# Selecting statistical tests for your quantitative research

Selecting a statistic test

In the measures, we define and identify our outcomes or endpoints. We can identify one outcome or endpoint as our primary outcome and we can have several other secondary outcomes or endpoints

We will look at tests pertaining to quantitative research and focus on some of the basic or commonly used tests. We will not run a discussion of the theoretical background of statistical tests in this module.

You can use this module to identify some of the common tests that you can employ in your research (and based on your research design and question)

Note:  Earlier, we mentioned the need to note down anticipated answers. Your research question and anticipated answers will help you plan the tests that will be useful for your research. Please be aware that your anticipated choice of test may change after you conduct your research based on the data you obtain.

STEP 1: IDENTIFY THE DEPENDENT VARIABLE OF INTEREST

STEP 2: IDENTIFY THE INDEPENDENT VARIABLE(S) OF INTEREST

 Identify One Dependent Variable No Independent Variable Univariate Analysis Can be Continuous Dependent VariableOrdinal Dependent  VariableNominal Dependent Variable One Independent Variable Bivariate Analysis Can be Continuous Dependent VariableOrdinal Dependent  VariableNominal Dependent Variable More than one Independent Variable Multivariate Analysis Can be Continuous Dependent VariableOrdinal Dependent  VariableNominal Dependent Variable

Let us look at each of these scenarios

Univariate Analysis

Assumptions

1. Population from which sample is drawn is normally distributed
2. Sample (s) are randomly selected from the population
3. Samples have approximately equal variance (homogeneity of variance)
4. Parametric data- based on an interval or ratio based scale
 Continuous Dependent Variable & No Independent Variable Comparing Means Students t-test Continuous Dependent Variable & No independent Variable comparing one pre-and one post measure in same subject Paired t test

Assumptions

1. Distribution free or non-parametric data
2. Samples are randomly selected or representative of a general population
 Ordinal Dependent Variable & No independent Variable Comparing Medians Wilcoxon Sign Rank test Nominal Dependent Variable Affected by Time & no independent variable Rate Normal Approximation to Poisson Nominal Dependent Variable NOT affected by time– Outcome Common & No independent Variable Proportion Normal Approximation to Binomial Nominal Dependent Variable NOT affected by time– Outcome Uncommon &  No independent Variable Proportion Normal Approximation to Poisson

Bivariate Analysis

 Ordinal Dependent Variable & No independent Variable Comparing Medians Wilcoxon Sign Rank test Nominal Dependent Variable Affected by Time & no independent variable Rate Normal Approximation to Poisson Nominal Dependent Variable NOT affected by time- Outcome Common & No independent Variable Proportion Normal Approximation to Binomial Nominal Dependent Variable NOT affected by time- Outcome Uncommon &  No independent Variable Proportion Normal Approximation to Poisson Ordinal Dependent Variable & No independent Variable Comparing Medians Wilcoxon Sign Rank test Nominal Dependent Variable Affected by Time & no independent variable Rate Normal Approximation to Poisson Nominal Dependent Variable NOT affected by time- Outcome Common & No independent Variable Proportion Normal Approximation to Binomial Nominal Dependent Variable NOT affected by time- Outcome Uncommon &  No independent Variable Proportion Normal Approximation to Poisson Continuous Dependent Variable & Continuous Independent variable from naturalistic or purposive sampling Slope and Intercept Regression Analysis, F-Test Continuous Dependent Variable & Continuous Independent Variable from naturalistic sample Pearson’s correlation coefficient Correlation analysis, Students t-test Continuous Dependent Variable & Nominal Independent Variable from naturalistic sample or purposive sample Difference between means Students t-test Ordinal Dependent Variable & Ordinal Independent Variable from naturalistic sample Spearmans Correlation Coefficient Spearmans Correlation test Ordinal Dependent Variable & Nominal Independent Variable from a naturalistic or purposive sample Difference between medians Mann Whitney Test Nominal dependent Variable NOT AFFECTED by time  & Nominal Independent Variable- paired design Odds Ratio, Relative Risk, difference in proportions McNemars test Nominal dependent Variable NOT AFFECTED by time & Nominal Independent Variable- unpaired design Odds Ratio, Relative Risk, difference in proportions Chi-square test, normal approximation, Mantel Haenzel Test, Fishers Exact Test Nominal dependent Variable AFFECTED by time & Nominal Independent Variable- unpaired design Rate difference or ratio Normal approximation Nominal dependent Variable NOT AFFECTED by time & Continuous Independent Variable Slope and intercept Chi-square test for trend

Multivariate Analysis

 Continuous Dependent Variable & Nominal Independent variables representing one characteristic Means One-Way Analysis of Variance (ANOVA), F test, Student Newman Keuls Test Continuous Dependent Variable & Nominal Independent variables representing > 1 characteristic Means Factorial Analysis of Variance (ANOVA), F test, Student Newman Keuls Test Continuous Dependent Variable & Continuous Independent Variables from naturalistic sample or purposive sample Regression coefficients Multiple regression analysis, F test, partial F test Continuous Dependent Variable & Continuous Independent Variables from naturalistic sample Coefficient of determination Multiple correlation analysis, F test Continuous Dependent Variable & Nominal or continuous Independent Variables from a naturalistic or purposive sample Regression coefficients Analysis of Covariance (ANCOVA), F test, Partial F test Ordinal Dependent Variable & Ordinal Independent Variables Kendalls coefficient of concordance Chi-square test Ordinal Dependent Variable & Nominal Independent Variables Mean of Ranks Kruksal Wallis Test or Dunn’s test Nominal dependent Variable AFFECTED by time & Continuous and Nominal Independent Variables Incidence Ratio Cox Proportional Hazards Regression, Chi-square test Nominal dependent Variable NOT AFFECTED by time & Continuous and Nominal Independent Variables Odds Ratio Logistic Regression, chi square test Nominal dependent Variable AFFECTED by time & Nominal independent Variables Cumulative probabilities Kaplan Meier Life table analysis, Mantel Haenzel Test or logrank test Nominal dependent Variable NOT AFFECTED by time & Nominal independent Variables Odds ratio, relative risk or difference in proportions Stratified analysis, Mantel Haenzel test

In subsequent posts, we will look at how to do each of these tests and interpret them, using real life data examples.
Post attributed to Research Action Group AMMA ERF