Statistical Concepts 1: Variables

Think of variables as questions and values as answers.

• e.g. Two groups of participants (man and women). CCTV cameras should be used on public transport (Strongly agree, Agree, Neutral, Disagree, Strongly Disagree)

• If all the values are the same then that variable must be discarded. (e.g. Are you willing to participate in this experiment?)

Independent Variables aka Factors

• Fixed factors - manipulated (varied) by the experimenter. The different values the factor can take are known as values, levels or conditions.
• Subject variables - recorded by the experimenter, e.g. gender, age.
• Random factors - levels can't be repeated exactly, e.g. animal litter, household aka Randomised Blocks.

Dependent Variables

• What you measure, e.g. score, reaction time, number of errors, answer to a question.

Levels of Measurement

• Nominal aka Categorical, e.g. colour, political party.
• Ordinal, e.g. Likert scales, ice dancing scores (subjective scales). [Nominal variables with 2 values]
• Interval aka Scale, e.g. Temperature Celcius, IQ.
• Ratio, e.g. reaction time, number correct. A subset of Interval.

Distributions

• Flat, e.g. die
• Binomial, e.g. multiple coins
• Bell curve, e.g. sum of several dice
• Poisson, e.g waiting for a rare event to happen
• Normal
• Bi-modal

Describing Distributions

• Central tendancy - mean, median, mode
• Variation - range, interquartile range, standard deviation
• Skewness - how lop-sided is it? Normal distribution has a skewness of 0. Significantly skewed if |skewness| > 2 * SE skewness
• Kurtosis - how pointy is it? Normal distribution has a kurtosis of 0. Significantly skewed if |kurtosis| > 2 * SE kurtosis