Which concept is an example of standardization used in statistics?

Which concept is an example of standardization used in statistics?

• A. z-scores
• B. p-values
• C. t-statistics
• D. Correlation coefficients

Answer: (A)

Standardization means transforming data to a common scale so different measurements can be compared directly. A z-score is the standardization method that converts a raw value into the number of standard deviations it is from the mean, using z = (X − μ) / σ. This process creates a standardized scale with a mean of 0 and a standard deviation of 1, so values from different distributions or variables can be compared on the same footing, and we can interpret where a value lies relative to the typical spread of the data. Z-scores also connect to the standard normal distribution, enabling probability and percentile interpretation. P-values are probabilities about observing the data under a null hypothesis, not a way to standardize data. A t-statistic is a type of standardized statistic used in hypothesis testing, which involves standardizing a difference by an estimate of its standard error, but it’s more about testing than about transforming individual observations for comparison. Correlation coefficients describe the strength and direction of a linear relationship between two variables, not the standardization of a single observation.

Standardization means transforming data to a common scale so different measurements can be compared directly. A z-score is the standardization method that converts a raw value into the number of standard deviations it is from the mean, using z = (X − μ) / σ. This process creates a standardized scale with a mean of 0 and a standard deviation of 1, so values from different distributions or variables can be compared on the same footing, and we can interpret where a value lies relative to the typical spread of the data. Z-scores also connect to the standard normal distribution, enabling probability and percentile interpretation.

P-values are probabilities about observing the data under a null hypothesis, not a way to standardize data. A t-statistic is a type of standardized statistic used in hypothesis testing, which involves standardizing a difference by an estimate of its standard error, but it’s more about testing than about transforming individual observations for comparison. Correlation coefficients describe the strength and direction of a linear relationship between two variables, not the standardization of a single observation.