RESEARCH NOTES
HOW TO ANALYSE YOUR RESEARCH DATA? ILLUSTRATIONS WITH HANDS-ON EXERCISES USING SPSS.
The SPSS commands for obtaining the above statistics are as follows:
From the menus choose:
- Analyze
- Descriptive Statistics
- Crosstabs
- Select ‘sex’ and ‘race’ into the ‘Rows’
- Select ‘hba1c category’ into the ‘Column’
- Click on the icon ‘Cells’, check the box ‘Percentages Row’, and click ‘Continue’
- Click ‘OK’
Chi-square test
Table 2 is in reality a cross-tabulation of gender (and ethnicity) with HbA1c categories. Chi-square test is used to compare frequencies (counts) in two or more groups.
- When you perform a chi-square test to look for association between gender and HbA1c categories, you will get this output: c2=0.984, df=2, p=0.611. Since p is >0.05, you may conclude that the HbA1c categories did not differ significantly among the two genders.
- When you perform a chi-square test to look for association between ethnicity and HbA1c categories, you will get this output: c2=2.196, df=4, p=0.700. Since p is >0.05, you may conclude that the HbA1c categories did not differ significant among the three ethnic groups.
- You may be wondering why there is no statistical significant difference in the chi-square test among the ethnic groups and HbA1c categories, but the ANOVA found statistical significant different in the mean HbA1c by ethnicity. By categorizing 160 HbA1c values into three groups only, you have actually lost quite a lot of useful information, thus producing a “non-significant” chi-square test.
The SPSS commands for obtaining the above Chi-square statistics are as follows:
From the menus choose:
- Analyze
- Descriptive Statistics
- Crosstabs
- Select ‘sex’ and ‘race’ into the ‘Rows’
- Select ‘hba1c category’ into the ‘Column’
- Click on the icon ‘Statistics’, check the box ‘Chi Square’, and click ‘Continue’
- Click ‘OK’
Other non-parametric tests
Non-parametric tests can be used in situations where the parametric tests are inappropriate, e.g. the dependent variable is not normally distributed (highly skewed data, ordinal data), sample size of study is small (<30), or when the assumptions of parametric tests may be violated (e.g. variances in subgroups highly unequal). When the independent variable has two groups, we use Mann-Whitney U test. When the independent variable has three or more groups, we use Kruskal-Wallis test. In both tests mentioned above, the “mean rank” of values in the dependent variables is compared instead of the arithmetic means (as in t-test or ANOVA).Word of caution and further analysis
- Chi-square is a “big sample test”, i.e. the sample size should be relatively large (to the extent that the “expected count” in each of the cells in the chi-square contingency table should be more than 5), otherwise this test becomes invalid. If your dependent or independent variables have more than two groups, you may attempt to combine some of the groups together to obtain a bigger sample size within a group. Nonetheless, if you have a study with small sample size, and both dependent and independent variables only have two groups, you may opt to perform Fisher Exact test.
- When the dependent variable is actually paired data, McNemar test is the correct test rather than Chi-square test. For example, when a group of patients with migraine are assessed twice (before and after intervention) for the presence of visual aura (present or absent).
- When the dependent variable has binary outcome (two possible responses, e.g. dead/alive), and you wish to determine the association with many other independent variables (may be continuous or categorical), logistic regression can be performed.
CONCLUSION
Choosing the correct statistical tests for your analysis depends on a good grasp of your research question (e.g. properly established research objectives), some understanding of the measurement you have made (is the variable continuous or categorical), the complexity of your analysis (one variable, 2 variables or multiple variables) and what the statistical test can or cannot do (its assumptions, its statistical output, etc). Table 3 is a summary of the commonly used statistical tests and their link to the characteristics of the variables.
REFERENCES
- Khoo EM. Research questions and research objectives. The Family Physician. 2005;13(3):25-26 [PDF]
FURTHER READINGS
- Dawson B and Trapp R G. Basic & clinical biostatistics. 4th edition. Mc Graw Hill, Boston, 2004.
- Taylor G and Harris M. Medical statistics made easy. 1st edition. Taylor & Francis Group, UK, 2004.
- Wong KC, Phua KL. Statistics Made Simple for Healthcare and Social Science Professionals and Students. University Putra Malaysia. 2006 (http://eprint.uq.edu.au/archive/00003913/).