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sampling procedures:

random
stratified:randomly sample from groups of interest cluster: sample group rather than individuals convenience: sample p's that are readily available quota: representative proportions 


statistics vs. parameters

statconcrete
paraabstract 


statistics

a set of mathematical procedures for organizing, summarizing, and interpreting information



parameters

a value that describes the population
ex. the average household income in the us (all in us) 


descriptive vs. inferential statistics

descriptive  describing amt
inferential  describing an effect 


variables vs. constructs

..



descriptive statistics

used to simplify data
describing amount ex. avg. household income just saying what you see, not explain anything 


inferential statistics

used to make generalizations from sample to population
describing an effect p value only provided for inferential 


variables

a characteristic or condition that changes or has different values for different individuals
something that varies flipside of constant descriptive # of crimes committed categorical age ranges race gender recieving drug or placebo exposure to violent media or no media construct (usually psy construct) age acceptance of gender roles aggression level 


constructs

elements that the researcher claims to be measuring and manipulating

construct validity: the degree to which the study measures and manipulates the underlying psychological elements that the researcher claims to be measuring and manipulating


operational definitions

how you measure it
the measure 


categorical vs. continuous variables

..



categorical variables

separate categories only
ex. who is still alive in the sample all statistical analyses involve knowing the difference b/w categorical and continuous no values in b/w your in or not, male or female #'s designate outcome or category used in advanved correlational studies 


continuous variables

based on a range of values
ex. hormone levels in the sample can have whole # or something b/w #'s ex. temperatures 


categorical vs. discrete variables




discrete variables

separate categories or whole numbers
ex. # of ppl. in room, counting things up no "in betweens" 


real vs. apparent limits of numbers

real limit = .5 below and .5 above
apparent limit = as it appears 


real limits of numbers

the boundaries of scores that are represented on a continuous number line
the real limit separating two adjacent scores is located halfway between the scores upper limit at the top of the interval lower limit at the bottom of the interval ex. 1 = .51.5 


apparent limits of numbers

ex. 3, 4, 5, 6, 7
 apparent limit = 37, not 2.57.5 (real limit) 


statistical notation

raw score = x
set of raw scores = xi a number next to x regers to the order in which it appears in the data set so, xi is the first score in the set sum of raw scores = Σxi score multiplied by itself = x^2 number of people in the population = N number of people in the sample = n 


order of mathematical operations

PEMDΣAS



mode

the most frequent score
can be more than 1 1,2,2,3,3,3,3,4,4,5,5,5 m=3 pro: uses a real number and picks up on existence of multiple groups cons: may not really be in the middle 


median

 the middle score
50% are above it and 50% are below it determine N, cf, and c% then find the score that contains 50 as the c% be able to hand calculate 
requires ordering the scores from the lowest to the highest
if an odd # of scores, find the score the is exactly in the middle if an even # of scores, find the midpoint b/w the 2 middle scores 

mean

the average score
Σxi/n n=number of scores be able to hand calculate 
pro: accounts for clusters of scores
con: affected by outliers 

when do you use mode?

when you have a categorical variable
uses a nominal scale (0=male 1=female) discrete variables (ex. # of computers in a home) 
advantages:
most common score actually exsists (ex. can't have 2.3 computers  want to see the most freq. # of comp. in home) helps describe the shape of the distribution useful when multiple groupings exsist (ex. bimodal distributions) 

when do you use median?

when weird scores exist
extreme scores > skewed dist. throws off the mean, not the median 
advantages:
can calculate when undetermined scores exist ex. participant took too long to finish task so had to stop can calculate when openended categories exist ex. # of computers:1,2,3,4 or more more appropriate for ordinal scale (rank) 

when do you use mean?

typical measure of central tendency

advantages:
accounts for all scores in dist. related to measure of variability (distribution) useful for stats involving hypothesis testing (aka inferential statistics) 

central tendency

a single sore that defines the center of a distribution (i.e. the most representative score)



shape of distribution

bellcurved or 2humped



create a twogroup histrogram

draw normal curves for each group
interpreting mean differences 


simple vs. grouped frequency distributions

simplenumber of ppl with each score
groupednumber of ppl in a particular subset ex. A's, B's, C's, D's, F's on exam 


Σxi

sum of scores



obtaining Σxi from a distribution

add up all f's



obtaining the mean from a distribution

number that appears the most  biggest frequency #
create a frequency dist. table, find the largest value(s) in the f column 


proportions and percentages in distribution

determine N by adding up the frequencies, divide f by N to get the proportion (p), then multiply p by 100 to get the percentage (%)



real limits

the boundries of scores that are represented on a continuous number line
the real limit separating 2 adjacent scores is located halfway b/w the scores upper limit at the top of the interval lower limit at the bottom of the interval 3,4,5,6,7 =2.57.5 not 37 


frequency distribution

an organized tabulation of the number of individules located in each category on the scale of measurement



frequency distribution graph (histogram)

possible values on xaxis
number of times calue appears on yaxis 


how can graphs be misused?

toying with yaxis
making it appear big deal or no big deal 


shapes of frequency distribution

graph is skewed
bellcurved 2humped 


positively skewed

most scores grouped at bottome but some are extremely high _/^\_____



negatively skewed

most scores grouped at top, but some scores are extremely low ___/^^^^\__



percentiles and percentile ranks

def
finding them in frequency dist. interpolating a percentile using a formula 


problem with inferential stats

there will always be a difference between the sample statistic and the population parameter
difference: sampling error (can be big or small; if big > can't report as real finding) most often seen in political polls ex. approval rating has a sampling error of +/ 3 percentage points (sampling error) 45% approval rating > statistic act. b/w 4842% > parameter statistical dead heat > sampling range overlap eachother 


interpolation

Int=(Dsco*Dper)/D%
add this to the lower SCORE, and you will have the desired percentile 
