There are many statistical tests in the subject BRM. They are sometimes difficult to distinguish and you also need to know exactly what each test is for and how to perform it. This brief summary shows exactly which tests exist and what you need to know about them. Every fact is in it. It will give ...
Discrete vs. Continuous
● Discrete: finite number of outcomes
● Continious: a range of possible values. Infinite number of possible values
between any two and points. Uniform, normal, exponential, other
Properties of distributions:
● Variability: range, standard deviation and variance
● Central tendency: mode, median, mean
● Model classes: unimodal, bimodal
● Shape: symmetric and skewed
The normal distribution
● Bell shaped and symmetrical
● Mean, median and mode are equal
● Has infinite till infinity range
● An increasing mean shifts the curve to the right
● Decreasing mean shifts curve to the left
● Wider values of standard deviation widens the curve and smaller ones narrow it
● Normal density function: the probability density function of a normal random variable
Statistical inference
● Parameter: descriptive measure of a population
● Statistic: descriptive measure of a sample
● CI 95%: 95% chance outcome is right
● Significance level 5%: 5% that the conclusion is wrong
Describing a set of nominal data
● Univariate: technique applied to single sets of data
● Bivariate: depict relationship between variables (cross classification table)
Graphical descriptive techniques
Graphical techniques to describe interval data
● Histogram: helps explain important aspects probability (classes=1+3.3 log(n))
, Shapes histogram:
- Symmetry: two sides identical
- Skewness: positively = aflopend, negatively = oplopend
- Unimodel: single peak
- Bimodel: two peaks, not necessarily equal in height
- Bell shaped: special type of symmetric unimodel histogram (empirical rule)
● Stem-and-leaf display
● Relative frequency distribution: dividing frequencies by number of observations (%)
Graphical techniques to describe time-series data
● Cross-sectional data
● Line chart
If the difference between two categories is positive, the result is a surplus, if the difference is
negative, the result is a deficit.
Graphical techniques to describe the relationship between to interval variables
● Scatter diagram: relationship between two interval variables
Dependent y variable and independent x variable
→ measures of linear relationships
Positive linear relationship: if one variable increases when other does
Negative linear relationship: variables tend to move in opposite directions
Numerical descriptive techniques
Measures of central location
● Mean
● Median (better when: there is a small number of extreme observations and to measure
how well you performed relative to the class)
● Mode
Measures of variability (interval data)
● Range largest observation - smallest observation
● Variance how far the data is spread out
- Population variance
- Sample variance s2
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