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1.2 Biostatistics > Equations For Exam > Flashcards

Equations For Exam Flashcards

1
Q

(Population Proportion)

Give the equation for a one sample confidence interval

A

p^ +_ Z sqrt ((p^q^)\n)

Sample proportion +- z score x square root (sample proportion x 1 - sample proportion) divided by number of samples

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2
Q

How do you find a z score?

A

Use Table 5

Use the value you want in each individual tail e.g. 5.0

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3
Q

What is the equation for a p value

A

2[1 - chi (z statistic)]

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4
Q

How do you find chi of a z statistic?

A

Use table 4 - Normal tables

Use your z statistic value previously worked out

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5
Q

Population Proportions

What is the equation for a z statistic?

A

(P^ - p0)/ sqrt(p0q0/n)

P^ = sample proportion
P0 = value under Ho
Q0 = 1 - p0
N = number of samples
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6
Q

What can you conclude if a p value is greater than 0.05?

A

Fail to reject Ho

Not enough evidence to accept Ha or the contrary of Ho etc

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7
Q

What is a z score for a 95% CI?

A

1.96

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8
Q

(Sample)

Equation for construction a CI of a mean

A

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
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9
Q

(2 Sample t-test)

Construct a 95% CI for mean difference

A

(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
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10
Q

(T-test)

How do you find a t-value?

A

Use T-tables
Degrees of freedom = Na + Nb -2
Look up % you want in individual tail

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11
Q

(T-test)

How do you find a t-critical value?

A

Use T tables
Use d.f Na+Nb-2
Use sigma = 0.5

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12
Q

What does it mean if t test statistic is greater than the t-critical value?

A

Reject Ho

Accept Ha

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13
Q

How do you find expected values for chi square test?

A

EV = (row total x column total)/(overall total)

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14
Q

How do you find chi critical value?

A

Df = (# of rows -1)(# of columns-1)

Use chi square tables
Use df and 5 % column

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15
Q

What do you need for a least squares table?

5

A

x
y
x squared
xy

and the sums of all of these numbers

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16
Q

What do you calculate from the least squares table?

2

A

Sxx

Sxy

17
Q

What do you calculate from Sxx and Sxy?

A

Beta hat one

18
Q

What is the formula for Beta hat one?

A

Sxx/Sxy

19
Q

What do you calculate from Beta hat one?

A

Beta hat 0

20
Q

How do you carry out a wilcoxon rank sum test?

4

A

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

21
Q

How do you find R1 in a wilcoxon rank sum?

A

R1 = sum of all the ranks from the sample with the smallest sum of ranks

22
Q

How do you find the expected value of R1?

A

n1(n+1)/2

Given equation

23
Q

How do you find the sample error of R1

A

Given equation

se[R1]

24
Q

List the order of calculations in a wilcoxon rank sum.

A 
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
25
Q

How do you calculate the p value for a wilcoxon rank sum?

A

Use p value equation
Use calculated z score from test statistic
Make conclusion

26
Q

What does it mean if chi test statistic is smaller than the chi critical value?
t

A

We fail to reject Ho

27
Q

(Two sample t-test)

Calculate the CI of mean difference when Ho says the means are different.

A

(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
28
Q

(One sample t test)

What CI should you use for a small one sample test, n<30

A

t-test

X_ +_ t (s\ sqrt(n))

X_ =sample mean
t = t-tables where d.f = n-1

29
Q

What do you need for an Anova Table?

A 
Source (model, residual and total)
Df
Ss
Ms
F
30
Q

How do you work out residual MS?

A

Square S

31
Q

How do you work out F for Model

A

It’s given to you

32
Q

How do you work out MS for model?

A

Multiply F (Model) by MS (residual)

33
Q

How do you get the DF for Model?

A

P-1

34
Q

How do you get the DF for residual?

A

N - p

35
Q

How do you find the SS for both residual and model?

A

Multiply the DF by the Ms for each

36
Q

How do you find an f critical value?

A

Use F tables
Use 5%
Use two df values e.g. (2,38) = column 2 and row 38

1.2 Biostatistics (2 decks)

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