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Side ASide B
Two sets of data have the same variance
Two sets of data have different varieances
F-test tests for...
Equality of variance
Hypothesis of F test
H0= sigma^2sub1 = sigma^2sub2HA=sigma^2sub1 not equal to sigma^2sub2
Can F stat be skewed?
Yes, unlike normal and t distributions
Population of larger sample variance is #1
Because all numbers in the table are greater than one, they assume we know not to put smaller number in the numerator
If F is in the white area, between two tails of F distribution... and smaller than the critical f (alpha)...
We fail to reject null hypothesis. Rejection zone is in the tail. This means variances are close enough to equal to use equal variances version of the difference of means...
Non parametric tests
Less strict in their requirements (don't need a normal distribution)
Why would we ever use parametric tests then?
Parametric tests have greater power relative to samaple size (ability to reject H0 when HA is true)
Advantages of Non parametric tests
Can be used in skewed, bimodal, nomial and ordinal populations, and smaller sample sizes. Easier to compute, more resistant to data errors (ex mean is influenced by a large error,...
Sign test for the median
In a non normal population, the median is a robust measure of centrality, mean is not. You do not need normality!
n(with stem down) is "eta" or population median. n0 is hypothesized median.
If eta0 is the true median, then half of the population values re larger than eta0
# of observations with values greater than median. pi=.5 (pi is number of "successes).
In table A-1, for sign of the meidan test, always use pi=.5
Tests hypothesis that two populations have the same median. Requires ordinal data, test is based on ranks
Steps of mann whitney
Pool the sample data for populations x and y and rank them, 1 is the lowest.Convert sample statistic (S (the sum of ranks)) to a Z-score.P-value comes from Standard Normal Probabilities...
If there is a tie in ranks for mann whitney
Assign both observations the average of the ranks. So if there are two tied for 15, give them 15.5 for 15 and 16
Two Sample Number of Runs Test
Tests asks if distributions of 2 populations are the same or different. Sample statistic is R = # of runs
Procedure of Two sample number of runs test
Combine the 2 samples and rank them. a run is a continuous string of ranks from the same population. count the number of runs. A large R, or number of runs, means the distributions...
Convert normally distributed R to a z score
We reject the null only when R is smaller than mu-sub-r
Goodness of Fit test
Tests whether a random variable follows specific probability distribution. Checking if it is normally distributed
Compare observed frequencies for each category to frequencies expected under hypothesized distribution
f(Y) is the theoretical probability distributionf(A) is the random variable's distributionH0: f(A) = f(Y)HA: f(A) not equal f(Y)
Compares sample distribution to theoretical distribution like chi squared test, but this one, the random variable is continuous, not nominal. It compares cumulitive frequencies...
Kolomogorov Smirnov Test
H0: The sample is from the population F(x)HA: THe sample is not from the population F(x)
Which table for Kolomogorov Smirnov?
Contingency Tables Hypothesis
The variables are statistically independentTHe variables are statistically dependent
Sum rows and columns, compare observed frequencies to frequencies that would be expected if no relationship exists between variables
Expected frequency Eij for each cell
Eij= (RiCi)/n. Use table A-8
Goal of Regression analysis and defining X and Y
Examine influence of X on Y
to fit the regression line
We find the sum of the squared errors
Three ways to evaluate the goodness of fit on the line
1. Pearsons product-moment correlation coefficient, r2. Coefficient of determination, r^23. Standard error of the estimate Ssubyx
Standard error of the estimate
Measures accuracy associated with predicting Y. Also called the RMSE. and it is Ssub-x
Difference between actual and predictided value of Y. esubi = Ysubi - Yhatsubi. From examining residuals, we find out the amount of error and direction of error