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BioStatistics Final > Bivariable Associations > Flashcards

Bivariable Associations Flashcards

1
Q

if p ≤ .05 then we…

A

REJECT NULL

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2
Q

if REJECT p > .05 then we…

A

FAIL TO REJECT NULL

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3
Q

What are the different bivariable statistical methods?

A

– T-test (independent samples t-test) and
ANOVA
– Chi-square test of independence
– Correlation

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4
Q

What test do you use if you have a categorical variable and a continuous variable? (less than 3 categories)

A

T-test

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5
Q

What test do you use if you have a categorical variable and a continuous variable? (more than 3 categories)

A

ANOVA

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6
Q

What test do you use if you have two categorical variables?

A

Chi-square test of independence

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7
Q

What test do you use if you have two continuous variables?

A

Correlation

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8
Q

What is a critical value

A

the value associated with a particular

significance level

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9
Q

Remember

A

Z tests use the z distribution
– T tests use the t distribution
– ANOVA uses the F distribution
– Chi-square test of independence uses the Χ2 distribution.

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10
Q

List each statistic for the test of association

A

– t statistic (t-test)
– F statistic (ANOVA)
– Χ2 statistic (chi-square test of independence)

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11
Q

What is a t test

A

A statistical procedure that allows us to test whether the data from the two groups are the same or different.

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12
Q

What is the null hypothesis for t tests. Put equation and words

A

–H0: μ1 = μ2
μ1 – μ2 = 0
–Mean of the data from sample 1 = mean of the data from sample 2
–Rejecting the null hypothesis implies that the means of the sample are
statistically significantly different
• Failure to reject the null hypothesis implies that the two means of the
sample are statistically insignificantly different (the same).
• And thus we assume this is true for the populations.

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13
Q

what is the t test formula

A

For numerator: [(x1 – x2) – (x bar1 – x bar2)]

For denominator: √[s2 pooled[(1 / n1) + (1 / n2)] ]

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14
Q

Two assumptions of the t test

A

•Both parent populations are normally distributed
• Both populations have equal variance
(homogeneity of variance)

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15
Q

How do you calculate homogeneity of variance

A

– Levene’s test for equality of variances:
• Null hypothesis: variance1 = variance2
• p ≤ 0.05 implies that the variances are different
• p > 0.05 implies that the variances are the same
(– Violations of homogeneity of variance may be ignored as long as the samples being used have equal or
approximately equal sizes)

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16
Q

How do you calculate degrees of freedom for t test (t-test degrees of freedom POOLED)

A

Degrees of freedom (df) = (n1+n2-2)

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17
Q

How do you calculate t-test degrees of freedom (unequal df’s)

A

df conservative = the smaller of df1 and df2

df1 = (n1 – 1) and df2 = (n2 – 1)

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18
Q

When should you use ANOVA

A

Used with 3 or more groups to test for MEAN DIFFS

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19
Q

What is the null hypothesis for ANOVA

A

H0: μ1=μ2=μ3

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20
Q

What is the alternative hypothesis for ANOVA

A

H1: μ1”≠μ2”≠μ3

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21
Q

What is the null hypothesis for ANOVA in words

A

All populations have the same mean

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22
Q

What is the alt hypothesis for ANOVA in words

A

Not all populations have the same mean

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23
Q

What is the statistic for ANOVA

A

f stat

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24
Q

If F > Fcrit then we…

A

reject the null hypothesis, meaning that there is some significant difference across all means

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25
Q

IF F < Fcrit then we…

A

fail to reject the null hypothesis bc the means are equivalent

26
Q

What is the summary of procedures for testing

bivariable associations

A

Step 1: determine what kind of variables you have
• Step 2: determine which statistical procedure to use based
on the two variables
• Step 3: compute the appropriate test statistic
• Step 4: determine if the test statistic exceeds the critical
value (the value that corresponds to p ≤ 0.05)
– If it exceeds the critical value: REJECT the null hypothesis
– If it does not exceed the critical value: FAIL TO REJECT the null
hypothesis

27
Q

Purpose of ANOVA (f crit)

A

ANOVA determines F statistic which we test for

significance (Is F > Fcrit at p =.05 level?)

28
Q

Note about leven’s test for equality of varianes

A

We use Levene’s test for equality of variances—If the p-value associated with Levene’s test is less than alpha, the homogeneity of variance assumption is violated. If p > α, the homogeneity of variance assumption is met.

29
Q

What is the ANOVA f statistic

A

A ratio of the Between Group Variation divided by
the Within Group Variation: F=between/within=MSB/MSW
*A large F is evidence against H0, since it indicates that there is more difference between groups than within groups.

30
Q

How do you calculate F

A

Mean Square Between / Mean Square Within

= MSB / MSW

31
Q

For f crit, we need to know two things:

A

-The # of groups

– The total N

32
Q

How do we find f crit

A

WE LOOK ACROSS TOP OF TABLE DF NUMERATOR

AND ALONG SIDE DF DENOMINATOR

33
Q

How to calculate degrees of freedom for ANOVA–there are two the D.O.F. for numerator and the one for denominator

A 
#groups-1 (for numerator)
N(pop.)-K
N= total sample size (how many people are in the study)
F(dfn, dfd)
Ex: Example N= 45; 4 groups 45 – 4 = 41
We look at DF (3, 41)
34
Q

Which test do you use if you have two continuous variables

A

Correlation: Pearson Product Moment Correlation

35
Q

Steps to complete t-test:

A

– State the null hypothesis (H0: μ1 = μ2)
– Assess Levene’s test (H0: variance1 = variance2)
– Compute appropriate t statistic and df
• Fail to reject levene’s -> equal variance -> pooled method
– df = n1 + n2 – 2
• Reject levene’s -> unequal variance -> unequal variance method
– dfconservative = the smaller of df1 and df2
– Compare t-test statistic to critical value
• If t-test stat > t crit -> reject the null
• If t-test stat < t crit -> fail to reject the null

36
Q

Steps to complete ANOVA test:

A

Compute F statistic and use F distribution
• df
– Numerator: Groups-1
– Denominator: N – (# Groups)
– At the given df at at p < .05
» if F > Fcrit, then we reject null hypothesis

37
Q

What does correlation test measure

A

– Strength of the relationship: strong, moderate, weak, or no
relationship
– Direction of the relationship: positive (+) or negative (-)
(a measure of the linear association between two variables, X and Y)

38
Q

What does -1, 0, and 1 represent for correlation test

A

+ 1 is total positive correlation; all the data points fall on a
line with positive slope.
– 0 is no correlation,
– −1 is total negative correlation ; all the data points fall on a line with a negative slope.

39
Q

What does it mean if r is greater than or equal to .7, is greater than or equal to .3 but is less than .7, and is less than .3

A

– |r| ≥ 0.7 indicates a strong association
– 0.3 ≤ |r| < 0.7 indicates a moderate association
– |r| < 0.3 indicates a weak association

40
Q

What is the symbol of Pearson Product Moment Correlation Coefficient

A

r

41
Q

What is the null hypothesis for PPM correlation test? Equation and words

A

Ho :ρ= 0
HA :ρ≠ 0
– If we reject we are saying that r is not like 0 and thus there
is a real association between the variables
– If we fail to reject we are saying that r is like 0 and thus
there is not a real association between the variables

42
Q

The significance of the correlation (r) is tested using a t- statistic:

A

tstat = r/SEr

43
Q

How do you calculate D.O.F. for PPM

A

n-2 (total sample size)

44
Q

If tstat ≥ tcrit at p < .05 and df=n-2, then we reject the

null hypothesis then we…

A

REJECT NULL

45
Q

If tstat < tcrit at p < .05 and df=n-2, then we fail to

reject the null hypothesis then we…

A

FAIL TO REJECT NULL

46
Q

What are the two ways that we report PPM

A

r (df) = XXX p < .05 OR r (df) = XXX p > .05
Ex: (r (129) = .82, p < .05)
r = .82, df = 129 , p < .05 significant

47
Q

When do you use chi square test of independence

A

when you are measuring two categorical variables

48
Q

What are the parametric tests and what does parametric mean

A

t test, ANOVA, PPM

make assumptions about the shape or form of the probability distribution from which the data were drawn

49
Q

What are non parametric tests and list an ex.

A

A family of tests that do not rely on assumptions about the shape or form of the probability distribution from which the data were drawn
Chi square

50
Q

What is a contingency table

A

A two-way table showing the cross-tabulations between two variables where the variables have been classified into mutually exclusive categories and the cell entries are frequencies.

51
Q

what is the symbol for expected frequencies and how do you determine this.

A

fe
-Add the columns and the rows to get the totals
as shown in previous slide.
-Multiply the row total and the column total for the cell in
question and then divide that product by the Total
number of all respondents.

52
Q

What is the null hypothesis for chi square. equation and words.

A

the two variables are independent (not related).

53
Q

How do you test null hypothesis for chi square

A

– Compute chi-square test statistic χ2
– Determine df
– Determine if χ2 > χ2 critical at p ≤ .05

54
Q

What is alternative hypothesis for chi square

A

Ha: variables are dependent/related

55
Q

How do you calculate D.OF. for chi square

A

(rows-1) * (columns -1)

56
Q

How do you calculate chi square stat

A

(1) the sum over all cells of
(2) the difference between the observed value and the
expected value SQUARED, which is then
(3) divided by the expected frequency.

57
Q

What is the ANOVA f test for and what is it’s null hypothesis, what is its equation

A

Used to test whether y is linearly related to x
• H0: β1=0 Ha: β1≠0
The null hypothesis states that y is not linearly related to x

58
Q

• F = MSR/MSE

A

(explained variance / unexplained variance)

59
Q

DFR =

A

number of covariates (for simple linear regression =1)

60
Q

DFE=

A

DFT-DFR (DFT is n-1 because only one mean is calculated) = n-2 in simple linear regression

BioStatistics Final (5 decks)

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