
Statistics is A branch of mathematics focused on
 *organization
 *analysis
 *interpretation of numbers

goal of statistics
to organize and interpret data

Characteristics or conditions that can change.
 Variables
 (most research begins with a question about the relationship between 2 variables for a specific group of individuals.)

The entire group of individuals is
population

examples of population
* relationship between class size and academic performance for 3rd graders

selected to represent the population
(populations are usually so large that researchers cannot examine the entire group)
Sample

measurements obtained in a study
Datat

Two types of Statistical Methods
 *Descriptive statistics
 *Inferential statistics

Organize and summarize data
 Descriptive statistics
 examples:
 * tables, grapshs, average score

parameter
a descriptive value for a population

Statistic
a descriptive value for a sample

Use sample data to make general conclusions about population
Inferential Statistics

1. a sample is only a part of the whole _____
2. sample data provide limited info about the___
3. sample statistics are imperfect representatives of the corresponding ___ parameters
population

the discrepancy between a sample statistic and its population parameter is called
Sampling error

2 classifications of variables
 1. discrete variables
 2. continuous variables

discrete variables
 indivisible categories
 examples
 *gender
 *car*sex

infinitely dividable
 Continuous variables
 examples
 *height,pain, time, weight

to establish relations between 2 variables...
 *Variables must be measured
 *Variables must be classified into one category

2 scales of measurement
 1.nonimal scale
 2.ordinal scale
 3.interval scale
 4.ratio scale

an unordered set of categories
 Nominal scale
 examples
 *gender
 *martial status

an ordered set or categories
 Ordinal scale
 example
 *horse races, contests with places 1st, 2nd, 3rd

an ordered series of equalsized categories
 Interval scale
 examples
 *6point likert scale (rate 110)
 *IQ

An ordered series of equalsized categories
A value of zero indicates none of the variable
 Ratio Scale
 examples
 *lenth, volume

3 major classifications
  experiemental studies
 correlation studies
 quasiexperiemetal studies

one variable is manipulated IV
a second variable is observed for changes DV
all other variables are controlled to prevent them from influencing the results.
Experimental Studies

what is teh goal of experimental studies ?
and give an example?
 to establish a causeeffect relationship between the IV and the DV
  i.e., does noise decrease test scores
 amount of noise=IV
 test scores=DV
 environment and time = controlled

observe two variables as they exist naturally..
I.e., is high school GPA related to SAT scores?
Correlation Studies

similar to an experiment but is missing either the manipulated IV or the control necessary for a true experiment
 Quasiexperimental study
  the IV is usually a preexisting variable
 i.e., parent child relationship, cancer.

the number of scores with a value
frequency

the pattern of frequencies over different values
frequency distribution

frequency tables
 make sense of a set of numbers.
 show how many times a number is used

bar graph.
provide a picture of distribution
histograms

line graph
frequency polygons

a frequency distribution with 2 or more high points
multimodal


Negative Skew
points to the left, peak is in the right.

ceiling effects means what skew?
and if the table was test grades what would the result tell you
ceiling effect is a negative skew, most scores piled up at the right meaning the test was too easy.

floor effect means what? and what a floor effect mean for a test?
floor effect is a positive skew. most scores piled up at the left, meaning the test was too hard.

a representative or typical value in a distribution
Central Tendency

3 meausres of central tendency

of the best measure of central tendency.
most frequently reported in research articles
think of the mean as the "balancy point" of distribution.
Mean

Middle value in a group of scores.
half the scores are above, half the scores are below (aka the "50h percentile")
 Median
  unafftected by extreme individual scores
  unlike the mean prefereable as a measure of central tendency when a distribution has EXTREME scores or when SKEWED.

most common single number in distribution.
IF distribution is symmetrical and unimodal ____ = the mean
 typical way of describing central tendency of a nominal variable
Mode

the second way to describe numbers
Dispersion

3 measures of dispersion
 1.range
 2.vairance
 3. standard deviation

simpliest measure of dispersion. The distance from the lowest to the highest score
Range

how spreadout the scores are from the mean.
variance

another measure of variation. Roughly the average amount scores differ from the mean. used more widely than variance.
standard diviation

are standardized scores used to compare numbers from different distributions.
describe particular scores. where a score fits in a group of scores in a distribution.
 Z scores
  raw scores are meaningless.
 i.e., i got a score of 565 in meaningless.
 vs, i got a zscore of 1.64

z scores continued.
the sign of the z score ( or +) indeciateds. the score is located above the mean (+). or below the mean ().
the value of z indicates the number of standard deviation between x and the mean of distribution.
 z score of 1.0 is one SD aboce the mean
 z score of 2.5 is two and a half SDs below the mean
 z score of 0 is AT the mean

measure and describe the relationship between 2 variables
 Correlation
  X = one score
 y = other score
 pair of XYsocres is usually from the same subject

descriptive statistic
 single number (e.g. r=.78)
 summarizes and describes a relationship
correlation coefficient

Coffee and nervousness, are correlation coefficient but they DONT ____ each other
 COEFFICIENTS DO NOT CAUSE EACH OTHER.
 need a true experiment

as X scores increase, Y scores also increase
positive linear relationship

as X scores increase, Y scores decrease
negative linear relationship

as X scores increase, Y scores do NOT only increaseor only decrease.
 at some point the Y scores change their direction of change
 nonlinear relationships
 (curvilinear)

The larger the absolute value of the correlation coefficient, the _____ the relationship
 Stronger.
 the sign only indicates the direction of the linear relationship, NOT the strength.
 i.e., .78 and .78 are strong relationships

describe relationships of 2 variables in a sample luck of the draw may produce a correlation, so you'll also need statistical significance.
correlatoin coefficients

only accept a correlation as "real" if it's significiant.
"income was related to agression (r=.78, p<.05).
what does this tell you...
 that it is significant.
 that there is less than a 5% chacne that the correlation in a population is NOT REAL
 (which means a 95% chance that it is real)

Research articles report: Correlation coefficientts : put single correlations _____
 in text.
 i.e., there was a significant correlation (r=.51, p<.05) between age and depression.

Research Articles Report:
Correlation Coefficients, put several correlations ____
 in table.
 (variables listed down left and across top)

The correlation of each pair of variables is shown in tables the table is called a ____
Correlation Matrix

Correlations help in making ____
 predictions
 e.g., prediction college GPA from HS SAT

what is the variable being predicted from
predictor variable (X)

whats the variable being predicted to
criterion variable (Y)

social scientists call prediction
 regression.
  can predict using 2 scores or raw scores

prediction using 2+ predictor variables is called
 multiple regression
 *** mutiple regression and correlation are frequently reported in research articles, so its important to have a general understanding of them.

