QUANTITATIVE data analysis

Let us commence our look at data analysis by looking at a hypothetical research study.

Remember that there are different ways of approaching a research question and how we put together our research question will determine the type of methodology, data collection method, statistics, analysis and presentation that we will use to approach our research problem.

 Example of research question Are females more likely to be nurses than males? Is the proportion of males who are nurses the same as the proportion of females? Is there a relationship between gender and becoming a nurse?

In the example in the box above, you can see that there are three different ways of approaching the research problem, which is concerned with the relationship between males and females in nursing.

Another research problem with variables

In another research problem - the relationship between gender and smoking, there are 2 categorical variables (gender & smoker), with two or more categories in each, for example:

Gender (male/female)

Smoker (yes/no)

You are looking for whether or not there is any significance in the results

 Reflection Before we proceed, you may want to briefly refresh your knowledge and understanding of some basics, namely:

To recap on statistics, read chapter 9 of the accompanying book, and/or click on the hyperlink below:

statistics are fun

Alpha level (p level)

In statistical analysis we are looking to see if there is any significance in the results. The acceptance or rejection of a hypothesis is based upon a level of significance the alpha (a) level

This is usually set at the 5% (0.05) a level, followed in popularity by the 1% (0.01) a level

We usually designate these as p, i.e. p =0.05 or p = 0.01

So, what do we mean by levels of significance that the 'p' value can give us?

Statistical tests

There are many tests that we can use to analyse our data, and which particular one we use to analyse our data depends upon what we are looking for, and what data we collected (and how we collected it).

Below are just a few of the more common ones that you may come across in research papers.

 Mann-Whitney U-test This test is used to test for differences between 2 independent groups on a continuous measure, e.g. do males and females differ in terms of their levels of self-esteem. This test requires two variables (e.g. male/female gender) and one continuous variable (e.g. self-esteem). It actually compares medians. It converts the scores on the continuous variable to ranks, across the two groups. It then evaluates whether the medians for the two groups differ significantly.

 Spearman rank correlation test This test is used to demonstrate the relationship between two ranked variables Frequently used to compare judgements by a group of judges on two objects, or the scores of a group of subjects on two measures. This is a coefficient correlation based on ranks.  It shows the association between two variables (X and Y), which are not normally distributed. Don’t worry about the details – just remember that it is an acceptable method for parametric data when there are less than 30 but more than 9 paired variables.

 Kruskal-Wallis test This test is used to compare the means among more than two samples, when either the data are ordinal or the distribution is not normal. If there are only two groups then it is the equivalent of the Mann-Whitney U-test, so you may as well use that test. This test would normally be used when you wanted to determine the significance of difference among three or more groups.

Below is a very brief look at other common tests - for more information on statistical tests, read chapter 9 of the accompanying book.

Other Common Statistical Tests/Procedures

 t-test The t-test assesses whether the means of two groups are statistically different from each other. This analysis is appropriate whenever you want to compare the means of two groups.

 Pearson Correlation We use the Pearson's correlation in order to find a correlation between at least two continuous variables. The value for such a correlation lies between 0.00 (no correlation) and 1.00 (perfect correlation).

 ANOVA (Analysis of Variance) ANOVA is one of a number of tests (ANCOVA - analysis of covariance - and MANOVA - multivariate analysis of variance) that are used to describe/compare the relationship among a number of groups.

 Chi-square test There are two different types of chi-square tests - but both involve categorical data (Pallant 2001). One type of chi-square test compares the frequency count of what is expected in theory against what is actually observed. The second type of chi-square test is known as a chi-square test with two variables or the chi-square test for independence.

 Wilcoxon signed-rank test This is the most common nonparametric test for the two-sampled repeated measures design of research study, and is also known as the Wilcoxon matched-pairs test.

This has just been a very brief look at some of the more common statistical tests for the analysis of data obtained from quantitative research - more details are given in chapter 9 of the accompanying book. There are, of course, many others, and any good statistics book will have details of them.

When it comes to the selection of the appropriate test for your research in order to determine the p-value, you need to base the selection of four major factors, namely:

• The level of data (nominal, ordinal, ratio, or interval).

• The number of groups/samples in your research study (one, two, or more).

• Were the data collected from independent groups/samples or from related groups? Remember that independent groups are two or more separated groups of participants, whilst related groups are often the same group, but at a different time in the study, e.g. pre- and post-testing, or even a different environment.

• The characteristics of the data (i.e. the distribution of the data).

Now all these statistical tests may look very complicated, but if ever you are involved in quantitative research and have to do statistical analysis, don't worry because help is at hand.

There is a computer package for statistical analysis known as SPSS

SPSS stands for:

Statistical Package for Social Sciences

SPSS is one of a number of computer packages that can do just about any calculation that you want, using any statistical test.

Before we finish this section, we just need to remind you to be careful when you are looking at research that uses statistics.

Limitations of research study/data/statistical tests

Always look for these the researchers should reflect on their study and discuss anything that did not make it perfect, for example:

•  size of sample
•  tests used
•  initial question

It is easy to tie yourself up into knots when either doing statistics as part of your research, or when reading research papers, so remember two things:

1. Keep things simple

2. Statistics by themselves are meaningless, it is the analysis and

discussion of statistics which makes them meaningful and brings

them to life.

Finally

The time has come for you to decide which statistical test you will be using for your own quantitative research. As we keep mentioning, if all this is new to you, do not hesitate to seek the advice of an experienced quantitative researcher and/or a statistician - at as early a stage as possible.

 TO DO Click on to the icon below for the example of a quantitative research study proposal: Y

When  you are satisfied that you have the correct statistical test(s), and you can justify it/them, then write them into your research proposal.