Statistics
Lecture 1.
Descriptive statistics includes statistical procedures that we use to describe the population we are studying. The data could be collected from either a sample or a population, but the results help us organize and describe data. Descriptive statistics can only be used to describe the group that is being studying. That is, the results cannot be generalized to any larger group.
Inferential statistics is concerned with making predictions or inferences about a population from observations and analyses of a sample. That is, we can take the results of an analysis using a sample and can generalize it to the larger population that the sample represents. In order to do this, however, it is imperative that the sample is representative of the group to which it is being generalized.
Starting point of analysis is determining the level of measurement of unit of analysis.
Measures of central tendency
Aim: to (univariately) describe the distribution of variables on different levels of measurement
MEAN
Mean: a first a first measure of central tendency for the sample: for the population:
Characteristics of the mean: * Changing a score will change mean * Adding or removing a score will change mean (unless the score is equal to mean) * Adding, subtracting, multiplying, dividing each score by a constant value causes mean to change accordingly * Sum of differences from the mean is zero: * Sum of squared differences from the mean is minimal or Sum of Squares (SS) a larger SS means that scores deviate more from the mean
Why minimal?
‘Minimal’ because if we had used any other value than the mean (5) to subtract, SS would have been larger than 42
MEDIAN
A second measure of central tendency: the median (ordinal) to find the median:
1) sort all cases based on their value on x
2) the value of the „middle case“ equals the median (equal amount of cases below and above)
Note that the median is not responsive to outliers
Descriptive statistics includes statistical procedures that we use to describe the population we are studying. The data could be collected from either a sample or a population, but the results help us organize and describe data. Descriptive statistics can only be used to describe the group that is being studying. That is, the results cannot be generalized to any larger group.
Inferential statistics is concerned with making predictions or inferences about a population from observations and analyses of a sample. That is, we can take the results of an analysis using a sample and can generalize it to the larger population that the sample represents. In order to do this, however, it is imperative that the sample is representative of the group to which it is being generalized.
Starting point of analysis is determining the level of measurement of unit of analysis.
Measures of central tendency
Aim: to (univariately) describe the distribution of variables on different levels of measurement
MEAN
Mean: a first a first measure of central tendency for the sample: for the population:
Characteristics of the mean: * Changing a score will change mean * Adding or removing a score will change mean (unless the score is equal to mean) * Adding, subtracting, multiplying, dividing each score by a constant value causes mean to change accordingly * Sum of differences from the mean is zero: * Sum of squared differences from the mean is minimal or Sum of Squares (SS) a larger SS means that scores deviate more from the mean
Why minimal?
‘Minimal’ because if we had used any other value than the mean (5) to subtract, SS would have been larger than 42
MEDIAN
A second measure of central tendency: the median (ordinal) to find the median:
1) sort all cases based on their value on x
2) the value of the „middle case“ equals the median (equal amount of cases below and above)
Note that the median is not responsive to outliers