Comparing 2 Means Flashcards
(23 cards)
Hypothesis testing
Basic idea , example you out two opposing things against each other, your favourite team is your research hypothesis vs your enemy team . You want them to be different, you want your team to win ( reject the null)
Null hypothesis
There is no difference between group scores
You expect to find:
1. No difference between group scores ( t-tests, ANOVA families ) u
2. No relationships between variables( regression families p, chi- square
Alternative hypothesis
There is a difference in group scores
Relationship between variables
Hypothesis testing, rockem sockem robots if statistics
How do we determine which robot won?
P values
Cut off scores
But we usually use p values , cut off scores is a different way of doing hypothesis testing
- we want to reject the null hypothesis , this is the success, this is when we can say something is statistically significant
What do we do if we do not have enough evidence to reject the null ?
We say it’s not statistically significant, this doesn’t mean that there is not difference between the groups but we won’t have enough evidence to support rejecting the null hypothesis
P-values ?
The probability of getting that results ( t values , f values , chi square ) if the NULL were true if there is no difference between the groups the NULL is true
- you want the null to be false , so you want the probability of being wrong to be low
Alpha
The probability of type 1 error , alpha does not equal p- value
- alpha set as a criterion for a low type 1 error, it is not same as your p actual found in your experiment
A false positive or type 1 error is …
Is alpha
Here you reject the null although the null is true but we get a small p value thus we think it’s significant and reject the null
Beta
The probability of type 2 error, the opposite of power
Type 2 error , failing to reject the null when you should reject it
( aka your research hypothesis is supported but you missed it )
- this is a false negative
Power
The probability of rejecting the null when you should reject the null
- your hypothesis is supported and you showed that
Normally we use the power to calculate our sample size, how many individuals we need in an experiment to find statistical significance
A power of 80% means that even though there is a real difference in the world, your analysis will only show that 80% of the time
Assumptions
Things that must be true for your test to return an answer that is reasonably correct
- when assumptions aren’t met you do not know what the answer you got means
Effect size
Is a measure of how big an effect was in your experiment
Ex: you might reject the null hypothesis, the experiment worked, but then determine that the group differences of relationships were small
- effect size is seen as a measure of strength of a phenomenon for a technical definition
Cohen’s d
Is one of the most well known calculations for effect size
The general formula gives the standardized distance between the two populations means,
- formula is very adaptive and can be used for many differences between sample and within sample tests
- based on difference between the mean, and pooled standard deviation
Small: 0,02
Medium: 0,05
Large: 0.8
Variance overlap for anova and regression
N^2 for ANOVA
R^2 regression
These stats are based on the amount of variance that you have accounted for by your manipulation ( groups ) or independent variable ( like predictors in regression) out of the total variance
Different values will be used in different analysis
Effect size ( n squared)
There are partial versions of all three of these statistics for when you have more than one IV
Small :0.01
Medium:0.09
Large:0.25
Since the statistic is the proportion of variance over a total, it ranges from 0 to 1 and cannot be negative
T-tests single (or one-sample)
Consist of one group of people
One population mean
No population standard deviation
- one group of people that we are comparing to a group population mean but we don’t actually have any information about what the pop standard deviation is
T test - dependent (or paired)
One group of people tested twice
- when you are testing some sort of intervention , you test everybody once and then you test again and if there was any effect you would see it in the different results
T-test , independent
Two groups of people
- testing two groups of people to see if they’re the same, and this is where maybe have the control group and the intervention group
T test :6 steps of hypothesis testing
- Identify the population distributions, assumptions
- State the hypothesis
- Characteristics of comparison distribution
- Identify critical values
- Calculate
- Decide
There’s always a 7th step , reporting
Assumptions of t test
Normal distribution n> or equal to 30
Dv is scale
Random selection
Outliers
Checking for outliers
One of the best ways is to make a box plot and label outliers
Independent sample t test and dependent sample t test (assumptions)
Same assumptions but for these we have an extra assumption that we need to test for and that is the variance in each group is the same
- for this we use Levene’s test
For this test if p <0.05 you would not meet the assumption of homogeneity
If this happens you will have to use a correction for unequal variances ex: Welch correction
If p > 0.05 you’re good
How to report t test
Ex: the advertisement was more engaging to male viewers (M = 5.5, SD= 0.35) than female viewers ( M=.. , Sd= ..) a large significant difference, t ( 38) =2.37. P= 0.023, d= 0.075
