Sampling, Standard Error of the Mean, Confidence Intervals Flashcards
All cases (usually people) that you are interested in, is known as ______.
population
Ideally you want to have the whole population’s results however this isn’t realistic, so what do studies do instead?
They study samples.
What is a sample?
A subset of the population.
What do you need to do in order to generalise the results of your study to the whole population?
Look at how representative your sample is of the population.
Using the class as the population- the class mean on the class test was 74.87. What will give us different means?
We take samples of this population e.g. 5 students and find the mean of their scores, and plot this on the graph.
Why do different samples have different means?
Due to random error :)
What does random error reflect?
Random error simply reflects that we aren’t all perfect representations of the population- people are different!
What happens if you keep taking the means from lots of different samples of the class/population, and plot it?
We end up with a normal distribution- peaking at the population mean :)
Each dot on the graph represents a different sample.
Sample means closer to the population mean will occur ____ frequently than sample means which are further away from the population mean.
MORE
Although the sample means might differ- where do the majority congregate?
Around the population mean :)
How do you get a better estimate of your population?
Have a big sample size :)
As sample size increases….
standard error decreases.
Why do we calculate standard error?
To tell if our sample is a good estimate of the population mean.
The _____ tells us about the variability in sample means.
standard error.
What is standard error similar to?
Standard deviation! But instead of variation in scores, it’s variation in sample means :)
What does a small standard error suggest?
That you have a relatively accurate estimate of the population mean.
What does a large standard error suggest?
That you have a less accurate estimate of the population mean :(
How do you calculate standard error?
SD/ square root of N
N= number of scores
Calculate the standard error:
N= 5
SD= 11.71
Mean= 72.60
11.71/ square root of 5
SE= 5.23
If the standard error is 5.23 and the mean is 72.60 what does this tell us about the means of the samples?
It tells us that 68% of the means of samples of 5 students will land between
(72.6+/- 5.23) 67.37 and 77.83.
What percent of sample means will fall 1 SD below and 1 SD above the population mean?
34.13 + 34.13 = 68.26% 0r normally just say 68%.
Saying 68% of the sample will fall within a range isn’t v helpful, this is why we use ________
confidence intervals!
_______ allows us to express a range of scores around the mean with greater confidence
Confidence Intervals
A larger sample size will mean that the CI becomes ______.
Smaller- because you are confident about the true mean lying within a smaller range of values.
What is the standard CI that is used?
95% CI :)
95% of all scores fall within ______ standard deviations above and below the mean.
1.96
(like SD)95% of sampling means fall within +/- 1.96 ______ _______.
standard errors.
How do you calculate the 95% CI?
Multiple the standard error by 1.96.
Then add that value to the mean to find the upper limit and subtract it from the mean to find the lower limit.
Calculate the 95% CI:
mean = 72.6
SE= 5.23
- 23 x 1.96 = 10.25
- 6 + 10.25 = 82.85
- 6 - 10.25 = 62.35
If the confidence intervals (for samples) are 62.35 and 82.25, what does this mean?
95% of the mean samples will have a mean between 62.35 and 82.25.
The _____ the sample size the smaller the CI.
Bigger.
How can CI’s be displayed?
on graphs- like we used to draw for bio at school!
What tells you about variability in sample means?
Standard error
CI (more informative)
What is more informative than Standard error?
Confidence Intervals
