Describing data via Measures of Central Tendency and Measures of Dispersion - see Quantitative Data - are not the only statistical techniques available to the researcher. By using inferential statistics, the researcher can draw conclusions about the wider population from which a particular sample has been drawn - specifically the the probability of having obtained a particular set of results by chance. This enables the researcher to decide whether the null hypothesis can be retained or rejected and whether the alternative (experimental) hypothesis can be accepted.

 

Statistical Significance

Statistical significance means the results obtained are unlikely to be due to chance. When the likelihood of the results having been obtained through chance is only very slim, then the researcher will prefer to reject the null hypothesis and accept the alternative one.

 

A level of significance is an arbitrary value used to ascertain whether a particular set of data differs from what would be expected if only chance factors were operating.

 

The usual way of writing a level of significance is, for example, P ≤ 0.05 for the 5% level of significance - P being the probability of the result and ≤ meaning less than or equal to.

 

The 5% significance level is the one used in most research, meaning that the likelihood of the results having occurred by chance is one in 20 or  less. When this level of significance is used in experimental research, it means that any difference  between sets of scores is so large that it is unlikely to have arisen due to chance. Provided the difference is not due to some unanticipated confounding variable, the researcher can conclude that the effects on the dependent variable are due to changes in the independent variable and, therefore, can assign cause-and-effect to the results.

 

Sometimes it is appropriate to set a more stringent level of significance - eg: 1% (P ≤ 0.01), or 0.5% (P ≤ 0.005) or even 0.1% (P ≤ 0.001). In instances where there is a risk of harm to the participants - eg: medical research - then more stringent levels of significance are often used. The key to what level of significance to set, if varying from 5%, is how sure does the researcher need to be that results are unlikely to be to chance,

 

A Type I error - rejecting the null hypothesis when it should be accepted - can occur if the level of significance set is not stringent enough. A Type II error - accepting the null hypothesis when it should be rejected - can occur when the level of significance is too stringent.

 

Difference and Correlation

Parametric statistical tests are for use with interval and ratio data and assume that the data are normally distributed. Non-parametric statistical tests are for use with nominal and ordinal data and don't make an assumption about the distribution of data. They are better suited for situations where the data are skewed. Parametric tests are more powerful and sophisticated.

 

Other factors influencing choice of test include whether the test is for one of difference or correlation.

 

Tests of difference are concerned with experimental data and the difference in effect on the dependent variable thought to be caused by some change in the independent variable - thus, creating 2 or more conditions producing different data sets (results).

 

The experimental design will influence the choice of test for difference.

- ie, whether the researcher is placing participants in independent groups, repeated measures or matched pairs. Data from independent groups designs - independent data - is treated differently from designs using repeated measures and matched pairs - data from which is related. (Because participants in matched pairs designs are paired, it is considered that there is a relationship between each pair and, therefore, the data is related.)

 

A correlation is concerned with the relationship between 2 co-variables - variables which change together. Related scores of the 2 co-variables - eg: scores in 2 types of behaviour from participants - are usually plotted on a scattergraph.

 

The example - top left - shows a positive correlation - ie: as one variable has increased, so has the other. Due to other variables potentially influencing the change, it is not possible to assign cause-and-effect. Merely that there is a relationship between the 2 co-variables.

 

 

 

 

The strength of the relationship between the 2 co-variables is the correlational coefficient. With a strong correlation, it is possible to predict the scores on the other co-variable. Thus, the stronger the correlation, the more reliable the prediction.

 

A perfect positive correlation has a coefficient of +1. This means that the two sets of scores increase together in exactly the same proportion.

 

The scattergraph example - lower left - is of a negative correlation. As one co-variable increases, the other decreases by exactly the same proportion.

 

A perfect negative correlation has a coefficient of -1.

 

The scattergraph example - bottom left - shows zero correlation. In other words, there

Scattergraphs copyright © 2009 BBC

is no relationship between the 2 variables.

 

A line of best fit can be drawn - see examples, bottom-most left - to highlight the trend in the correlation.

 

Observed Values & Critical (Tabled) Values

Inferential tests produce what is termed an ‘observed value’ - ie: observed from the data the researcher has collected, the result in statistical terms of whatever is being   Investigated.

 

To know if the observed value is significant, it needs to be compared to the pertinent critical value. Critical values are listed in tables - hence they are sometimes called ‘tabled values’. What value will be critical for any observed value will depend not only on the test structure and level of measurement of the data concerned - ie: nominal, ordinal or interval/ratio but also on the number of participants and whether in independent groups, repeated measures or matched pairs. Also of key importance is whether the alternate hypothesis is 1-tailed (directional) or 2-tailed (non-directional) and what the level of significance set by the researcher is.

 

The example - left - shows 2 of the tables for the Wilcoxon Signed Ranks Test.

Significance level: 0.05 1-tailed;  0.1 2-tailed

Significance level: 0.025 1-tailed; 0.05 1-tailed

Tables copyright © 2006 Andrew Wills