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Statistics is A branch of mathematics focused on
- *organization
- *analysis
- *interpretation of numbers
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goal of statistics
to organize and interpret data
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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.)
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The entire group of individuals is
population
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examples of population
* relationship between class size and academic performance for 3rd graders
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selected to represent the population
(populations are usually so large that researchers cannot examine the entire group)
Sample
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measurements obtained in a study
Datat
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Two types of Statistical Methods
- *Descriptive statistics
- *Inferential statistics
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Organize and summarize data
- Descriptive statistics
- examples:
- * tables, grapshs, average score
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parameter
a descriptive value for a population
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Statistic
a descriptive value for a sample
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Use sample data to make general conclusions about population
Inferential Statistics
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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
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the discrepancy between a sample statistic and its population parameter is called
Sampling error
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2 classifications of variables
- 1. discrete variables
- 2. continuous variables
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discrete variables
- indivisible categories
- examples
- *gender
- *car*sex
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infinitely dividable
- Continuous variables
- examples
- *height,pain, time, weight
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to establish relations between 2 variables...
- *Variables must be measured
- *Variables must be classified into one category
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2 scales of measurement
- 1.nonimal scale
- 2.ordinal scale
- 3.interval scale
- 4.ratio scale
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an unordered set of categories
- Nominal scale
- examples
- *gender
- *martial status
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an ordered set or categories
- Ordinal scale
- example
- *horse races, contests with places 1st, 2nd, 3rd
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an ordered series of equal-sized categories
- Interval scale
- examples
- *6-point likert scale (rate 1-10)
- *IQ
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An ordered series of equal-sized categories
A value of zero indicates none of the variable
- Ratio Scale
- examples
- *lenth, volume
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3 major classifications
- - experiemental studies
- -correlation studies
- -quasi-experiemetal studies
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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
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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
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observe two variables as they exist naturally..
I.e., is high school GPA related to SAT scores?
Correlation Studies
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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.
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the number of scores with a value
frequency
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the pattern of frequencies over different values
frequency distribution
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frequency tables
- make sense of a set of numbers.
- show how many times a number is used
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bar graph.
provide a picture of distribution
histograms
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line graph
frequency polygons
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a frequency distribution with 2 or more high points
multimodal
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Negative Skew
points to the left, peak is in the right.
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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.
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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.
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a representative or typical value in a distribution
Central Tendency
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3 meausres of central tendency
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of the best measure of central tendency.
most frequently reported in research articles
think of the mean as the "balancy point" of distribution.
Mean
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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.
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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
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the second way to describe numbers
Dispersion
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3 measures of dispersion
- 1.range
- 2.vairance
- 3. standard deviation
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simpliest measure of dispersion. The distance from the lowest to the highest score
Range
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how spreadout the scores are from the mean.
variance
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another measure of variation. Roughly the average amount scores differ from the mean. used more widely than variance.
standard diviation
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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
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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
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measure and describe the relationship between 2 variables
- Correlation
- - X = one score
- -y = other score
- pair of XYsocres is usually from the same subject
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descriptive statistic
- single number (e.g. r=.78)
- summarizes and describes a relationship
correlation coefficient
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Coffee and nervousness, are correlation coefficient but they DONT ____ each other
- COEFFICIENTS DO NOT CAUSE EACH OTHER.
- need a true experiment
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as X scores increase, Y scores also increase
positive linear relationship
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as X scores increase, Y scores decrease
negative linear relationship
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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)
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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
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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
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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)
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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.
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Research Articles Report:
Correlation Coefficients, put several correlations ____
- in table.
- (variables listed down left and across top)
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The correlation of each pair of variables is shown in tables the table is called a ____
Correlation Matrix
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Correlations help in making ____
- predictions
- e.g., prediction college GPA from HS SAT
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what is the variable being predicted from
predictor variable (X)
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whats the variable being predicted to
criterion variable (Y)
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social scientists call prediction
- regression.
- - can predict using 2 scores or raw scores
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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.
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