The Assumptions. Fundamental Concepts of Statistics.
Measurement - any result from any procedure that assigns a value to an observable phenomenon. Problems - our observations are based on our ability to observe, count, etc. Accuracy is always an issue. It is very difficult to achieve the same measurement twice.
Variation - this brings us to the idea of variation. Statistics is based on the idea that almost everything varies in someway or has variation.
Two reasons for variation:
1. measurement inaccuracies or random error
2. true differences b/w observations, measurement and groups
Probabilisticcausation - because of this property we can only deal with probabilities of being correct or incorrect in our determination of differences in crime rates.
3. ELIMINATION OF ALTERNATIVE EXPLANATIONS: there must be no equally plausible explanations for the presumed effect
Formula: ∑x / n
Range - high and lows.
Interquartile range - measures variablility based on percentiles.
Q3(75th percentile) -Q1 (25th percentile)
Limitations: Leaves our many observations
Mean Deviation – the average of the absolute deviations.
∑|x-µ| / n
Limitations: Less sensitive to deviations in the distribution
Variance - Based on distances from the mean (X - mean).
Takes the square of each deviation from the average and then
averages the squares.
∑(x-µ)2 / n
StandardDeviation - the square root of the variance
The rational choice and cost/benefit analysis is said to miss out on a lot of the subjectivity of politics and policy analysis
Even those who support the scientific method are skeptical of being able to quantify social and political phenomenon.
What are some problems with apply statistical, quantitative methods to the social sciences?