Distributions Flashcards
distribution in statistics
A set of data values or scores organised in a way which enables the shape of the data to be seen/’eyeballed’
frequency of normal distribution
perfectly symmetrical around its average value, the ‘mean’
mean of normal distribution
The mean splits the area under the distribution curve in half
differences between the mean, median and mode of normal distribution
equal
description of physical normal distribution curve
smooth and symetrical
non-normal distributions mean median and mods
mean, median and mode are different
types of non-normal distributions
skew and kurtosis
positive skew
mean and median > mode
negative skew
mean and median < mode
how to visually work out the type of skew
if flipped round it look like a “p” its positively skewed
kurtosis
a steep curve with short fat tails
difference between normal distribution and kurtosis
kurtosis = steep (leptokurtic) , normal = shallow (platykurtic)
mesokurtic
no skew and neutral distribution - like a bell
poisson distribution
he number of times an event happens in a period, where the event is independent of the number of times it happened in the previous periods.
Biomodal distributions
a mixture of two distributions with different means eg height
parametric tests
uses normally distributed data
non parametric tests
uses non-normally distributed data
standard deviation
average deviation from the mean
High SD
a lot of variation
Low SD
little variation
+/- 1 SD of mean
68.26% of individuals
+/- 2 SDs of mean
95.44% of individuals
+/- 3 SDs of mean
99.75% of individuals
+ves SD
- Based on all the scores in a data set.
- Good measure for interval/ratio data.
- The value is meaningful in terms of the original units of the data. e.g. grammes, km/h, milliseconds.
-ves SD
- Not meaningful for ordinal data e.g. degree rankings.
* Can be distorted by extreme values/outliers in the data set
z-scores
standardised unit of measurement which is independent of the specific characteristics of a measure
z-score in terms of SD
the number of standard deviations it is from the mean of the distribution
negative z score
score is bellow the mean
z-score for normal distribution
SD of that value expressed to 2dp
z-score formulae
(individual score x sample mean) / sample SD
