The calculation of basic statistics is fundamental to all of our work. They provide valuable insights into data, summarising large volumes of information, suggesting possible relationships, and informing the design of more complex analyses. NFER statisticians are experts in using basic statistics to ensure that investigations are carried out accurately and economically. Close attention to detail ensures the quality of projects from the initial design to the final report, and we recognise the need throughout such analysis to consider the bigger picture and whether findings make intuitive sense.
There is a wide range of basic statistics that we use. We may begin with a count of the data – is it the number we were expecting, and is it large enough for analysis? When considering a sample we check that it is representative of the population from which it was drawn. We can then calculate statistics such as the mean with its associated standard error and confidence intervals, which tell us how sure we can be of the accuracy of our estimates and whether our results are significantly different to those expected. The median, minimum and maximum values and the range alert us to outliers or extreme values in the data which may distort our findings.
Cross tabulations and the associated chi-square statistics are used to examine the relationship between two categorical variables. This is often used to look at the relationship between background variables such as gender or school year group with responses from a survey question. For continuous variables such as number of GCSEs we can test the difference between groups using analysis of variance (ANOVA). If both variables are continuous we can measure their association with a correlation coefficient. We often summarise information form surveys by calculating scores such as indices of wellbeing from pupil attitude surveys, and can test the reliability of such measures using Cronbach’s Alpha for example.