Research Methods

A Guide to Applying Statistical Literacy to Nursing Research for

Evidence-Based Practice

MSN5300

Dr. K. Richards, Professor

Director, Center ƒor Excellence

How to Determine Appropriate Use of:

▪ Parametric vs. Non-Parametric Statistical Tests

▪ Parametric Test vs. Non-Parametric Analog

▪ Statistics to Answer Questions of: • relationships

• predictions

• differences

How to decide if Parametric or non-Parametric group of statistical tests is appropriate to analyze the data:

Steps:

1. Identify the level of measurement (on the NOIR Scale) of the dependent (outcome) variable (DV).

2. If DV is measured at Nominal or Ordinal level, ! Non-Parametric group of statistical tests is appropriate. No further steps necessary.

3. If DV is measured at Interval or Ratio level, think Parametric, BUT ! You must take another step (4) before deciding the Parametric group is appropriate.

4. You must next determine if ALL assumptions are met: 1. Normality: Are data normally distributed under the bell curve?

2. Homogeneity of Variance: Are data equally dispersed out in the tails of the bell curve ?

3. Outliers: Are there any scores in the data set that are outside the normal distribution of the data?

4. Randomness: Are study subjects chosen using a random sampling strategy?

5. Independence: Does each subject contribute only 1 answer per variable?

If even 1 assumption is violated (not met), then Parametric statistics are not appropriate to use. Non-Parametric tests are the

appropriate group of statistical tests to use.

If ALL assumptions are met AND DV is measured at Interval or Ratio level, Parametric statistics are appropriate to use.

1

Determine Level of Measurement of Dependent (Outcome) Variable

Nominal or Ordinal: Interval or Ratio:

?Parametric?

Non-Parametric Assumptions Assumptions met not met

Parametric Non-Parametric

How to decide if Parametric or non-Parametric group of statistical tests is appropriate to analyze the data:

Step 1:

Step 2: Step 3:

Step 4:

Questions: -Relationship -Prediction -Differences

This diagram represents the text explanation on the previous page

See the next page for continuation of this diagram starting here

2

INFERENTIAL STATISTICS:

Parametric Statistical Tests, Non-Parametric Analogs of each Parametric test, and

types of research questions (Q’s) answered by each Note:

INFERENTIAL

Parametric Non-Parametric Used for:

1. Correlation:

Pearson (r) Spearman Rho (rs / ρ) (Relationship Q’s)

2. Linear Regression:  Simple (Prediction Q’s)  Multiple

3. Independent t-tests (t) Chi Square (χ2)* (Difference Q’s when 2 groups) Mann-Whitney (U)**

4. Dependent t-tests (t) Wilcoxon (W) (Difference Q’s for pre- and post- design)

5. ANOVA (F) (Difference Q’s when 3 or more groups) (Post hoc tests when F test is statistically significant = p<a)

(Not covered)

(Not covered)

Non-Parametric Analogs for

Independent t-test:

use χ2* when DV= counts (frequency data)

use U** when DV is Ordinal

3

COMPARISON OF DESCRIPTIVE AND INFERENTIAL

BRANCHES OF STATISTICS

DESCRIPTIVE

Central Tendency Dispersion Mean Range

Median Variance

Mode Standard Deviation

INFERENTIAL

Parametric Non-Parametric

Pearson (r) Spearman Rho (rs / ρ)

Linear Regression:  Simple  Multiple

Independent t-tests (t) Chi Square (χ2) Mann-Whitney (U)

Dependent t-tests (t) Wilcoxon (W)

ANOVA (F) (Post hoc tests)

(Not covered)

(Not covered)

Mean

Median

Mode

(center)

Range, Variance, SD

(tails) Range, Variance, SD

(tails)

Perfectly symmetrical bell curve represents

Normality, Homogeneity of Variance, No Outliers (Trifecta)

Trifecta PLUS: Independence and Randomness

=

4

Research Methodologies

Qualitative Quantitative

Non-Interventional Interventional

Descriptive design (used for research questions that describe)

Correlational design (used for research questions that test relationships)

Exp. design Characteristics: 1. Randomness 2. Control 3. Manipulation

Quasi-Exp. design

Missing 1 or more of Exp. Design

characteristics

1. Phenomenology 2. Grounded

Theory 3. Ethnography 4. Historical

Relationship Qs

Prediction QsDifference Qs

Mixed Methods design

Research Designs

Research Questions Hope this helps!

5

A Guide to Applying Statistical Literacy to Nursing Research for

Evidence-Based Practice

MSN5300

Dr. K. Richards, Professor

Director, Center ƒor Excellence

How to Determine Appropriate Use of:

▪ Parametric vs. Non-Parametric Statistical Tests

▪ Parametric Test vs. Non-Parametric Analog

▪ Statistics to Answer Questions of: • relationships

• predictions

• differences

How to decide if Parametric or non-Parametric group of statistical tests is appropriate to analyze the data:

Steps:

1. Identify the level of measurement (on the NOIR Scale) of the dependent (outcome) variable (DV).

2. If DV is measured at Nominal or Ordinal level, ! Non-Parametric group of statistical tests is appropriate. No further steps necessary.

3. If DV is measured at Interval or Ratio level, think Parametric, BUT ! You must take another step (4) before deciding the Parametric group is appropriate.

4. You must next determine if ALL assumptions are met: 1. Normality: Are data normally distributed under the bell curve?

2. Homogeneity of Variance: Are data equally dispersed out in the tails of the bell curve ?

3. Outliers: Are there any scores in the data set that are outside the normal distribution of the data?

4. Randomness: Are study subjects chosen using a random sampling strategy?

5. Independence: Does each subject contribute only 1 answer per variable?

If even 1 assumption is violated (not met), then Parametric statistics are not appropriate to use. Non-Parametric tests are the

appropriate group of statistical tests to use.

If ALL assumptions are met AND DV is measured at Interval or Ratio level, Parametric statistics are appropriate to use.

1

Determine Level of Measurement of Dependent (Outcome) Variable

Nominal or Ordinal: Interval or Ratio:

?Parametric?

Non-Parametric Assumptions Assumptions met not met

Parametric Non-Parametric

How to decide if Parametric or non-Parametric group of statistical tests is appropriate to analyze the data:

Step 1:

Step 2: Step 3:

Step 4:

Questions: -Relationship -Prediction -Differences

This diagram represents the text explanation on the previous page

See the next page for continuation of this diagram starting here

2

INFERENTIAL STATISTICS:

Parametric Statistical Tests, Non-Parametric Analogs of each Parametric test, and

types of research questions (Q’s) answered by each Note:

INFERENTIAL

Parametric Non-Parametric Used for:

1. Correlation:

Pearson (r) Spearman Rho (rs / ρ) (Relationship Q’s)

2. Linear Regression:  Simple (Prediction Q’s)  Multiple

3. Independent t-tests (t) Chi Square (χ2)* (Difference Q’s when 2 groups) Mann-Whitney (U)**

4. Dependent t-tests (t) Wilcoxon (W) (Difference Q’s for pre- and post- design)

5. ANOVA (F) (Difference Q’s when 3 or more groups) (Post hoc tests when F test is statistically significant = p<a)

(Not covered)

(Not covered)

Non-Parametric Analogs for

Independent t-test:

use χ2* when DV= counts (frequency data)

use U** when DV is Ordinal

3

COMPARISON OF DESCRIPTIVE AND INFERENTIAL

BRANCHES OF STATISTICS

DESCRIPTIVE

Central Tendency Dispersion Mean Range

Median Variance

Mode Standard Deviation

INFERENTIAL

Parametric Non-Parametric

Pearson (r) Spearman Rho (rs / ρ)

Linear Regression:  Simple  Multiple

Independent t-tests (t) Chi Square (χ2) Mann-Whitney (U)

Dependent t-tests (t) Wilcoxon (W)

ANOVA (F) (Post hoc tests)

(Not covered)

(Not covered)

Mean

Median

Mode

(center)

Range, Variance, SD

(tails) Range, Variance, SD

(tails)

Perfectly symmetrical bell curve represents

Normality, Homogeneity of Variance, No Outliers (Trifecta)

Trifecta PLUS: Independence and Randomness

=

4

Research Methodologies

Qualitative Quantitative

Non-Interventional Interventional

Descriptive design (used for research questions that describe)

Correlational design (used for research questions that test relationships)

Exp. design Characteristics: 1. Randomness 2. Control 3. Manipulation

Quasi-Exp. design

Missing 1 or more of Exp. Design

characteristics

1. Phenomenology 2. Grounded

Theory 3. Ethnography 4. Historical

Relationship Qs

Prediction QsDifference Qs

Mixed Methods design

Research Designs

Research Questions Hope this helps!

5