Stats: Selecting Appropriate Analysis Techniques and the Elements of Power Analysis

Suitability of a Statistical Procedure

factors involved are related to:

• nature of the researcher

• nature of the study

• nature of the statistical theory

Specific Related Factors Research Suitability

1. purpose of the study

2. study hypotheses, questions, or objectives

3. study design

4. level of measurement of variables in a study

5. previous experience in statistical analysis

6. statistical knowledge level

7. availability of statistical consultant

8. financial resources

9. access and knowledge of statistical software

Decision Tree

• approach to selecting an appropriate statistical procedure or judging the appropriateness of an analysis technique

• directs your choices by gradually narrowing options through the decisions you make

• the disadvantage - if you make an incorrect or uninformed decision, you can be led down the wrong path

T-Test for independent samples

one of the most common statistical tests to investigate the differences between two independent samples

• parametric and inferential

• only compares two groups at the same time

• dependent variable must be continuous and normally distributed

  • continuous - uncountable (infinite: age, distance, temperature)

T-Test for paired samples

also referred to as a dependent sample t-test

• compares two sets of data from one group of people

• parametric and inferential

• dependent variable must be continuous and normally distributed

• repeated assessment of the same group of people

One Way Analysis of Variance (ANOVA)

statistical procedure that compares data between two or more groups or conditions to investigate the presence of differences between those groups

• parametric and inferential

• dependent variable must be continuous and normally distributed

• one way ANOVA tests one independent variable and one dependent variable

Repeated Measures ANOVA

procedure that compares multiple sets of data from one group of people

• dependent variable must be continuous and normally distributed

• repeated measures indicates that the research design is to repeatedly assess the same group of people over time

• can also refer to naturally occurring pairs (i.e siblings or spouses)

Mann Whitney U

nonparametric alternative to an independent samples t-test

• test compares differences between two independent samples

• preferred when the distribution of the dependent variable data significantly deviates from normality or when the dependent variable is ordinal and cannot be treated as an interval/ratio scaled variable

Kruskal-Wallis Test

nonparametric alternative to the one way ANOVA

• compares the differences between two or more groups

• preferred over the ANOVA when the distribution of the dependent variable data significantly deviates from normality or the dependent variable is ordinal and cannot be treated an an interval/ratio scaled variable

Friedman test

nonparametric alternative to the repeated measures ANOVA

• compares multiple sets of data from one group of people

• preferred over the repeated measure ANOVA when the dependent variable data significantly deviates from normality or the dependent variable is ordinal and cannot be treated as an interval/ratio scaled variable

Wilcoxon Signed Rank test

nonparametric alternative to the paired samples t-test

• compares two sets of data from one group of people

• preferred over the paired samples t-test when the dependent variable data significantly deviates from normality or if the dependent variable is ordinal and cannot be treated as an interval/ratio scaled variable

Pearson Chi Square test

nonparametric inferential statistical test that compares differences between groups on variables measured at the nominal level

• compared the frequencies that are observed with those that are expected

• can reveal if the difference in proportions between categories is statistically improbable

one way chi square - compared different levels of one variable

two way chi square - tests whether proportions in levels of one nominal variable are significantly different than the proportions in a second nominal variable

Pearson Product Moment Correlation Coefficient

parametric, inferential statistic computed by two continuous, normally distributed variables

• represented by the statistic r

• value of r is always between -1.00 and +1.00

• value of 0 indicates no relationship

• positive correlation indicates that higher values of x are associated with higher values of y

• negative correlation indicates that lower values of x are associated with lower values of y

Spearman Rank Order Correlation Coefficient

nonparametric alternative to pearson’s r

• examines the association between two continuous variables

• preferred over the pearson r when one or both variables significantly deviate from normality or the variables are ordinal and cannot be converted to interval/ratio

Phi

nonparametric alternative to the pearson’s r when the two variables being correlated are dichotomous

• yields values between -1.0 and 1.0 when 0 represents no association

Cramer’s V

nonparametric alternative to the peason’s r when the two variables being correlated are both nominal

• yields a value between 0 and 1 where 0 represents no association between the variables and a 1 represents a perfect association

Odds Ratio

commonly used to obtain an indication of association when both the predictor (independent) and the dependent variables are dichotomous

• defined as the ratio of the odds of an event occurring in one group to the odds of it occurring in another group

• can be computed when the dependent variable is dichotomous and the predictor is continuous and would be computed by performing a logistic regression analysis

  • OR of 1.0 indicated that the predictor does not affect the odds of the outcome

  • OR of greater than 1.0 indicates that the predictor is associated with a higher odds of an outcome

  • OR of less that 1.0 indicates the predictor data is associated with a lower odds of the outcome

Simple and Multiple Linear Regression

procedure that provides an estimate of the value of the dependent variable based upon the vaule of an independent variable or set of indepentent variables (predictors)

• this is used to predict the value of one variable if we know the value of another

• the score on variable y is predicted from the same subject’s known score or variable x