(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 equal-sized categories
Interval scale
examples
*6-point likert scale (rate 1-10)
*IQ
An ordered series of equal-sized categories
A value of zero indicates none of the variable
Ratio Scale
examples
*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.
Experimental Studies
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?
Correlation Studies
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
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
1. mean
2. median
3.mode
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 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
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
non-linear 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.