Statistics Review Of Terms

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.

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.

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.

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 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.

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

Parametric: tests that require normally distributed populations
Non-parametric: if the samples do not meet the requirement for parametric

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

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 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

Dividing up the variance into the difference sources of variance

F= between group variability divided by within group variabililty

Total SS= within group SS + between group SS

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

/ high correlation between independent variables= this can be a problem

score has been produced using an interval scale of measurement
classification results in nominal(category) scaling

how the scores vary from the mean

squared deviation scores- thus it is the variance of the scores/data

number of scores free to take on a value in the range, always one score has no freedom

unsquare the sum of squares/df
if sum =10 /4 df=2.5, sq root of that number is 1.58=sd

Most scores occur in the middle with decreasing frequencies for high and low

within-variance on individuals within the group, between variance between two+ groups

error

mean squares

dividing up the total variability into its component
NOTE: Sum of squares add up to the total SS

dividing the between variance by the within (error), The more it rises above 1 the more we can say there are between group difference

dividing between/total SS then multiplied by 100 to give % of total variability

ratio of within/SS-unexplained variance
eta and Wilks are mirror images of each other

to analyze whether score differences on a dependent variable can by accounted for by scores on an indep. variable-use simple regression

summarizes the relationship between variables
dependent on Y axis and indep. on X axis

The point where the regression line intercepts the Y axis

slope and the Y intercept jointly define the regression coefficient

summarizes the relationship between any X and Y variable
Y = slope(X) + Y intercept

divide the regression SS by total SS
direct parallel to eta(Squared)
can be multiplied by 100 to explain % of variability

Pearson's correlation coefficient or r
can be positive or negative

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.

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

category- male female

survey 1-5 least to most

distance between each number is equal and continous scoring

how far the data are contaminated with random erros that make them inconsistent

to how far the data are subject to systematic errors or bias that makes them inaccurate

how well elements of the measure operate in concert

correlating the item scores for a sample of respondents, .7 min. reassurance of internal consistency, higher is better

same respondents tested twice- look for consistency of response

does it test the important facets of the content

parameters

accepted or rejected

null hypothesis

the alternate or research hypothesis

that the direction of the difference is not specified at a higher or lower level; mean difference is just NOT zero

we hypothesize not only difference but the direction of the difference

sampling distribution

assumptions

significance level or alpha
p<.05

Type I error

Type II error

beta

of the statistical analysis to avoid Type II error or to detect a relationship or difference that is actually present

both Type I and Type II error