Tests of Differences (wk 7) Flashcards
What is a SHT that tests whether two means collected from two independent samples differ significantly?
Independent t-test (student’s ttest)
What is a SHT that tests whether two means collected from the same sample (or paired observations) differ significantly?
Paired t-test
What is the null for a Independent t-test (student’s ttest)?
the mean value of group 1 is the same as that of group 2
What is the null for a Paired t-test?
the mean value in pre session is the same as that in post session
ex:
Experimental and control groups. ROM measurements taken and improvement was calculated. Reported are the mean improvement (SD) = 16.4 (5.7) degrees for the treatment group, the mean improvement (SD) = 1.0 (5.2) degree for the control group, p-value = 0.001.
1. Null is mean improvement of treatment group was ____ the mean improvement in control group.
2. Which SHT would they have applied?
3. Based on p-value, would they have rejected the null?
- Null is mean improvement of treatment group was THE SAME AS the mean improvement in control group.
- Which SHT would they have applied?
Independent t-test - Based on p-value, would they have rejected the null?
reject
ex:
Data were matched between pre and post sessions and change was tested using SHT.
mean (SD) = 9.2 (11.7) for the outcome in pre session
mean (SD) = 17.0 (19.3) for the outcome in post session
p-value = 0.025
1. Null is mean improvement of treatment group was ____ the mean improvement in control group.
2. Which SHT would they have applied?
3. Based on p-value, would they have rejected the null?
- Null is mean improvement of treatment group was THE SAME AS the mean improvement in control group.
- Which SHT would they have applied? Paired t-test
- Based on p-value, would they have rejected the null?
Reject
What statistical procedure is a test of whether multiple groups’ means differ?
ANOVA
What statistical procedure is a test for data that has been measured repeatedly on the same subjects?
Repeated Measures ANOVA (RM-ANOVA)
What is the null for an ANOVA?
the mean values of all groups are the same
What is the alternative hypothesis for an ANOVA?
for at least a pair of the groups, mean values are not the same
What is the null for a Repeated Measures ANOVA (RM-ANOVA)?
the mean values of all sessions are the same
What is the alternative hypothesis for a Repeated Measures ANOVA (RM-ANOVA)?
for at least a pair of the sessions, mean values are not the same
Ex: Compared mean scores over three different points in time (end of yr 1, 2, 3).
Null?
Alt?
Which SHT?
Null: the mean outcome values were the same in all three time points
Alt: the mean outcome values were not the same in at least two time points
Repeated measures ANOVA
What SHT is used when a continuous outcome has been measured with multiple groups repeatedly over time?
Mixed ANOVA
EX of mixed ANOVA: Patients’ quality of life associated with their chronic low back pain was measured repeatedly (at baseline, 3 months, 6 months) hypothesizing that the factor, treatment 1, would have effect of improving their quality of life associated with low back pain.
What is the outcome?
Measured how many times?
What is the factor/s?
What is the outcome?
quality of life associated with low back pain (continuous)
Measured how many times? three times (baseline, 3m, 6m)
What is the factor/s?
factor 1 = treatment 1 (with / without)
What SHT is used when a continuous outcome has been measured with a confounding variable for the purpose of adjusting for the confounder?
Analysis of Covariance (ANCOVA)
EX of Analysis of Covariance (ANCOVA): Patients’ level of low back pain was measured hypothesizing that the factor, treatment 1, would have effect of lessening the pain after adjusting for age. What is the outcome? What is the factor/s? What is the cofunder?
What is the outcome?
level of low back pain (continuous)
What is the factor/s?
factor 1 = treatment 1 (with / without)
What is the cofounder?
age
EX: A researcher designed a study for the effects of a new drug on hypertension measured once on a rest day and once on a work day. The study has one treatment group and one control group. The researcher wanted to study the treatment effect on hypertension that might be different between the rest day and the work day. Which version of ANOVA would be a best choice to test the effects of a new drug on hypertension that might be different between the rest day vs. work day?
Mixed ANOVA
EX: A researcher designed a study for the effects of a new drug on depression. The study has two treatment groups and one control group. The researcher decided to measure the subject’s age also because she wanted to adjust for the age difference. Which version of ANOVA would be a best choice to test the effects of a new drug on depression adjusting for the age?
Analysis of covariance (adjusts for a cofounder)
EX: Is the mean BMI different between men and women?
Outcome:
Grouping Factor:
What SHT?
Outcome: BMI in continuous scale
Grouping Factor: Gender with two categories (men and women)
What SHT? Student’s t-test
EX: Is the mean DBP at 30 min different among the three age groups?
Outcome:
Grouping Factor:
What SHT?
Outcome: DBP at 30 min in continuous scale
Grouping Factor: Age group with three categories (<30yrs; 30-50yrs; >50yrs)
What SHT? ANOVA
EX: Is the mean DBP at 30 min different by their gender and age group?
Outcome:
Grouping Factor:
What SHT?
Outcome: DBP at 30 min in continuous scale
Grouping Factor:
1. Gender with two categories (men and women
2. Age group with three categories (<30yrs; 30-50yrs; >50yrs)
What SHT? Factorial ANOVA; specifically, 2-way ANOVA
EX: Does the mean DBP change over time from baseline through 30 min to 60 min?
Outcome:
Grouping Factor:
What SHT?
Outcome: DBP at baseline, 30 min, and 60 min in continuous scale
Grouping Factor: None
What SHT? Repeated measures anova
Is the mean DBP change over time different by their gender?
Outcome:
Grouping Factor:
What SHT?
Outcome: DBP at baseline, 30 min, 60 min in continuous scale
Grouping Factor: Gender with two categories (men and women)
What SHT? Mixed ANOVA; specifically, 2-way repeated measures ANOVA
Ex: Is the mean DBP at 30 min different by their age group after adjusting for the effect of baseline DBP?
Outcome:
Grouping Factor:
What SHT?
Outcome: DBP at 30 min in continuous scale
Grouping Factor: Gender with two categories (men and women)
What SHT? ANCOVA
