Descriptive Statistics

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Descriptive Statistics

The mean, median, and mode are measures of central tendency and provide an average figure from a set of data. The range and standard deviation are measures of dispersion and show the spread of data.

Central tendency

There are three key measures of central tendency:
The mean is calculated by adding together every score from the data set, and dividing by the number of scores.
The median is the midpoint of the scores, when placed in numerical order from low to high. If there is an even number, the median is calculated by finding the mean of the middle two scores.
The mode is the most common score. Sometimes there is no mode because no score appears more than once, or there could be two or more modes.

Measures of dispersion

Measures of dispersion provide an idea of how spread out a set of scores are.
- For example, the data 10,20,30 have the same mean and median as 19,20,21, but the latter are less spread out.

Range and standard deviation

There are two key measures of dispersion:
- The range is calculated by subtracting the lowest score from the highest score.
- The standard deviation is carried out following a simple formula, and shows the typical amount by which scores differ from the mean.

Power of statistics

The mean and standard deviation are more powerful statistics, as they take every score into account.
But the other statistics are also useful, especially when describing skewed sets of data.

Percentages

Percentages are a useful form of data handling in psychology. They are widely used to summarise the data from self-report methods, and can make it easier to compare scores.

Standardised scores

Percentages are standardised scores, converting any fraction or test score into the equivalent score out of a hundred.
With any percentage, the number 100 represents the whole or maximum, and the percentage represents the fraction of that whole or maximum.

Calculation

Percentages are calculated from a fraction by dividing the smaller number by the larger number, and then multiplying the result by 100.

Uses of percentage

A percentage can be a useful way of summarising the results of self-report methods such as a survey.
- For example, the percentage of people who strongly agreed with a statement can be calculated.

Easy comparison

Percentages also allow standardisation of scores to make them easier to compare.
- For example, when comparing the number of people who have depression from two differently-sized groups of participants.

Correlation

Correlation is a statistical technique which shows how closely linked two sets of scores are.

Correlations

Correlation is a statistical technique which allows researchers to compare two sets of scores to see whether two variables are linked.
- For example, they could compare scores on a school exam with the number of hours that students had spent studying.

Positive vs negative

A positive correlation is where the scores rise and fall together. As one variable rises, so does the other.
A negative correlation is where the scores rise and fall in opposite directions. As one variable rises, the other falls.

Zero correlation

Sometimes, there is a zero correlation.
This is where there is simply no statistical link at all between the variables - the scores are not connected in any way.

Strength of correlation

Both positive and negative correlation can be weak or strong.
A strong correlation is where the scores rise and fall very closely, while a weak correlation suggests a much more distant relationship between the variables (for example a large rise in one might link to a very small rise in the other).

Correlation vs causation

Researchers must be careful not to conclude that a strong correlation means that one variable is having an effect on the other.
This could be the case, but it can’t be concluded from the correlation alone - further evidence would be needed.