Statistical Reasoning in Everyday Life PDF

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Using statistics in everyday sistuations - Dr. Horwath...

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Statistical Reasoning in Everyday Life Wednesday, September 14, 2016

1:40 PM

Statistics help us see and interpret what the naked eye often misses. Accurate statistical understanding benefits everyone. Being able to apply simple statistical principles will help with everyday reasoning. Doubt big, round, undocumented numbers.

Describing Data -

When viewing graphs, read the scale labels and note their range.

Measures of Central Tendency -

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Mode: the most frequent Median: the midpoint Mean: the average ○ Can become skewed if distribution of data is lopsided. ○ Can become biased. Always notes which measure of central tendency is reported. If it is the mean, consider if atypical scores could be distorting the figure.

Measure of Variation -

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Knowing how similar/diverse scores are illuminates information that central tendency leaves out. ○ Averages derived from low variation are more meaningful than those of high variation. The range only provides a crude estimate of variation. Extremes often distort the range. The Standard Deviation is much more useful in determining variation. This is a bell-shaped curve; in nature, most fall in the mean range, while fewer and fewer fall close to the end of the curve. This is called the normal curve. ○ About 95 percent of cases fall within two standard deviations.

Significant Differences When is an Observed Difference Reliable? 1. 2. 3.

Representative samples are better than biased samples. Observations with low-variability are more reliable. More cases are better than fewer.

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Smart thinkers are not impressed by a few anecdotes; generalizations based on a few unrepresentative cases are unreliable.

When is an Observe Difference Significant? -

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When averages from two samples are reliable measures of their respective populations, then their differences are likely to be reliable as well. ○ If one group have low variability in aggression, and the same goes for the second group, then their differences are likely reliable. Statistical Significance: When sample averages are reliable, and when differences between them is large (The difference is likely not due to chance). ○ Something can have statistical significance, but little practical significance. ○ Statistical significance indicates the likelihood that a result will happen by chance, but it does not say anything about the importance of the result....