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Statistics is A branch of mathematics focused on
- *interpretation of numbers
goal of statistics
to organize and interpret data
Characteristics or conditions that can change.
- (most research begins with a question about the relationship between 2 variables for a specific group of individuals.)
The entire group of individuals is
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)
measurements obtained in a study
Two types of Statistical Methods
- *Descriptive statistics
- *Inferential statistics
Organize and summarize data
- Descriptive statistics
- * tables, grapshs, average score
a descriptive value for a population
a descriptive value for a sample
Use sample data to make general conclusions about population
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
the discrepancy between a sample statistic and its population parameter is called
2 classifications of variables
- 1. discrete variables
- 2. continuous variables
- indivisible categories
- Continuous variables
- *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
- *martial status
an ordered set or categories
- Ordinal scale
- *horse races, contests with places 1st, 2nd, 3rd
an ordered series of equal-sized categories
- Interval scale
- *6-point likert scale (rate 1-10)
An ordered series of equal-sized categories
A value of zero indicates none of the variable
- Ratio Scale
- *lenth, volume
3 major classifications
- - experiemental studies
- -correlation studies
- -quasi-experiemetal 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.
what is teh goal of experimental studies ?
and give an example?
- to establish a cause-effect 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?
similar to an experiment but is missing either the manipulated IV or the control necessary for a true experiment
- Quasi-experimental study
- - the IV is usually a pre-existing variable
- -i.e., parent child relationship, cancer.
the number of scores with a value
the pattern of frequencies over different values
- make sense of a set of numbers.
- show how many times a number is used
provide a picture of distribution
a frequency distribution with 2 or more high points
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
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.
Middle value in a group of scores.
half the scores are above, half the scores are below (aka the "50h percentile")
- - 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
the second way to describe numbers
3 measures of dispersion
- 3. standard deviation
simpliest measure of dispersion. The distance from the lowest to the highest score
how spreadout the scores are from the mean.
another measure of variation. Roughly the average amount scores differ from the mean. used more widely than variance.
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 z-score 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
- - X = one score
- -y = other score
- pair of XYsocres is usually from the same subject
- single number (e.g. r=.78)
- summarizes and describes a relationship
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
- non-linear relationships
The larger the absolute value of the correlation coefficient, the _____ the relationship
- 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.
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 ____
Correlations help in making ____
- 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
- - 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.