HP 3325: Biostatistics test 3 ch.11

Interval measure

A rank-order scale with equal intervals between units but no true zero ex. IQ score, GRE, SAT

Standardization

Allows us to compare correlations between data sets when variables are different or measured in different units.

Scatterplot caution

BOTH variables must be quantitative - relationships between categorical data cannot be positive or negative - No scatterplot for nominal variables ex. beetles on boards of different colors

Another word to describe strength

Effective Sample Size -# of cases -1

Ratio measure

Equal intervals between units and true zero. ex. weight, pulse and most other biological measures

Scatterplot relationship

Form: linear, curved, clusters, no pattern Direction: positive, negative, no direction Strength: how closely the points fit the "form" Deviations: Outliers

Positive association

High values of one variable occur with high values of the other variable -positive linear relationship

Negative Association

High values of one variable occur with lows values of the other variable -Negative linear relationship

Scaling a scatterplot

Inappropriate scale can give incorrect impression. Both variables should plot squarely with no blank space.

Explanatory (independent) variable

May explain changes in the response variable. -when the explanatory variable is obvious it is plotted on the x-axis.

Response (dependent) variable

Measures or records an outcome of a study.

Nominal measure

Numbers have no intrinsic meaning but merely label different categories ex. religion, ethnicity, health insurance status

Other types of Correlation

Phi- both variables being correlated has only two values Kendall's Tau- nonparametric measure as an alternative for Spearman correlation, sometimes used between two ordinal values Contingency coefficient- nonparametric technique that can be used to measure two nominal-level variables "Universal Measure"- for nonlinear relationships Partial Correlation- when you have two variables then add another Semipartial Correlation- when you have three variables and remove one Multiple Correlation- measures between one variable and multiple others

Correlation Coefficients measure?

Positive relationships and inverse relationships

Ordinal measure

Ranks participants on some variable. In between ranks may not be equal. ex. happy, kinda happy, not happy agree, strongly agree, disagree military rankings

If p-value is less than .05

Significant

Ranked base correlation coefficient is called?

Spearman Correlation -good for outliers

Variable Strength

The relationship between two variables can be seen by the scatter around its main form -Strong means X can predict y -Weak means X will predict a wide range of Y

The r^2 (squared) measures?

The variance shared by the two variables

Correlation Coefficient "r"

a measure of the direction and strength of a relationship. It is calculated by using the mean and standard deviation of both x & y variables. -Can only be used to describe QUANTITATIVE variables. Categorical variables don't have means and SD's -does not distinguish between explanatory and response variables. - has no unit -quantifies the strength and direction of a linear relationship between two quantitative variables. - ranges from +1 to -1 -will be positive number if going up and negative if going down

The Pearson correlation test is best described as?

a parametric test

Correlation

a procedure for quantifying the relationship between two or more variables to measure strength and direction of the relationship

The Pearson correlation coefficient is most appropriate to use when?

both variables are normally distributed

Outlier

A data value that has very low probability of occurrence. Points that fall outside the overall pattern.

r^2 or r squared

- from 0-1 - higher value means more variance is shared - the amount of variance in the dependent variable y as explained by the independent variable x

A perfect inverse relationship would have an "r" of?

-1

The Spearman correlation coefficient should be used instead of the Pearson correlation coefficient when?

-Neither of the variables is normally distributed -one of the variables is normally distributed

The Pearson and Spearman correlation coefficients can be used to measure?

-The relationship of two independent variables to each other -The relationship of two related variables to each other -test-retest reliability

Correlations Coefficients "r"

-indicate strength and direction -range from +1 to -1 - +1 = perfect positive relationship - -1 = perfect negative or inverse relationship - 0 = no relationship - closer to 0 indicates weaker relationship

Spearman Correlation Coefficient

-measures relationships in the same direction but don't have to be linear -nonparametric -can be used with ordinal, interval, and ratio variables

Spearman Correlation

-one or both variables are ordinal -one or both intervals are not normally distributed - direction of relationship does not change - this test is Less influenced by outliers

Pearson Correlation Coefficient

-only measures linear (straight line) relationships -parametric test -finds association between interval or ratio measurement scale -variables must be normally distributed

Pearson Correlation

-variables are either interval or ratio -normally distributed -related via linear (straight line) fashion -no outliers

Scatterplot

one axis is used to represent each variable and the data are plotted as points on the graph. -ment for homogeneous not heterogeneous

The Pearson correlation coefficient provides a measure of ?

the strength of linear relationships

The Spearman correlation coefficient is best used to examine the relationship of?

two non normally distributed ordinal, interval, or ratio variables to each other

The Pearson correlation coefficient test is best used to determine the association of?

two ratio variables to each other