Flashcards in Bivariable Associations Deck (60)
if p ≤ .05 then we...
if REJECT p > .05 then we...
FAIL TO REJECT NULL
What are the different bivariable statistical methods?
– T-test (independent samples t-test) and
– Chi-square test of independence
What test do you use if you have a categorical variable and a continuous variable? (less than 3 categories)
What test do you use if you have a categorical variable and a continuous variable? (more than 3 categories)
What test do you use if you have two categorical variables?
Chi-square test of independence
What test do you use if you have two continuous variables?
What is a critical value
the value associated with a particular
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.
List each statistic for the test of association
– t statistic (t-test)
– F statistic (ANOVA)
– Χ2 statistic (chi-square test of independence)
What is a t test
A statistical procedure that allows us to test whether the data from the two groups are the same or different.
What is the null hypothesis for t tests. Put equation and words
--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.
what is the t test formula
For numerator: [(x1 – x2) – (x bar1 – x bar2)]
For denominator: √[s2 pooled[(1 / n1) + (1 / n2)] ]
Two assumptions of the t test
•Both parent populations are normally distributed
• Both populations have equal variance
(homogeneity of variance)
How do you calculate homogeneity of variance
– 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)
How do you calculate degrees of freedom for t test (t-test degrees of freedom POOLED)
Degrees of freedom (df) = (n1+n2-2)
How do you calculate t-test degrees of freedom (unequal df’s)
df conservative = the smaller of df1 and df2
df1 = (n1 – 1) and df2 = (n2 – 1)
When should you use ANOVA
Used with 3 or more groups to test for MEAN DIFFS
What is the null hypothesis for ANOVA
What is the alternative hypothesis for ANOVA
What is the null hypothesis for ANOVA in words
All populations have the same mean
What is the alt hypothesis for ANOVA in words
Not all populations have the same mean
What is the statistic for ANOVA
If F > Fcrit then we...
reject the null hypothesis, meaning that there is some significant difference across all means
IF F < Fcrit then we...
fail to reject the null hypothesis bc the means are equivalent
What is the summary of procedures for testing
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
Purpose of ANOVA (f crit)
ANOVA determines F statistic which we test for
significance (Is F > Fcrit at p =.05 level?)
Note about leven's test for equality of varianes
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.
What is the ANOVA f statistic
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.