This podcast discusses z-scores and how they describe the distance of an observation from the mean. They explore the 68-95-99.7 rule, calculate z-scores for height, and discuss the likelihood of statistical results being due to chance.
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Quick takeaways
Z-scores measure how far an observation is from the mean, providing insights into the distribution of data.
The 68-95-99.7 rule states that most data points in a normally distributed population fall within one, two, or three standard deviations from the mean.
Deep dives
Z-Scores and the Bell Curve
The podcast discusses the concept of Z-scores and the bell curve, also known as the Gaussian distribution. Z-scores measure how far an observation is from the mean of its population. The bell curve, or Gaussian distribution, is characterized by a mean, which represents the average case, and a standard deviation, which indicates how peaked the distribution is. The standard deviation determines the range of values around the mean, with more precise measurements having a narrower standard deviation.
Z-Scores in Human Height
The podcast uses human height as an example to explain Z-scores. Assuming height follows a normal distribution, the podcast provides average heights for males and females in the US, along with the standard deviation. Z-scores can be used to determine an individual's percentile in terms of height compared to the population. The 68-95-99.7 rule states that approximately 68% of individuals fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Z-scores are useful in assessing the likelihood that a result is due to chance or coincidence.
This week's episode dicusses z-scores, also known as standard score. This score describes the distance (in standard deviations) that an observation is away from the mean of the population. A closely related top is the 68-95-99.7 rule which tells us that (approximately) 68% of a normally distributed population lies within one standard deviation of the mean, 95 within 2, and 99.7 within 3.
Kyle and Linh Da discuss z-scores in the context of human height. If you'd like to calculate your own z-score for height, you can do so below. They further discuss how a z-score can also describe the likelihood that some statistical result is due to chance. Thus, if the significance of a finding can be said to be 3σ, that means that it's 99.7% likely not due to chance, or only 0.3% likely to be due to chance.
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