Test 1 Flashcards
Study for Test 1
What are the five steps of hypothesis testing?
(1) State hypothesis (2) State alpha (3) Calculate statisitic (4) Find p-value (5) Draw conclusion
What is single sample t-test?
t=(xbar-mu)/(s/sqrt(n))
What are the assumptions of the t-test?
That the data come from a normal distribution
What is the two sample z-test (when variances are considered different)?
z=(ybar1-ybar2)/sqrt((sigma12/n1)+(sigma22/n2))
Why are the variances added?
Because variance cannot be negative: var(ybar1-ybar2)=var(ybar1)+var(ybar2)
What is the pooled variance?
((n1-1)*s12 + (n2-1)*s22)/(n1+n2-2)
What is the t-test when variances are considered the same?
t=(ybar1-ybar2)/(sp*sqrt(1/n1+1/n2))
What are the R commands for finding p-values?
Two sided: 2*pnorm() Lt: pnorm() Gt: 1-pnorm()
What is the test for equal/unequal variances?
F=s12/s22 where F follows a F(n1-1,n2-1) distribution and H0:sigma12==sigma22 and HA: sigma12 ne sigma22
What are the assumptions for ANOVA?
(1) Data comes from normal distribution (2) Two population variances are the same
What type of design is expected in ANOVA?
CRD or Completely Randomized Design
How to decompose the variation in ANOVA?
Total variability is measured by the total sum of squares: SST=Sum for all groups i through alpha, the sum for all individuals j through n, (yij - ybar..)**2
SST=SStreatments+SSerror
Sum bla i thru alpha, sum bla j thru n, (ybari - ybar.. + yij - ybari.)
The ybari - ybar.. is the SStreaments
The ybarij - ybari. is the SSerror
How to find the degrees of freedom for an ANOVA?
df for SStreatments is a-1
df for SSerror is n-a
df for SST is n-1
Is there a two-tailed test for an ANOVA?
No, F-tests are only one sided so use :
1-pf(f, df of numerator, df of denominator)
What is the connection between t-test and ANOVA?
F is t**2 where t is a two-sided test
