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Statistics 2: Central tendency and spread of data (Normal Distribution…
Statistics 2:
Central tendency and spread of data
Central Tendency
Median
Used for ordinal categorical data and interval data
Less sensitive to influence of outliers
The central datum when all the data are arranged (ranked) in numerical order
Mean
Used to summarize the interval data
Arithmetic mean: calculated by adding all the individual datum values in a dataset, and dividing by the number of values in the dataset
Mode
The only mean to measure nominal categorical values
can also be used for ordinal categorical data and interval data
A measure of most popular (frequent) value in a data set
Measurement of spread of data (variability)
Percentiles
Quartiles (25%), middle (median or 50%), upper (75%); Interquartile range (IQR) is often quoted when referring to the interval data that is not normally distributed
Percentiles and quartiles may be estimated from cumulative frequency curves
Defined as a cut off point such that x% of the sample has a value equal or less than the cut off point
Box and Whisker plot
Range
the interval between the highest value and the lowest value in a distribution
profoundly influence by extreme outliers
Normal Distribution
Non-parametric distribution: mean and IQR
Standard normal distribution: mean=0, SD=1; z= (xi-u)/d; sometimes referred as z-distribution; useful in comparing different normal distributions
Parametric distribution; mean and SD
Skewness: Positive and negative; Kurtosis: Peak;
Standard normal distribution has as kurtosis of zero
Standard deviation vs SEM (standard error of the mean); SEM decreases as the sample size increases;