TEST 1 HUMBEHV 3ST3

statistics

methods and procedures; a tool kit for analyzing data

correlational studies

measure associations between predictor and criterion variables, “subjects” come with their own set of variables

designed experiments

measure effects of indepedent variables on dependent variables, random assignment of “subjects” to experimental conditions

descriptive statistics

describes/summerizes important characteristics of data, uses graphs & statistics (mean or standard deviation), describes interesting features of sample

population

all events (subjects, scores, etc) of interest

sample

subset of a population

random sample

each member of the population has equal chance of being selected

convenience sample

taking a subset of a population that is easiest; may not be very representative

inferential statistics

use sample to make claims about a population; estimate parameters from sample statistics, investigate differences among populations by examining difference among group/sample

independent variable

manipulated by the experimenter, used in designed experiments

dependent variable

the things that are measured and constitute the data, or results, that will be analyzed; used in designed experiments

statistical idea of causality

when we intervene and change X, then the probability of Y also is changed (smoking causes cancer even though not all smokers get cancer and not all people with cancer are smokers)

regression

measures association between predictor and criterion variables

random assignment

designed experiments’ “subjects” come with their own characteristics, this procedure is done so that effects of subject differences should be unrelated to effects of independent variables

categorical variables

typically have a few discrete levels (s#x, marital status, brain area, profession), often lack numeric properties

numerical variables

typically have many levels though not always, (reaction time, body weight, income, age), the levels are ordered, differences between levels are meaningful

nomial scale

categorical, have no obvious numeric properties (eye colour, s#x, political party)

ordinal scale

order of the levels is meaningful, differences between levels may nit be meaningful (age, musical expertise, likert scales)

interval scale

numeric variables usually with many levels, but lack a true meaningful zero (time of day, fahrenheit and celsius), differences between levels are meaningful

ratio scale

numeric variables (reaction time, proportion correct, body weight), have a true non-arbirary zero on the scale, differences between levels are meaningful

need for graphs

highlight important features, patterns, trends, that cannot be visualized from the raw numbers

histogram

x aix is horizontal, binned variable, (bins defined by upper and lower limits, midpoints), y-axis → frequency count

bar graphs

value of interest is represented by height of ____, x-axis usually consists of levels on a qualitative/nominal variable

pie charts

used for visualizing proportions

line graphs

useful for illustrating trends, typically have a discrete variable on the x-axis

scatter plots

useful for visualizing the association between quantiative variables

unimodal distributions

single peak (INSERT PIC)

bimodal distributions

two peaks (INSERT PIC)

positive skew

INSERT PIC

negative skew

INSRET PIC

kurtosis

refers to the frequency/probability of scores that are far from the center of distribution

exploratory data analysis

goal to discover and summarize interesting aspects of data, discover interesting hypotheses to test, important with large and complex data sets

confirmatory data analysis

data gathered and analyzed to evaluate specific a priori hypotheses

(ex. clinical drug trials: “i think this will happen when i do this”) → find the real effect

between subjects design

randomly subject every person to one condition, minimizes chances of systematic differences between groups

within subjects design

every subject is tested in every condition, all conditions have the same subjects, so differences between conditions must be due to experimental treatments

mode

most common score, may be poorly defined, small changes in frequencies can produce big changes, actually appears in the data

median

middle score/50th percentile, robust to outliers

mean

msot commonly used measure of central tendency, average score, not robust to outliers (can trim both ends of data set to outset this effect → 10%)

mode advantages and disadvantages

A

robust to outliers, value actually appears in the data, the value with the highest probability of subjects having that score, can be found in nominal data

D

depends on how we bin scores, can be poorly defined/ unstable for flat or bimodal distributions

median advantages and disadvantages

a

robust to outliers, good index of typical scores, can be calculated even with flat distribution

d

no mathematical formula, difficult to use in equations

mean advantages and disadvantages

a

easy to use in statistical formulas, best estimate of typical score

d

value may not actually exist in the data, less robust to extreme values

range

difference between highest and lowest values, sensitive to extreme values

quartiles

most distributions can be divided into, sorted data into four subsets each containing 25% of data

interquartile range

difference between 3rd and 1st quartiles, the spread of the middle 50% of scores, stable against outliers

outliers

extreme values in data, sometimes real data (should be kept), sometimes experimental error (should be removed)

variability around the mean

use absolute values and squared deviations

variance

more common than MAD, calculate the sum of squared deviations, divide by the number of observations minus 1 (n-1), results in sample variance (s²)

why n-1 and not n

makes s² an unbiased estimator of the population variance

linearly related scales

when measures are perfectly correlated, most statistical analyses of those variables will yield the same results (celsius and fahrenheit)

bivariate

is data for which there are two variables for each observation (ex. the ages of husbands and wives of 10 married couples)

pearson’s product-moment correlation coefficient/correlation coefficient

is a measure of the strength of the linear relationship between two variables, represented with p for population and r for sample (range from 1 to -1)

properties of pearson’s r

it is unaffected by linear transformations (ex. the correlation of Weight and Height does not depend on whether Height is measured in inches, feet, or even miles)

point estimate

a single number used when trying to guess the parameter, limited in usefulness because it does not reveal the uncertainty associated with the estimate

parameter

A value calculated in a population. For example, the mean of the numbers in a population

confidence interval

are intervals constructed using a procedure that will contain the population mean a specified proportion of the time

null hypothesis

tested in significance testing. It is typically the hypothesis that a parameter is zero or that a difference between parameters is zero

criterion variable

The variable we are predicting and is referred to as Y

predictor variable

The variable we are basing our predictions and is referred to as X

simple regression

When there is only one predictor variable

simple linear regression

the predictions of Y when plotted as a function of X form a straight line

regression line

the best-fitting straight line through the points, the line that minimizes the sum of the squared errors of prediction

standard error of the estimate

a measure of the accuracy of predictions, is the square root of the average squared deviation

influence

how much the predicted scores for other observations would differ if the observation in question were not included (using Cook’s D)

leverage

based on how much the observation's value on the predictor variable differs from the mean of the predictor variable; The greater an observation's _______, the more potential it has to be an influential observationm

monotonic trend

as x increases, y increases, or decreases without reversal (may not be linear)

non-monotonic

as x increases, y changes direction at least once

linear relationship

the best fit line is straight

curvilinear relationship

best fit line is not straight

covariance

measures the degree to which two variables vary together, depends on the sum of products of deviation scores (positive when deviation scores have the same sign and negative when deviation scores have different signs): measure of association but is influenced by the spread of X and Y

heterogeneous subsamples

a statistical association observed in a population can be attenuated and even reversed within subgroups that make up a population; correlations calculated with these subgroups may be misleading

simpson’s paradox

correlation for population is positive but correlation within subgroups are negative

point-biserial correlation (rpb)

for one dichotomous and one continuous variable; calculate person’s r but call it rpb, not sensitive to units (ex. correct/incorrect answer on mc question and exam total score

spearman’s correlation

useful when observations have been replaced by their numerical ranks, is more robust to some types of extreme points (sensitive to scores affecting monotonicity), is an index of strength/direction of monotonic relationship

r phi

two dichotomous variables, code each binary variable value with two numbers (ex. gender (male/female) and pass/fail on exam)

percentile bootstrapping method

used for confidence interval, randomly selecting pairs from the data and resampling to use to estimate a confidence interval

Permutation distribution

Represents the differences we’d expect to see if they really were no difference between the groups

Permutation test

A way of testing a hypothesis by randomly rearranging the observed data To simulate what we’d expect if the hypothesis were true

P value

The probability of getting our data when the null hypothesis is true

Multiple regression

Relates y variable to multiple predictor variables X, Compute complex function/equation relating Y And x, Can be used to fit multiple lines to a set of XY data, Can be used to compute non-linear association between X and y

R² coefficient of determination

Component of regression line, Tells us how much of the variability in the outcome is explained by all of your predictors together