Independent T test Flashcards
What is the t distribution?
represents the means of all possible samples within a given sample size
How do we create a t distribution?
Start with a normal distribution
Pick 5 random ps from this sample, this creates a new sample
Calculate the mean for each ps
Combine these scores, and create a new mean for these scores
If we repeat this process with 5 new ps, we will make another new mean
After doing this multiple times, we will have many means of different samples
This creates a t distribution
How to calculate degrees of freedom?
degrees of freedom (n - 1)
more degrees of freedom = more likely to get statistical significance
What is the law of large numbers?
If we have more samples the means are less variable than fewer samples
More samples = means bunch together VS fewer samples
How will a large sample change the shape of the distribution? Does this impact the p value?
Lower, more narrow tails
This impacts the p value by making it smaller
What are the null and alternative hypothesis in a one sample t test?
Null hypothesis: population mean is a specific number you want to test against
Alternative: population mean is different from the specific number
What are the null and alternative hypothesis in a two sample t test?
Null hypothesis: 2 population means are not different
Alternative: 2 population means are different from each other
How to calculate significance from a t value?
Calculate t- statistic from means and standard deviations of each sample
Find the p value from how much the t-statistic cuts off in the tails of the t distribution
If the t value falls into the ‘rejection zone’ part of the tail, then it’s not statistically significant
What is standard error?
standard deviation of the differences between sample means
What is standard error? How does this impact the t value?
SE gets lower when there’s more ps in each sample
SE gets higher the more variable the samples are
The higher the t value will be
The lower the p value
More likely to be significant
What are the assumptions of a student’s t test? When can a t test be used?
Independence
Normality
Homogeneity of variance
If a study doesn’t meet these assumptions, another test should be used
What is the independence assumption?
Each ps should only be included once
The sampling method should be independent for each ps
What is the normality assumption?
Assume data is normally distributed for both groups
T value is then calculated from the tail of the sampling distribution, skewness makes tails unevenly fat or skinny
What is the homogeneity of variance assumption?
Both groups share the same standard deviation
(share a similar variability)
