Topic 11 - Tests for Means Flashcards
What are the different statistical tests that we could do?
Z test for mean
Z test for proportion
Paired T test
1 sample T test
2 sample T test
What is a Z test for mean used for
Used when comparing averages which are continuous (i.e. mean could be anything on a continuous scale)
What is a Z test for proportion used for
For looking at a precise % of responses in binary data. (I.e. 43% say yes, 57% say no)
When is the paired T test used?
When using the same sample (i.e. same 10 studies) whilst changing some independent variable, and comparing the effect before and after something for the same participants
I.e. differnece between same group but different points in time
When is the 1 sample T test used?
To see whether the population differs from a observed value. I.e. Difference between group and population
When is the 2 sample T test used?
When our data values are independent of each other, and we want to see the relationship between the two
I.e. Difference between two groups
What are the assumptions to use Z tests?
Independent sample - check context
Know popsd
Data describes a normal distribution
Why might we use a t test instead of z test
This could happen if the sample size is too small, but also if we need to know the population SD and it is unknown.
What does a t test do?
It is similar to a Z test and uses sample SD and “T distribution”
the “T distribution” varies in shape according to the sample size. The smaller the sample size, the more variable the sample SD –> distribution of test statistic should be “wider”. The degree of “wide-ness” (also called the degree of freedom) depends on the sample size, and is given by the formula ‘n-1’. There are n-1 degrees of freedom
The larger the degree of freedom, the smaller the tail, the smaller the df is, the larger the tail due to increased likelihood of being wrong with small sample size
What code can we use to find the area of a t-curve given df?
pt(x,df)
where df is the degree of freedom and x is the value that we want to find the area to
What is an example of a hypothesis for two sample t test?
Mean 1 = Mean 2 or Mean 1 - Mean 2 = 0
Mean 1 =/= Mean 2 or Mean 1 - Mean 2 =/= 0
What are the assumptions for two sample t tests?
These 2 samples are independent - The two samples contain different people –> check experimental design –> random?
The 2 populations have equal spread (SD / Variance) - Assume that 2 populations have same variation –> check boxplots, histograms, variance test. If no, use a Welch two sample t test
The 2 populations are normal - we assure that the 2 populations have normally distributed data points –> check boxplots (few or no outliers), histograms, QQ plot, normality test
What is the appropriate test (s) in response to 2 samples having unequal variance?
Welch 2 sample T test
What is the appropriate test (s) in response to 2 samples suggesting non-normality?
Transformations or Non parametric tests (exponential or log)
What is the appropriate test (s) in response to 2 samples which are matched pairs?
Use a Paired t test (using sample of differences)
