Statistics midterm 2

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LucinaAyvazian  on October 26, 2011

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Statistics midterm 2

 alternative hypothesiswhat you expect to see. (your hypothesis)
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Definitions

alternative hypothesis what you expect to see. (your hypothesis)
Null hypothesis any result that is not what you expect to see. We can not say that there is no relationship that we are finding. Trying to disprove the null hypothesis.
test statistic the variation explained (effect) over the variation not explained (error). if the amount of variation we explain with out model is significantly greater than the variation our model fails to explain, then we can be fairly certain that our model is good.
type 1 error occurs when we believe that there is a genuine effect in our population--when in fact there isnt.
type 2 error occurs when we believe there is no effect in the population when in reality there is.
Dummy Variables 2 categorical variables. becomes coded into 1 (yes) and 2 (no). mean of the dummy variable is the percentage of the time the variable is yes.
variance tells us how much scores deviate from the mean for a single variable.
covariance tells how much variables scores differ from its mean when taking into account another variable. as one is increasing/decreasing--what is the other doing?
covariance equation E(Xi-xbar)(Yi-ybar) / n-1
correlation a measure of the extent to which 2 variables are related by looking at the pattern of responses across variables. we want to see whether as one variable increases the other increases/decreases/stays the same.
correlation coefficient equation r= (E(Xi-xbar)(Yi-ybar))/(n-1)(SxSy)
Positive correlation as one variable increases the other variable increases
negative correlation as one variable increases, the other decreases
Pearsons R must be normally distributed. requires either continuous or dichotomous data. large samples
Spearmans Rho non-normally distributed. ranks data and then uses a persons r. for large samples.
Kendalls tau better for small samples. both normally and non-normally distributed data.
pairwise only excludes missing data in response to specific responses
listwise any missing data in response removes you from sample. We use this one.
chi squared test (X^2) tests significance. uses categorical data. lets you compare categories to see if there is a difference between what your seeing and what youd expect to see if one category is not affecting the other.
observed frequencies they are the cants we see in our sample
expected frequencies need some calculations for each cell.
degrees of freedom for Chi squared(rows-1)(columns-1)
dependent variables your main variable of interest. The variable that is acted by the independent variable. the one that would come after the independent in a timeline
independent variable the variable that causes changes in the dependent variable. the variable that explains the other. comes first in a timeline.
T-Test a dummy variable and a continous variable
difference b/t two groups in a continuois variable in a sample or within 1 group b/t a sample.
independent T-test compares 2 means based on independent data. --different groups same time
dependent t-test compares two means based on one group at different times. measures how much of a change happens over time because of a treatment.
standard error how your variation stacks up against what type of variation we would expect to see in the population.
t-test assumptions parametric test that assumes the test is normally distributed. data are measured at least the same interval scale
independent t-test assumptions i. Variances in these populations are roughly equal meaning each group has the same amount of internal variance.
ii. Scores in different treatment conditions are independent because they are from different people.
iii. Homogeneity of variance
(Levenes test:) significant If it is significant homogeneity cannot be assumed--equal variance not assumed--bottom row
(Levenes test:) not significant homogeneity can be assumed--equal variances assumed. use top row
Post hoc test Not planned (no hypothesis), compare all pairs of means
Games howell if full assumptions not met (variances are not equal) if significant
bonferoni if all assumptions are met--variances are equal. if not significant
between groups model
within groups residual
means squared variance
Correlation Is there are relationship between age (years) and hours spent reading?
two continuous variables Correlation
Dummy variable with continuous variable t-test
independent t-test i. Ex. Is there a relationship between gender (0=male, 1=female) and hours spent reading?
Dependent t test i. Ex. Is there are difference between hours spent reading at the beginning of college and at the end of college?
Chi squared test i. Ex. Is there a relationship between the type of book read (1= novel, 2=romance, 3=si-fi) and gender (male=0, female=1)?
Chi squared test ii. Ex. Is there a relationship between grade level (1=9th, 2=10th, 3=middler), and type of book read(1= novel, 2=romance, 3=si-fi)?
two categorical variables chi-squared test
categorical and continuous ANOVA
ANOVA i. Ex. Is there a relationship between grade level (1=9th, 2=10th, 3=middler) and hours spent reading?
sample Correlations r=
Population Correlation rho (P)=
SSt Total variation (total sum of squares)
SSm Model variation, model sum of squares
SSr residual variation, residual sum of squares
MSm model mean squared
MSr residual means squared
F ratio ratio of variation explained by the model and variation explained by unsystematic factors
Dbar difference between the mean
Mew (µ) differences of the means in a population always = 0
partial correlation a correlation between 2 variables in which the effects of the other variables are held constant
semipartial correlation qualifies the relationship between 2 variables while controlling the effects of the third variable
log linear analysis used when you have a categorical variable with 3 or more categories. for each model it calculates the expected values and the statistics and compares them to the observed data using the likelihood ratio

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LucinaAyvazian