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A characteristic or condition that varies and has different values in different people or at different times
Variable
Measuring variables
data
Scales of Measurement
NOIR
to classify -Diagnosis, Genotype, Dead/Alive etc.
Nominal (Qualitative)
Order-unequal intervals -social rank, race finish, birth order, intervals can be different
Ordinal (Qualitative)
Distance, magnitude -equal intervals, arbitrary "0", temperature (C,F), opinion
Interval (Quantitative)
Origin -Natural "0", temperature in K, brain volume, # of convictions, time
Ratio (Quantitative)
Describes data
Descriptive statistics
Lets us infer using samples to study populations, uses probability
Inferential statistics
Help us understand populations -represents population in a study -has "n" individuals
Sample
The entire set/group of individuals you could potentially observe
Population
characteristics of populations
Parameters
characteristics of samples
Statistics
(Hopefully small) discrepancies that almost always occur -Larger sample should have smaller sampling error from populations values
Sampling error
Links samples and populations -replication is important
Probability
What measurement scale? Inches
Ratio
What measurement scale? Weather conditions
Nominal
What measurement scale? Rank order of favorite NCAA teams
Ordinal
What measurement scale? Weight in pounds
Ratio
What measurement scale? Religious affiliation
Nominal
What measurement scale? Distance
Interval
An equal chance for inclusion in sample -each set of members is equally likely -discrepancy of M from Mu is random
Random Selection
Sample where demographics are in proportion (Good)
Stratified random sample
Sample of only Intro Psych students (randomly selected) (Not as good)
Convenience sample
Least useful sample, be cautious (Bad) -biased
Self-selected sample
-Pre-existing patterns -preexisting groups compared (difference in mean?) -don't know if causal or not
Correlation
-Artificially create groups that differ on a variable -record differences in another variable -what's the advantage? Causation
Experiment
Measure naturally occurring associations -quantify pattern in 2 observed random variables (x,y) -compares means
Nonexperimental, Correlational Studies
Finding cause 1) Manipulation of Independent variable 2) Control of confounding variables 3) Observe dependent variable
Experimental Study
A factor manipulated by the experimenter. The focus of the study.
Independent variable
Factor that may change in response to an independent variable. Can be multiple
Dependent variable
3 Preventing confounds practices
1) Random assignment - to treatment/control condition 2) Holding constant - same treatment for everyone (e.g. all surgeons right handed) 3) Matching (participants) e.g. anxiety level, R/L handed
Internal attributes or characteristics that can't be directly observed but are useful for explaining/describing behavior
Constructs
Identifies an observable variable theoretically related to a construct -defines the construct in terms of those measurements
Operational Definitions
Typically whole, countable numbers with no intermediate values possible
Discrete variables
Free to choose precision, indefinitely divisible categories -real limits=-1/2 unit, +1/2 unit
Continuous variables
Shows the number of individuals (f) in each category (x) on a scale of measurement -organizes and reveals trends
Frequency Distribution
"Intervals" of X values -summarize, condense measurement categories -lose precise frequencies -O/I/R scales
Grouped Frequency Distributions
Unequal intervals that don't touch -Nominal, Ordinal
Bar Graph
Quantitative scale, extends to real limits -Ratio, Interval
Histogram
Has to start and end at bottom (0) -Ratio, Interval -rarely used, except published research
Polygon
Positive skew: Too hard Negative skew: Too easy
Floor Effect
Higher percentiles always equal higher _______
scores
The sum of the scores divided by the number of scores
Mean
Distance from the Mean
Deviation score
The sum of the Deviation scores =
0
M=20 -add 1 to every score what is the new mean?
21
(SumX1 + SumX2) / (n1 + n2)
Weighted Mean
Mean is not appropriate for _____ & _______ scales
Nominal, Ordinal
Cares more about rank order than number values -midpoint in ordered list of scores -value dividing distribution in half
Median
Most frequent category or score -always the peak in distribution -always actual, observed value -can have multiple -N,O,I,R -highest frequency
Mode
Positive skew: left to right (M,Mdn,Mo)?
Mean, Median, Mode
Negative skew: left to right (M,Mdn,Mo)?
Mode, Median, Mean
For a negatively skewed distribution with a Mode of X=25 and a mean of M=20, the Median is probably?
Between 20 and 25
Describes a central point of the distribution
Central Tendency
How scattered/spread out the scores are -used to describe/summarize -used as a basis for most inferential stats
Variability
Low variability =
Better representation of sample
High variability =
Unrepresentative sample common -harder to detect relationships
Max distance between scores Continuous: Xmax - Xmin Discrete: Xmax - Xmin +1
Range
Distance covered by middle 50% of the distribution -useful with vary skewed distribution
Interquartile Range
The average distance between a score and the mean
Standard Deviation
Average squared distance from the mean
Variance
The square root of variance
Standard deviation
Sum of Squares (SS)
SS=Sum(X-M)^2
Convey each score's distance from the mean in standard deviation units -rarely used in applied settings (decimals, negative numbers are confusing)
Z-Score
Body-percentile rank Tail-proportion higher than the score
Positive Z-Score
Body-proportion higher than the score Tail-percentile rank
Negative Z-Score
p + q=
1

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