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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 sizestrength of relationship between 2+ variables d. type of statistical test. 

o “Statistical Significance”, pvalues

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. NonParametric

Parametric: tests that require normally distributed populations
Nonparametric: 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 relationshipeffect 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


FRatio

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 withingroup and between group differences

withinvariance 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 

Fratio

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/SSunexplained 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. variableuse 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 valuetighter distribution of data dots 

categorical scale

category male female


ordinal scale

survey 15 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


testretest 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
