# Dispersion and Central Tendency

I think people underestimate the amount of statistics that is necessary for psychological research. Luckily, as long as you understand the theory behind the statistics, most of the math is done by a computer. For my undergraduate course we use a programme called SPSS, which you can buy of amazon but most universities supply for a reduced price for their students. This post will be an introduction to the basics of statistical theory used in psychological research.

## Levels of Measurement

Nominal measurement is the lowest level of measurement, and includes categorical data and measures of frequencies.

Ordinal measurement involves rating scales to measure participant responses.

Interval measurement involves equal intervals; for example, measuring temperature. Interval measurement has no absolute zero worth.

Ratio measurement involves intervals with an absolute zero worth.

N.B: parametric tests can only be used with interval or ratio measurement unless you convert the data into numerical values.

## Types of Data Seen in Psychological Research

Continuous numerical data is data that can take any value within a certain range. The issue with continuous numerical data is that it is heavily dependent on the accuracy of measuring instrument.

For example: height, weight, reaction time

Discrete numerical data is data that can only take a specific value within a certain range. Questions that involve how many of something or the presence or absence of data is usually dealing with discrete numerical data.

For example: Numerical scores on a questionnaire: how many times have you been oversees?

Categorical data does not deal with a specific numerical value, but rather what group variables can be placed into. The issue with categorical data is that it can be too extreme. The people under one label can be very different from each other. Plus, it is very difficult to make appropriate intervals for categorical data.

For example: gender, nationality, etc.Categorical data can also come from continuos or discrete variables

## Types of Statistics

Descriptive statistics summarise the properties of a sample of data usually through measures of central tendency and dispersion. Measures of central tendency include: mean, median and mode. Dispersion refers to the spread of data, providing information about the mean accuracy. Different measures of dispersion include: range, variance, and standard deviation.

Inferential statistics use the properties found from the descriptive statistics to make estimations of of the properties of the population.

## Central Tendency

The mean is the average score. The mode is the most frequently occurring score, and the median is the middle score (when points are organised from lowest to highest value). The mean is the preferred measure of central tendency because it takes into account all the data of the population. The problem with using the mean, however, is that is easily influenced by extreme scores.

## Dispersion

Dispersion measured the spread of data and as mentioned above, gives the mean accuracy.

The most common approach for calculating the deviance is by calculating the variance. The variance is the: (sum of the squared deviances)/(the number of observations – 1). The unit is always the square of the measurement unit. The variances indicates how much the scores differ from one another.

N.B: The squared deviances is found by calculating the difference between each observation and the mean, and then squaring this value.

Standard deviation is the square root of the variance, and is much easier to deal with because it does not have squared units like the variance.

Bibliography:

ZHENG, Y. (2013). Referencing and citation – Harvard style, from PSY104 Methods and Reasoning for Psychologists. University of Sheffield, Richard Roberts Building on 4th February. Available from: Blackboard.
[Accessed 4/02/13].