1G89.2228 Lect 1a

Lecture 1a

• Perspectives on Statistics in Psychology

• Applications of statistical arguments

• Describing central tendency and variability

2G89.2228 Lect 1a

Statistics in psychology

• Three perspectives– Mathematical statistical theory– Conventions, norms, heuristics– Flexible methodology for making

empirical arguments

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Mathematical basis of statistics

• Formal definition of probability

• Formal sampling frames

• Explicit stochastic models

• Methods that follow deductively from assumptions

• Mathematical developments are based on theorems and proofs

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Conventions, norms and heuristics

• Rules of evidence become statistical rules (e.g. “p<.05”)

• Rules developed and sold by persons studying mathematics

• Masses learn rules, not statistical theory

• Efficient, easy to communicate

• Rules can become rigid, arguments may not be examined critically

5G89.2228 Lect 1a

Statistics as "principled argument" (Abelson)

• Recognition that many (most) applications of mathematical statistics are approximate, not exact

• Weighing information provided by data and statistical analyses

• Comparison of alternate methods and assumptions

• Requires conceptual understanding of statistical reasoning, if not formal mathematical basis

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Applications: Three papers from current literature

• What claims are made about psychological results?

• What statistical arguments support the claims?

• What must we know to evaluate these claims critically?

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Most Common Question in Statistical Applications

• Inferences about populations from samples

• Central tendency: average (mean), median and mode

• Variability around mean

• Population or Sample?– We may compare two sets of three

persons because we are interested in them as individuals.

– We may also compare two sets of three persons because we are interested in the populations they come from.

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Example

• Question: Are women who have a miscarriage more depressed than women in general? If so, how much more depressed?

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Strategy:

• Identify women who have miscarriage and measure their level of depression using a standard scale.

• Examine distribution in sample– Calculate mean, median, mode. – Calculate variance, range.– Make plot of distribution.– Examine central tendency in light

of variation.