of dispersion, relationship)
b. Inferential are used to determine whether there is a relationship
-- More precisely, they are used to determine what inference we will make from the sample to the population we are interested in |
|
|
Term
| is a measure of association descriptive or inferential? |
|
Definition
| Descriptive - tells us about the characteristics of any relationship like strength, direction (not nominal), and nature. |
|
|
Term
|
Definition
Test Statistic (inferential) which tells us whether or not there is as STATISTICALLY SIGNIFICANT relationship between two NOMINAL LEVEL variables.
"Tells us whether the same relationship would have been found by chance" assumes that no relationship is the right answer |
|
|
Term
| Phi - measure of association |
|
Definition
Nominal
changes Chi Square by taking the square root of it and dividing it by sample size. Lets you use it to determine the strength of a relationship.
0-1 for 2x2 table.
0-? for higher table
cannot hit upper limit of one (asymetrical) |
|
|
Term
|
Definition
Nominal
square root of Chi Square, then divided by sample size times (number of row or columns, which is smaller) minus 1.
0-1 for all sizes
asymetrical- cannot hit 1 |
|
|
Term
|
Definition
Nominal
square root of chi squre, divided by sample size plus chi square
0-? changes with table size
cannot hit upper limit |
|
|
Term
| Goodman and Kruskal's Tau |
|
Definition
Nominal
Asymmetrical measure of association
0-1
Interpretation: Proportional reduction in prediction error provided by knowledge of the independent variable |
|
|
Term
|
Definition
|
|
Term
| Ordinal Level Measure of Association |
|
Definition
Strength AND direction
-1 to 1
Kendall's taus
Gamma |
|
|
Term
|
Definition
Ordinal
Tau A - when all cases have different ranks
Tau B- when the two variables have the same number of ranks and categories. (square contingency table)
-1 to 1 |
|
|
Term
|
Definition
Ordinal
-1 to 1
Probability of correctly guessing the order of a pair on one variable knowing their order on the other.
OR
the difference between the probabilities of obtaining positive and negative pairs, ignoring all ties.
Tends to give inflated relationship when lots of ties are present
Strength - easy to calculate from grouped data and there is a multivariate version |
|
|
Term
| MoA for Interval and Ratio levels |
|
Definition
| Calculate regression line/plane then the correlation coefficient |
|
|
Term
|
Definition
is the contigency table, but for interval and ratio
can tell us:
Existence
Direction
Strength
Form |
|
|
Term
|
Definition
| Y = (o with cross over line) + B (slope) * X - e (error) |
|
|
Term
| Linear Least Squares Theory |
|
Definition
Sample linear regression line is an estimate of the population regression line.
Not biased if:
-Random sampling
-Error is random (thus cancels out)
-X and error are unrelated
Y = sigma + BX + e |
|
|
Term
|
Definition
If no relationship, slope is 0
If no relationship, intercept is grand mean of Y
Slope is not equal to zero, look at probability to see if the relationship is real.
If so, how strong? Slope cannot be used cuz it is based on strength and amount of variation |
|
|
Term
|
Definition
Interval and Ratio
r
-1 to 1
symmetrical
use coefficient of determination to interpret
Best use - goodness of fit of observed values to regression line values |
|
|
Term
| Coefficient of determination |
|
Definition
r squared
The coefficient of determination is the proportion of total variation in Y accounted for or explained by X
Explained Variation / Total Variation |
|
|
Term
|
Definition
| Can have serious effects on correlation and regression |
|
|
