Week 4. masterclass - Lecture notes 4 PDF

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Week 4 Masterclass: Measurement of (psychological) individual differences in populations. 1. Introducing Galton. The work of Francis Galton includes contributions in:        

Genetics. Evolution. Statistics. Fingerprint analysis. Psychometrics. Expertise. Visual imagery. Questionnaires.

The goal of Galton was to obtain measures in large samples to identify the differences among individuals (more popularly known as "individual differences"). He developed statistical methods to do so. For example, Regression and the correlation coefficient. 2. The famous cousin. Darwin was an older cousin of Galton, and Galton's work was heavily influenced by his cousin's. Darwin and Wallace proposed a theory of evolution by natural selection. Briefly, the theory has these components: 

When organisms replicate, their offspring may slightly vary in some characteristic or trait.

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Most of these variations are negligible.

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If organisms with a variation can reproduce before dying, they will pass this variation to their offspring.

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The accumulation of small variations leads to important variations in a species, and eventually the origin of new species.

Wallace excluded humans from this process. Darwin saw no reason why not to include humans in this process of evolution by natural selection. 3. Heredity and the quincunx. This section presents Galton's conception of statistics, the quincunx (or Galton board) and the concept of heredity. Francis Galton (1822-1911) Statistics – provide summaries of information concerning large groups. exploits the smooth continuity in which objects of the same species vary. Genetics explanation – the distribution of traits is caused by a combination of large number of small influences.

Galton indicates that statistics has the goal of collecting large samples to understand populations and provide a summary of the collected data. Summaries include distributions, means, standard deviation. He provides an evolutionary and causal explanation of the normal distribution. The normal distribution is smooth and continuous because traits are the consequence of numerous small differences (this anticipates problems identified in current research in genetics). He presented a board (the quincunx) to provide an intuitive understanding of the normal distribution. He also used updated version of this board to provide an explanation of why distributions of traits (e.g., height) remain constant, instead of more dispersed, as suggested by the original quincunx. 4. Normal distribution (part 1). Galton designed the quincunx to provide an intuitive understanding of the normal distribution. Normal distribution is probability distribution. Elements of the concept of probability: •

A random experiment.

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Possible outcomes.

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Probability assigned to outcomes.

The typical metaphors of random experiments (tossing a coin, rolling a die, playing roulette) are useful for discrete variables, but not for continuous variables. Guillermo Campitelli presents the drone delivery metaphor in order to give an insight of the concept of probability in continuous variables. Characteristics of the normal distribution: Possible values are in the interval from negative infinity to positive infinity. The distribution is symmetric and centred in the mean of the distribution. The mean equals the median. That means that observing a value in the interval of values above the mean has a probability of 0.5; likewise, observing a value in the interval of values below the mean has a probability of 0.5. Z scores are calculated by subtracting the mean from raw values and then dividing that result by the standard deviation. A normal distribution of Z scores is called a Standard Normal Distribution. The mean of the standard normal distribution is always 0 and the standard deviation is always 1. 5. Normal distribution (part 2). The normal distribution is partitioned following two criteria: Intervals of equal length. Intervals of equal probability.

The partitions of the distribution in intervals of equal length show that it is much more probable to observe values in the intervals closer to the mean than those further away from the mean. Dividing the distribution in intervals of equal probability requires the identification of quantiles. Quantile is a generic term. Examples of quantiles are: Quartiles: Values of the distribution which divide it in 4 intervals with probability 0.25. Deciles: Values of the distribution which divide it in 10 intervals with probability 0.10. Percentiles: Values of the distribution which divide it in 100 intervals with probability 0.01. 6. Legacy. Measurement of large samples study of individual difference regression to the mean. Galton leaves as with the following contributions to psychology and other sciences of a general nature: Focus of measuring large samples. Interest in differences among individuals (individual differences). Statistical methods such as regression and correlation coefficient....