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The Assumptions. Fundamental Concepts of Statistics.

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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.

Three Types of Statistics

- Descriptive - Techniques employed in the presentation of collected data. Tables, charts, graphs and the formulation of quantities that indicate concise information about our data.
- Inferential -Linked with the concept of probability. Statistical methods that permit us to infer (probabilistically) something about the real world and about the "true" population from knowledge derived from only part of that population. Methods that allow us to specify how likely we will be in error.
- Predictive- Deals with relationships and the idea that knowing information about on characteristic or variable can help us predict the behavior of another variable. Methods and tools that help predict future observations in other populations or time periods.

Determining Causation

- TIME-ORDER: the presumed cause must always precede the presumed effect
- COVARIATION: the presumed cause and effect must vary with each other
3. ELIMINATION OF ALTERNATIVE EXPLANATIONS: there must be no equally plausible explanations for the presumed effect

Descriptive: Central Tendency

- Mode - The most frequent observation. Usually used with nominal data to describe data. Limitation - limited information - could be multi-modal. Cannot be arithmetically manipulated
- Median - the middle observation. Usually used with ordinal level data. Relatively stable. Limitations - must have ordinal data or higher. Cannot be arithmetically manipulated
- Mean - Most widely used measure in statistics (i.e., most statistical tests are built around the mean). Can be arithmetically manipulated (calculated). Limitations - must have either interval or ration data, sensitive to outliers
Formula: ∑x / n

Measures of Variability or Dispersion

Range - high and lows.

- Limitations: Based on only two extreme observations
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

Why analyze statistics?

- Much of what policy is interested is increasing or reducing some phenomenon.
- Increase employment
- Reduce crime
- Reduce abortions
- Reduce auto fatalities
- Increase graduation rates

- “One common way to define a policy problem is to measure it.” (Stone, 2002)

Not everyone is convinced of positivist approach

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?

Choosing how to measure

- Inclusion vs. Exclusion
- Numbers tell a story, of decline and decay or bigger and worse.
- The goal is to create a sense of helplessness and control.
- How much is too much or too little
- If counting is used for evaluation, incentive to manipulate numbers