Introduction to Statistics and Research Design

Categorical variable

A variable that places an individual into one of several groups or categories.

Quantitative variable

A variable that takes numerical values for which arithmetic operations such as adding and averaging make sense.

Bar graph

A visual display better than pie charts for comparing category sizes, which can also display a variable's natural ordering along the horizontal axis with equally wide bars.

Pie chart

A chart showing the distribution of a categorical variable by displaying the percentage for each category, which only works if all categories are included so percentages sum to $100\%$.

Line graph

A display of a quantitative variable that plots each observation against time, placing variable values on the vertical scale and equally spaced time intervals on the horizontal scale.

Seasonal variation

A pattern in data that repeats itself at known regular intervals of time.

Number Sense

The habit of asking if numbers make sense.

Block

A group of experimental subjects known before an experiment to be similar in some way that is expected to affect the response to the treatments.

Block design

An experimental setup in which the random assignment of subjects to treatments is carried out separately within each block.

Measurement

The process of turning concepts such as length or employment status into precisely defined variables by assigning numbers to represent them.

Bias (in measurement)

A systematic tendency of a measurement process to overstate or understate the true value of the property it measures.

Random error

The condition where repeated measurements on the same individual yield different results.

Reliable measurement

A measurement process in which the random error is small.

Measured value formula

$$\text{measured value} = \text{true value} + \text{bias} + \text{random error}$$

Variance (of repeated measurements)

A calculation found by taking the arithmetic average of $n$ measurements, computing and squaring each difference from the average, and dividing the sum of squared differences by $n - 1$.

Institutional Review Board (IRB)

An organization committee that reviews all planned studies in advance to protect the rights and welfare of human subjects.

Informed consent

Permission granted by individual study subjects prior to data collection