Equations For Exam Flashcards
(Population Proportion)
Give the equation for a one sample confidence interval
p^ +_ Z sqrt ((p^q^)\n)
Sample proportion +- z score x square root (sample proportion x 1 - sample proportion) divided by number of samples
How do you find a z score?
Use Table 5
Use the value you want in each individual tail e.g. 5.0
What is the equation for a p value
2[1 - chi (z statistic)]
How do you find chi of a z statistic?
Use table 4 - Normal tables
Use your z statistic value previously worked out
Population Proportions
What is the equation for a z statistic?
(P^ - p0)/ sqrt(p0q0/n)
P^ = sample proportion P0 = value under Ho Q0 = 1 - p0 N = number of samples
What can you conclude if a p value is greater than 0.05?
Fail to reject Ho
Not enough evidence to accept Ha or the contrary of Ho etc
What is a z score for a 95% CI?
1.96
(Sample)
Equation for construction a CI of a mean
X_ +- Z (Sa/ sqrt(Na))
X_ = sample mean Z = table 5 value for CI wanted Sa = standard deviation for A Na = number of samples in A
(2 Sample t-test)
Construct a 95% CI for mean difference
(X_1 - X_2) +_ t (S^2p (1/Na + 1/Nb)
X_1 = sample mean of 1 X_2 = sample mean of 2 t = t value S^2p = pooled estimate of variance Na = # samples in 1 Nb = # samples in 2
(T-test)
How do you find a t-value?
Use T-tables
Degrees of freedom = Na + Nb -2
Look up % you want in individual tail
(T-test)
How do you find a t-critical value?
Use T tables
Use d.f Na+Nb-2
Use sigma = 0.5
What does it mean if t test statistic is greater than the t-critical value?
Reject Ho
Accept Ha
How do you find expected values for chi square test?
EV = (row total x column total)/(overall total)
How do you find chi critical value?
Df = (# of rows -1)(# of columns-1)
Use chi square tables
Use df and 5 % column
What do you need for a least squares table?
5
x
y
x squared
xy
and the sums of all of these numbers
What do you calculate from the least squares table?
2
Sxx
Sxy
What do you calculate from Sxx and Sxy?
Beta hat one
What is the formula for Beta hat one?
Sxx/Sxy
What do you calculate from Beta hat one?
Beta hat 0
How do you carry out a wilcoxon rank sum test?
4
Let n1 and n2 = number in group 1 and 2
Let n = n1 + n2
Let group one = group with smallest # of ranks
Rank the values - largest value gets rank 1
How do you find R1 in a wilcoxon rank sum?
R1 = sum of all the ranks from the sample with the smallest sum of ranks
How do you find the expected value of R1?
n1(n+1)/2
Given equation
How do you find the sample error of R1
Given equation
se[R1]
List the order of calculations in a wilcoxon rank sum.
Rank sums Find R1 Find expected value of R1 (E[R1]) Find sample error of R1 (se[R1]) Find test statistic (z =...) Calculate p-vale
How do you calculate the p value for a wilcoxon rank sum?
Use p value equation
Use calculated z score from test statistic
Make conclusion
What does it mean if chi test statistic is smaller than the chi critical value?
t
We fail to reject Ho
(Two sample t-test)
Calculate the CI of mean difference when Ho says the means are different.
(X_A - X_B) +_ t (sqrt (Sa^2/Na) + (Sb^2/Nb) )
X_ = sample mean T = t - tables, d.f. = Na + Nb -2 S = standard variance N = number
(One sample t test)
What CI should you use for a small one sample test, n<30
t-test
X_ +_ t (s\ sqrt(n))
X_ =sample mean
t = t-tables where d.f = n-1
What do you need for an Anova Table?
Source (model, residual and total) Df Ss Ms F
How do you work out residual MS?
Square S
How do you work out F for Model
It’s given to you
How do you work out MS for model?
Multiply F (Model) by MS (residual)
How do you get the DF for Model?
P-1
How do you get the DF for residual?
N - p
How do you find the SS for both residual and model?
Multiply the DF by the Ms for each
How do you find an f critical value?
Use F tables
Use 5%
Use two df values e.g. (2,38) = column 2 and row 38
