The Effect - - Describing Variables, except (Theoretical Distributions)
10 important questions on The Effect - - Describing Variables, except (Theoretical Distributions)
What are the main steps figuring out how to describe a variable?
- What kind of variable is it?
- What is the distribution of that variable?
- Summarise the distribution
What is meant with the distribution of a variable?
Distribution of the number of limbs a person has will most often be 4, but can also be 1, 2, 3, and 5+.
This will be displayed in a frequency table or bar graph.
What is the difference between a probability density and a density distribution?
Probability density if you're describing it.
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What is meant with summarising the distribution?
What are the most known ways to describe a distribution and so summarise it?
- Mean (representative value)
- Percentiles
- Median (50th percentile) (representative observation)
- Minimum (0th percentile)
- Maximum (100th percentile)
- Range (difference between max and min.)
- Variance/Variation
- Skew
What are the steps of calculating the variance?
- Find the mean
- Substract the mean from each value (variation around the mean)
- Square each of these values
- Add them up
- Divide by the number of observations minus 1
What is a downside of the variance and how do you solve this?
Therefore, we take the standard deviation (the square root of the variance)
What two commonpercentile based measures of Variation?
- Interquartile Range (IQR)
- difference between 75th and 25th percentile.
- 90/10 Ratio
- 90th percentile divided by the 10th percentile, commonly used in inequality studies to show how different the top and bottom of the distriubtion are.
What are some of the reasons one might use the IQR?
- You know that the value covers exactly half of your sample, this gives a good sense of how close to the median this half is.
- Unlike the variance, the IQR is not very strongly affected by big tail observations
What is meant with 'right skew' and 'left skew'?
Similarly, a distribution with lots of observations in the left tail would have a left skew.
A distribution with similar tails on both sides is symmetric.
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