Week 14 Flashcards
What is normal distribution?
Most common type of distribution
Sometimes called the Gaussian or Parametric distribution (bell-shaped curve).
This curve is centred on the mean (average) of the data
Most of the data are clustered around the centre of the distribution
In a perfect normal distribution the mean, median and mode would all be the same value and there would be an equal number of data points either side of the mean.
What is non-normal distribution: Skewness?
Second most common type of distribution
Majority of data is found either left or right of the centre of the data
Often described by the term “skewed”
Right skewed = positive (tail of distribution reaches right side of x-axis)
Left skewed = negative (tail of distribution reaches left side of x-axis)
What is Kurtosis?
a measure of how wide or narrow the tails of a distribution are
- think of this tailedness as a representation of how often outliers occur.
- always measure the kurtosis of a distribution relative to normal distribution.
A true normal distribution is a mathematical probability model (typically with a mean = median = mode = ?)
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What is Z-scores?
The number of standard deviation units that an observation is away from the population mean
(If an observation has a value above the population mean then it has a positive z score therefore: +1SD gives a z-score of 1
A value below the mean has a negative z-score, thus:
-1SD gives a z score of -1)
How do you calculate the Z-score?
the deviation minus the mean divided by the standard deviation
Why are z-scores useful?
allow you to standardise differences across different distributions.
The most common way you may come across z-scores in the real world is infant birth weight/growth.
Can be useful to determine malnutrition etc in human growth.
Uses an international standard mean.
Central Limit Theorem graph called?
Samling distribution of the sample mean
(A separate histogram showing each sample mean, showing the distribution of these across a normal distribution)
Key features of the central limit theorem?
“The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. “
( tells us that gathering more samples ( an in particular large samples) will result in a graph of the sample means that will look more like a normal distribution.)
Why is central limit theorem useful?
Very often when we carry out an experiment, we don’t know the shape of the underlying population distribution ; Central limit theorem often means we don’t need to know this! ( because the sampling distribution of the sample means will be normally distributed)
- It allows us to make useful judgements/estimates to be made without underlying distribution shape, enabling predictions, etc.
- We can also perform a statistical test on graphs produced by this eg T-test, etc
Central limit theorem only works if we are working with…?
Working with truly independent random samples
