UBC PSYC 218-952 Analysis of Behavioural Data - Days 1-4

$$N$$

The symbol used to represent the overall sample size or total number of observations in a dataset.

$$n$$

The symbol used to represent the size of a subsample within a larger group.

Nominal

A level of measurement consisting of named categories for observations, such as dog, mouse, or cat.

Ordinal

A level of measurement consisting of rankings or orderings, such as first, second, or third.

Interval

Numerical observations where the distance between values is meaningful, but there is no meaningful zero point, such as temperature in Celsius.

Ratio

Numerical observations with a meaningful zero point, where both the distance and the ratio between values are meaningful, such as height or weight.

Independent Variable (IV)

The variable in an experiment that is manipulated by the researcher.

Dependent Variable (DV)

The variable that is measured by the researcher to determine if it is affected by the independent variable.

Population

The collection of all instances of people or things to which a specific research question refers.

Sample

A selected subset of a population used in a study, ideally chosen through random selection.

Parameter

A characteristic of a population, typically represented by Greek letters such as $\mu$ (mean) or $\sigma$ (standard deviation).

Statistic

A characteristic of a sample, typically represented by Latin letters such as $M$ or $\bar{x}$ (mean) and $s$ or $SD$ (standard deviation).

Descriptive Statistics

A branch of statistics used to describe and summarize data, such as calculating the mean, variance, or standard deviation.

Inferential Statistics

The branch of statistics used to make inferences or determinations about a population based on sample data through processes like hypothesis testing.

Positive Skew (Right Skew)

A distribution where most scores are clustered at the lower end and the tail extends toward the positive (right) side of the x-axis.

Negative Skew (Left Skew)

A distribution where most scores are clustered at the upper end and the tail extends toward the negative (left) side of the x-axis.

Floor Effect

A phenomenon that prevents or discourages scores from dropping below a certain point, often resulting in a positive skew.

Ceiling Effect

A phenomenon that prevents or discourages scores from rising above a certain point, often resulting in a negative skew.

Pareto Chart

A specific type of bar graph where the bars are ordered from the highest frequency to the lowest frequency to facilitate comparisons across categories.

Central Tendency

A descriptive value that represents the center of a data set or the value around which data is grouped, including mean, median, and mode.

Mean

The arithmetic average calculated by adding all values and dividing by the number of observations ($\bar{x}$ or $M = \frac{\sum X}{N}$).

Median

The middle score in a set of observations when the values are arranged from lowest to highest.

Mode

The most frequently occurring value in a distribution; a distribution can be unimodal, bimodal, or multimodal.

Outlier

An extreme value of a variable relative to the rest of the distribution of data, which can significantly affect the mean.

Variability

A numerical way of describing how widely spread out the observations are within a distribution.

Range

The simplest measure of variability, calculated as the highest score minus the lowest score ($X_{highest} - X_{lowest}$).

Interquartile Range (IQR)

The distance between the first quartile ($25^{th}$ percentile) and the third quartile ($75^{th}$ percentile), representing the middle $50\%$ of observations.

Variance

The average squared deviation from the mean, calculated as $\frac{\sum (X_i - \mu)^2}{N}$ for a population.

Standard Deviation

The square root of the variance ($\sigma$ or $SD$), representing the average distance of observations from the mean in the original units.

Corrected Sample Standard Deviation

A version of the standard deviation formula that uses $N - 1$ in the denominator to provide a better estimate of the population standard deviation ($s = \sqrt{\frac{\sum (X_i - M)^2}{N - 1}}$).

Random Sampling

A procedure using a random method to select participants from a population, ensuring the sample is representative.

Random Assignment

The process of using random methods to place participants into different groups (e.g., Group A vs. Group B) to ensure equivalence.

Expected Relative-Frequency Probability

The likelihood of an event occurring based on the actual outcome of a very large number of trials.

Law of Large Numbers

The principle stating that as the number of trials increases, the percentage of successes tends to get closer to the actual underlying probability.

Research Hypothesis

The hypothesis that follows directly from a theory, predicting a specific outcome or difference.

Null Hypothesis

The negation of the research hypothesis, which researchers formally test with the goal of rejecting it.

Type 1 Error

An error