Statistical Glossary

• Categorical variable (nominal variable)

  May have two or more categories, like a color variable with 3 possible values: ["Red", "Blue", "Green"].

• Coefficient of Variation (CV)

  A standardized measure of dispersion, representing the ratio between the standard deviation and the mean.

• Confidence level

  The confidence level represents the level of certainty that the true value of the parameter will be within the confidence interval

• Dichotomous variable

  A special case of the categorical variable with only two possible values, like True/False, Yes/No, Success/Failure.

• Ordinal variable

  A special case of a categorical variable when you may order the possible values, like the following Likert scale: Strongly disagree, Disagree, Neither agree nor disagree, Agree, Strongly agree.

• Continuous variable

  A numeric variable with an infinite number of values. Between any two values, you have more values. For example, between 0.01 and 0.02 you have 0.011).

• Interval scale

  There is a meaning for the distances between the values but not for the ratio between the values. For example, in degrees Celsius, increasing the temperature from 40°C to 60°C is double the increase from 40°C to 50°C, but 60°C is not twice as hot as 30°C.

• Ratio scale

  Like interval scale, there is a meaning for the distances between the values and also for the ratio between the values, there is a meaning to the zero. For example, a duration of 60 minutes is twice as long as a duration of 30 minutes.

• CDF

  Cumulative Distribution Function, F(x)=P(X≤x).

• PDF

  Probability Density Function, which describes the likelihood of obtaining a specific value for a continuous random variable. The area under the PDF curve between x₁ and x₂ represents the probability of obtaining a value within that range. The total area under the PDF curve is equal to 1.

• PMF

  Probability Mass Function, of obtaining a specific value for a discrete random variable. It is defined as F(x)=P(X=x), which is the equivalent of the PDF for continuous random variables."

• Mean

  The mean is a value that represents the middle of a set of numbers.
  Usually, the mean refers to to the arithmetic mean or arithmetic average.

• Sample data

  usually we don't have the data of the entire population, a random sample data represent the entire population.

• Sample average

  The average of the sample data.

• Standard deviation (σ)

  The standard deviation is a statistic that measures the data variability. It is derived from the square root of the distances between each value in the population and the population's mean squared.

• Sample standard deviation (S)

  The standard deviation of the sample data, the calculation is the same as for the standard deviation, but to get an unbias estimation of the standard deviation, the division is by (n - 1) instead of n.

  S2 =	Σ(𝑥i - x̄)2
  	n-1

• Sphericity

  Equal variance of the differences between the treatments (groups).

• Standard Error (SE)

  The standard deviation of a statistic.

• Standard Error of the Mean (SEM)

  The standard deviation of the mean. If you know the standard deviation: SEM=σ/√n. If you estimate the standard deviation: SEM=S/√n

• Type I error

  Rejecting a correct null assumption (H₀).

• Type II error

  Failing to reject an incorrect null assumption (H₀).

• Power

  The statistical power is the probability that a test will reject an incorrect H0 for a defined effect size. Researchers usually use a priori power of 0.8. More

• P-value

  The probability to get the sample results, or more extreme results, under the assumption that the null assumption (H₀) is correct, when the p-value is very small, p-value ≤ significance level (α), you should reject the null assumption.

• Significance level (α)

  The maximum chance allowed rejecting H₀ while H₀ is correct, the maximum probability of Type1 Error. significance level of 0.05 is commonly used, but if the price of rejecting a correct null assumption is big, you may use a smaller value like 0.01. The test result is significant when p-value is not bigger than the significance level.

• Surprisal

  The measure of how unexpected an event is. For instance, if the surprisal value is 4, it means that the probability of that event occurring is equivalent to getting 4 consecutive heads when flipping a fair coin.
  When reporting the results of a statistical test, you may report the surprisal of the p-value, which is calculated as S-value = -log₂(p-value).

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