Exam 4 Lecture 3 Flashcards
Inferential Statistics
Tests of significance
What you have vs. what you want
What you have: ages (Independent variable)
What you want: # of resistance-related injuries (Dependent variable)
Independent Variable
- What you have (already know).
- It is independent of other variables/what’s being investigated by the study.
- It’s the thing you set up in advance of the experiment (groups, subjects).
- It isn’t affected by ‘what comes next’.
Dependent Variable
- What you want (to know)
- It’s the thing being investigated.
- it is dependent on the independent variable/the study you are doing
- You are asking: does the thing you know influence this thing…
What you have vs. what you want
Independent Variable-> Dependent Variable
- Resistance exercisers vs. aerobic exercisers -> Muscle mass change
-$5 skin serum vs. $500 skin serum-> # blemishes/month - 4-week diet vs. 4-week control-> weight loss
- Recreational vs. medicinal cannabis users-> Days of missed work per year
Categorical independent variable, categorical dependent variable
Chi square test
Fischer’s Exact test
Likelihood that endurance exercisers also engage in resistance training
When Dependent Variable and Independent Variable are both categorical
Chi-square (x^2) test
- You are comparing frequency of something in multiple groups (IV, categorical)
- Comparing counts (actual #, not % or means)
- DV is categorical (also a group)
- Asks: are observed frequencies different than expected
x^2= (0-E)^2/E
Null= no group differences in frequencies (this is what is expected)
What should we expect?
- H1= drinkers exercise less
- H0 (NULL)= drinker and non-drinkers exercise the same, so ROWS should be equal for both groups
- Observed value are entered from the experimental data
- Expected value is the ‘no difference’ number
The p-value is obtained by
= chisq.test (observed, expected)
Categorical Independent Variable, Continuous Dependent Variable
t-test
ANOVA
Comparing endurance exercisers to resistance exercisers on daily protein intake
Study design AGAIN!
Between subjects (I am comparing one person to another)
- This phrase means that some people in your study do one thing and the other people in your study do a different thing (everyone does not do everything)
- You are comparing Person 1 (or Group 1) to Person 2 (or Group 2)
Comparing heart rate (DV) in runners versus non-runners-> Usually considered cross-sectional
Within subjects (I am comparing one person to themselves)
- This phrase means that you have everyone do everything in your study.
- You compare Person 1 t time 1 to Person 1 at time 2, etc
- This is “stronger” because no one is a better control for you than you.
Comparing heart rate (DV) before versus after a 1-mile run-> Time passes= typically longitudinal
Experimental design affects your statistical test choice!
Participants are assigned to different groups (either/or, but not both)
- Based on inclusion criteria (to be in the ‘exerciser’ group, you must exercise)
- Based on random assignment (person 1 goes to Group A, person 2 goes to Group B)
Assumes that the measures in each group are independent
- The groups don’t overlap at all
- The people in each group are completely distinct
- You are comparing effects BETWEEN SUBJECTS
We report between-subjects results as DIFFERENCES
(Group A is stronger than Group B, Group A is more depressed than Group B, Group A and B are not different)
Experimental design affects your statistical test choice!
- There’s no one more like you than you!
- Participants aren’t assigned to a group, everyone in 1 group
Everyone gets each condition (everyone gets the placebo and the active drug)
The order of the conditions varies (sometimes placebo, then active drug; sometimes the opposite)
Assumes that the measures in each group are dependent
- The groups totally overlap
- The data in both conditions comes from the same people
- You are comparing effects WITHIN SUBJECTS
We report within-subject results as CHANGES
- Depression was reduced by active drug, not placebo
- People drank less after starting exercise
- There was no change in pain related to CBD
IV= categorical, DV = continuous
T-test
- You are comparing groups on how much of something
- Compares means of a single variable between groups
- DV is continuous
- Variance (SD) is important
- Asks: Are the groups different from one another, and if so, is that because of change
Two types of t-test
- Independent (unpaired)= the two samples are distinct
BETWEEN SUBJECTS!
(ex: one group gets meds, one doesn’t)
- Dependent (paired)= the two samples are the same
WITHIN SUBJECTS
(ex: before vs after medication)
Unpaired= BETWEEN, Paired= WITHIN
make sure u know how to do the equation
Unpaired t-test- analyzing drinker vs. non-drinker
Paired t-test- Participants stopped drinking for 1 month between baseline and follow up. Same people in both groups, so the observations are not distinct.
t-tests (strategy 1)- straightforward
Each group/ each time point in a separate column
Label well
= t.test (array 1, array 2, tails, type)
- array1= the first column of interest
- array2= the second column of interest
- tails -> 1 or 2 sided [we will stick with 2]
- type
- 1= paired [we will stick with this]
- 2= unpaired, with equal variances [or this]
- 3= unpaired, with unequal variances
t-tests (strategy 2)- sophisticated
Data tab-> Data analysis
This way gives you the “t” value and the p-value. You need both when you publish your findings.
- Variable 1 range= the first column of interest
- Variable 2 range= the second column of interest
Alpha set at 0.005 (5 out of 100 times it’ll be a false positive)
(to be significant, the p-value must be a SMALLER NUMBER than that)
Output-> wherever you want!
F(3,73)= 3.22, p<0.028
F tells us what test was done.
3,73 tell us the degrees of freedom
df= n-1 (simplified)
Degrees of freedom- The number of independent pieces of information used when performing a statistical (inferential) analysis
- The number of data points that are ‘free to vary’
- Used in statistical tests like chi-square, t-test, ANOVA
- Chi square-> df= (r-1)(c-1)
- T-test-> df= sample size- # parameters analyzing
- ANOVA-> df= # groups- 1, # of participants- 1
- Bigger is better
- More data, more precision
- Larger df= more confidence in your finding (less error), this changes the likelihood that you result is chance (makes it easier to reject the null)
There were 48 people in the study.
t(47)=-10.44, p<.05
F(1,33)=12.33, p<.05
There were two groups and 33 people in the study
