Probability, Normal Distributions, and z Scores
4 important questions on Probability, Normal Distributions, and z Scores
What are the three preconditions necessary for making claims of causality?
- Empirical evidence.
- There needs to bee empirical evidence for a relationship between two variables.
- Temporal sequence.
- Variable X (independent variable) needs to occur before a change in variable Y (dependent variable) occurs.
- Reason & theory.
- The claim of causality needs to be supported by reason and theory.
What has happened when we speak of 'sampling bias' and how is it different from a 'sampling error'?
- Sampling bias:
- Due to a flawed sampling procedure, there is a bias in the sample.
- I.e., The sample is not representative of the entire population.
- Sampling error.
- There is a deviation of a sample characteristic (like the mean of a variable) from what actually exists in the population.
- Omnipresent: There is always a degree of sampling error (otherwise you'd have to study the whole population); there's no way around this.
- Inferential statistics are used to minimise the deviation of the sample characteristic to what actually exists in the population.
When our interval/ratio variables are normally distributed, which four characteristics does its distribution have?
- Unimodal.
- It only has one mode (peak).
- Symmetric.
- Just as many cases above as below the mean.
- Asymptotic to the x-axis.
- The curve never reaches the x-axis (mathematical assumption).
- I.e., Extreme cases are rare, but never impossible.
- Theoretical.
- A normal distribution is a mathematical model and therefore an idealised concept. It never exists perfectly in the real world.
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Can you explain what a 'z-score' is, how we can calculate it, and why it is useful for statistical analysis?
- The z-score represents the number of standard deviations an observation is above or below the mean.
- Calculation:
- (see formula), divide the (σ)standard deviation by the (x)score minus the (μ)mean.
- Functionality:
- Z-scores can tell us about the proportion of a population falling above/below a specific score.
- Z-table.
- When you know the z-score, you can look up in the z score how much the distance is between places and the z-score in a normal distribution.
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