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60 Cards in this Set

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What is the central limit theorem?
The central limit theorem:1.describes the relationship between sampling distribution m and population m. 2.shows as the sq root of sample increase, the sd of sample decreases 3. states that the sampling distribution tends to normally distributed if sample is of sufficient size.
What is sampling distribution?
A sampling distribution is the distribution of a sample statistic that would be obtained if all possible samples of the same size were drawn from given population.
Confidence interval?
A limit around a particular statistic that states that the population m would likely fall in that interval, 95% conf. interval will contain population parameter 95% of the time.
o Sample Size Issues/Power
Statistical power is the ability of a statistical test to detect relationships between variables.

Small sample sizes effectively reduce power and may make it very difficult to achieve statistical significance at even the .05 level
Power is a result of 4 factors:
Power is a direct function of four variables:
a. alpha level (.05)
b. sample size
c. effect size-strength of relationship between 2+ variables
d. type of statistical test.
o “Statistical Significance”, p-values
the likelihood that sample chosen is different because of the ‘treatment” as opposed to chance , sample chosen before treatment is representative of the total population
o Parametric vs. Non-Parametric
Parametric: tests that require normally distributed populations
Non-parametric: if the samples do not meet the requirement for parametric
o Assumptions (HOV, NORM, independence) & related tests
HOV= Homogeneity of Variance or homoscedasiticity=variance of both groups the same
NORM=normality of distribution
Standard deviation and psd(pseudo stand. dev) are about the same- normal distribution.
( skew or kurtosis of distribution)
Independence =Independence of observations, that one item selected has nothing to do with the other item being selected.
**consequences are the level of significance and F test will be seriously compromised
Interclass correlation coefiicient
Lack of independence is tested by the Interclass correlation coefiicient
**Stevens (1992) says this is the one of the most important assumptions that has to be met as it can totally impact power and lead to false results.
Effect Size
Effect size is a function of the actual size of the relationship-effect of the relationship on one or more variables by another



Cohen’s suggested that effect size effect (Cohen’s d) be constructed based on the difference between experimental and control group means, expressed in SDunits.
M (exp) – M (control) divided by SD
Variance Partitioning
Dividing up the variance into the difference sources of variance
F-Ratio
F= between group variability divided by within group variabililty
Sums of Squares
Total SS= within group SS + between group SS
o Types of regression (sequential, standard, stepwise)
1. uniqueness regression=Standard regression
standard- is looking at each variable as if it would be last
every thing put in as last, ( so nothing takes shared variance) so

data driven- no recommended—can be used tosnoop data

2. hierachial/sequential- regression ( you enter the order)
If you know your theory then you would use hierarchical or standard

3. data drive regression (stepwise)=order of entry
o Mutlicollinearity
/ high correlation between independent variables= this can be a problem
discuss how score and category differ?
score has been produced using an interval scale of measurement
classification results in nominal(category) scaling
what is meant by deviation scores?
how the scores vary from the mean
Sum of squares
squared deviation scores- thus it is the variance of the scores/data
degrees of freedom
number of scores free to take on a value in the range, always one score has no freedom
standard deviation
unsquare the sum of squares/df
if sum =10 /4 df=2.5, sq root of that number is 1.58=sd
normal distribution
Most scores occur in the middle with decreasing frequencies for high and low
discuss differences in within-group and between group differences
within-variance on individuals within the group, between variance between two+ groups
what is the other term for within group
error
variances are also called
mean squares
partitioning refers to?
dividing up the total variability into its component
NOTE: Sum of squares add up to the total SS
F-ratio
dividing the between variance by the within (error), The more it rises above 1 the more we can say there are between group difference
eta(squared)
dividing between/total SS then multiplied by 100 to give % of total variability
Wilks's lambda
ratio of within/SS-unexplained variance
eta and Wilks are mirror images of each other
simple regression is used for what?
to analyze whether score differences on a dependent variable can by accounted for by scores on an indep. variable-use simple regression
bivariate scatter plot
summarizes the relationship between variables
dependent on Y axis and indep. on X axis
Y intercept? on a regression line
The point where the regression line intercepts the Y axis
regression coefficients
slope and the Y intercept jointly define the regression coefficient
regression equation
summarizes the relationship between any X and Y variable
Y = slope(X) + Y intercept
r (squared) or coefficient of determination
divide the regression SS by total SS
direct parallel to eta(Squared)
can be multiplied by 100 to explain % of variability
square root of r(squared)
Pearson's correlation coefficient or r
can be positive or negative
discuss difference in types of information provided by regression and correlation coefficients
Regression: (the slope) indicates how the indep. variable accounts for group differences in the scores
Correlation coef. accounts for how far individual differences can be accounted for.
difference between regression/correlation (in terms of scatterplot)
regression is the slope (line)-higher value steeper line
correlation is how tightly the data points cluster around the line
higher value-tighter distribution of data dots
categorical scale
category- male female
ordinal scale
survey 1-5 least to most
interval scale
distance between each number is equal and continous scoring
Reliability of measurement refers to
how far the data are contaminated with random erros that make them inconsistent
Validity of measurement refers
to how far the data are subject to systematic errors or bias that makes them inaccurate
internal consistency
how well elements of the measure operate in concert
Cronbach's alpha
correlating the item scores for a sample of respondents, .7 min. reassurance of internal consistency, higher is better
test-retest reliability values
same respondents tested twice- look for consistency of response
content validity
does it test the important facets of the content
Characteristics of the population can be described with summary numbers that are called___________
parameters
Null hypothesis is either __________ or ______________
accepted or rejected
The ____states that the mean difference of the groups being tested is zero (refers to parameters)
null hypothesis
the other side of the null is
the alternate or research hypothesis
what is meant by the two tailed, form of the alternative hypothesis?
that the direction of the difference is not specified at a higher or lower level; mean difference is just NOT zero
what is meant by the onetailed form of alternative hypothesis?
we hypothesize not only difference but the direction of the difference
all of the different possible values of the mean differences and their associated probabilities are referred to as a
sampling distribution
test statistic probabilities only map accurately onto sampling distributions if certain ____________are met
assumptions
p value is called
significance level or alpha
p<.05
Risk of rejecting null hypothesis when it is true is called
Type I error
Risk of accepting null when it is not is called
Type II error
the degree of Type II error in an analysis is referred to as
beta
the power of an analyis refers to its capability of
of the statistical analysis to avoid Type II error or to detect a relationship or difference that is actually present
Increasing the sample size reduces
both Type I and Type II error