Topic 2 - Standard Errors, Confidence Intervals and T-tests. Flashcards
What is the standard error?
The standard deviation of a sample population from the mean.
Measures the accuracy with which a sample represents a population.
How to calculate the standard error?
σ/√n
In a sample of 99 heights, mean is 108.34cm and SE is 0.52cm, how can we use this measure of error?
Don’t quote mean as 108.34 + or - 0.52cm as this invites the reader to think the mean is between 107.82cm and 108.86cm which is false.
Distribution of sample means is normal and 95% of a normal sample is within 2 SDs of the mean so 95% confident that µ is between + or - 2SE which would be 107.3cm and 109.38cm (larger than above).
Multiply the SE given by 2 then +/- from the mean to get the measure of error.
What is a confidence interval?
A range of values bounded above and below the mean that would likely contain an unknown population parameter.
When would you use a paired t test?
When you want to compare the means of the same group or item under 2 separate scenarios.
When would you use an unpaired t-test?
When you want to compare the means of 2 independent or unrelated groups where the variance between groups is assumed to be equal.
Why can’t we conclude that sample means will be the same as population means?
Because sample means are for random samples only so it is unlikely that they will be equal to one another even if population means are due to random variation of sample data. Need hypothesis testing.
What is the t-test statistic calculation?
m1-m2 divided by SE.
When do we retain the null hypothesis in t-testing?
If t-test statistic lies in between -2, +2 as there is no significant difference between the 2 samples at the 5% level.
When do we reject the null hypothesis in t-testing?
If t-test statistic is not lying in between -2, +2 as there is a significant difference between the 2 samples at the 5% levels.
What is the P value?
The sum of the area outside the t range.
What does the p value measure?
The probability of obtaining the observed results - assuming the null hypothesis is true.
When do you reject a null hypothesis regarding a p value?
When it = <5%.
When do you retain the null hypothesis regarding a p value?
When it = >5%.
What are the assumptions fro a 2 sample unpaired t test?
- 2 samples are independent to each other (if not use paired t test)
- 2 samples follow normal distribution (if not use non-parametric test)
- population standard deviations are equal (if not use approximate t test)
