Learning Activity 9:
Quantitative Data Analysis
Inferential - NonParametric Statistics
Method: Chi-Square Test
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“Inferential statistics are based on the law of probability. The word chance is used
in discussing probability. All inferential statistical tests are based on the assumption
that chance (sampling error, random error) is the only explanation for relationships
found in research studies. For example, if one group scores higher than another group
on a test, the assumption is made that the difference is due to chance. A researcher
wants to demonstrate that chance is not the reason for the relationships that are found
in the research. The larger the difference that is found between groups, the lower
the probability that the difference occurred by chance. In other words, the groups really
are different in regard to the variable that is being measured.”
- Leedy and Ormrod (2001).
Practical Research: Planning & Design, (p. 191).
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Overview
Inferential statistics are calculated for two specific purposes: the first is to estimate population parameters from sample data, and the second is to test hypotheses. The second purpose is the most common reason for performing inferential statistics in nursing research. Inferential statistical tests are classified as parametric or nonparametric. Parametric tests relate to population parameters while nonparametric tests relate only to the sample - they make no assumptions about the related population. They can also be done on nominal and ordinal data even if the sample size is small. Parametric tests require interval or ratio data from a normally distributed representative sample from a relatively large sample of the population.
One common nonparametric test used in nursing research is the chi-square test. This test is appropriate for comparing sets of data that are in frequency form for nominal or higher data. The chi-square is used to determine if the observed frequencies of events in certain categories fall within the range of frequencies expected in these categories. "Byers used the chi-square statistic in her study of the relationship between infant crying and bottle feeding during aircraft descent. Byers found that there was a significant difference in the amount of crying as a result of changes in air pressure in infant's ears between infants who were bottle fed during the descent and infants who were not bottle fed during the descent. Bottle fed infants cried significantly less than their unfed counterparts," (Dempsey & Dempsey, 1996, p. 140).
Using this technique, the researcher compares the frequencies that are observed or obtained in categories with the frequencies that would be expected to occur if the null hypothesis were true. Thus, observed frequencies are compared with expected frequencies. If the two are quite different at an expected level of significance, the null hypothesis can be rejected.
There are some specific requirements of data before the chi-square test can be used:
a) The sample must be randomly drawn from the population.
b) Data must be reported in raw frequencies or proportions (not percentages);
c) Measured variables must be independent;
d) Values/categories on independent and dependent variables must be mutually exclusive and exhaustive;
e) Observed frequencies cannot be too small.
Chi-square analysis can be done for a number of different reasons, but the most common is the Chi-square Test of Independence - a test to make inferences about the existence of a relationship between two categorical variables. It tests the relationship between two variables that are cross tabulated in a contingency table to see if they are independent from one another – or not related (Polit, 1996). A contingency table is a sort of matrix with a certain number of rows and columns. If the test data requires two rows and two columns, a 2 x 2 contingency table.
Another well used variation is the Chi-square Goodness-of-Fit Test. This method is used when a researcher wishes to make inferences about only one nominal level variable. "As with the chi-square test of independence, the goodness-of-fit test contrasts expected and observed frequencies," (p. 201).
Ends In View
This learning activity is intended to provide learners with the opportunity to:
1. Explore the nature of statistical hypothesis testing.
2. Understand the rationale for inferential data analysis.
3. Explore the process of visually reporting inferential qualitative data.
4.Practice Chi-Square analysis using a computer software program.
5.Critique the inferential data analysis process described in a select research study.
In Preparation
1.Read: Mathbeans Project. (n.d.). The Chi Square Statistic.
2. READ: Malloy, T. (2000). Chi Square Goodness of Fit
3. READ: Rodriguez, C. (1998). Chi Square Test of Independence
4.READ THE STUDY: (pay attention to the data analysis process):
Smith, R., Curran, J., Weinstein, S. & Griffiths, L. (2001). Investigation of glutathione S-transferase zeta and the development of sporadic breast cancer. Breast Cancer Research, 3, 409 – 411.
Assignment 2: Complete the assigned Worksheet 2: Chi Square (will be given out in class, or can be downloaded from the Kwantlen protected site on the campus Online Courses site). Save your work and submit with the other four worksheets given out in the other four quantitative learning activities. NOTE This is NOT the worksheet in your course materials - that one is for practice.
In Practice
1. Participate in class discussion related to the process of quantitative inferential data collection and analysis (review Figure 9 at end of learning activity).
2. In pairs, complete Worksheet No. 8 noticing the various aspects of using the chi-square statistic.
3. Explore the use of visual displays in the process of inferential data analysis with the Chi-Square statistic.
4. With the class, critique the inferential (chi-square) analysis process used in the assigned study by Smith, Curran, Weinstein and Griffiths.
In Lab - Introduction to Online Applet Program and Chi-Square Statistics
1. Attend lab to familiarize yourself with the VassarStats Chi-Square Analysis statistic software:.
1a. Vassar Stats Calculator for Chi Square Test of Independence
1b. Vassar Stats Calculator for One Way Goodness of Fit Test
2.a) Begin to work with quantitative data by performing Chi-Square statistics using the Applet as directed during lab session.
RESOURCES:
VassarStats Main Page (all calculators): http://faculty.vassar.edu/lowry/VassarStats.html
In Reflection
1.1.Reflect on your comfort level with using the online software for statistical analysis.
2.How does the Chi-Square statistic and inferential statistics in general add depth and understanding to nursing research and evidenced based practice?
References
Dempsey, P. & Dempsey, A. (1996). Nursing research: Textbook and workbook. Toronto: Little & Brown
Lo Biondo-Wood, G. & Haber, J. (2002). Nursing research: Methods, critical appraisal & utilization (5th ed). Toronto: Mosby.
Nieswiadomy, R. (2002). Foundations of nursing research. Stamford, CT: Appleton & Lange.
Polit, D. (1996). Data analysis and statistics for nursing research. Stamford, CT: Appleton & Lange.
Smith, R., Curran, J., Weinstein, S. & Griffiths, L. (2001). Investigation of glutathione S-transferase zeta and the development of sporadic breast cancer. Breast Cancer Research, 3, 409 - 411.
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Welcome to NRSG 4120!
Chi Square PPT
Figure 8: Testing Statistical Hypotheses
LA#9: Practice Worksheet
Chi Square Formula & DFs
Data and Contingency Tables
CHI SQUARE CALCULATORS
Vassar Stats Calculator for Chi Square Test of Independence
Vassar Stats Calculator for One Way Goodness of Fit Test
The Chi Square Statistic (has calculator, nice overview)
CRITICAL VALUE TABLES
Chi Square Critical Values Table
Vassar Chi Square Critical Values Table
Critical Value Table for small samples
VISUAL AIDS & PRACTICE
Ip and Nadi Video on Chi Squares (12 min - excellent!)
Ip and Nadi Assignment
Ip and Nadi Study Guide
Chi Square Workshop - (Nice simple intro)
Chi Square Test of Independence In-class Practice
Chi Square Goodness of Fit In-class Practice
FURTHER THEORY & PRACTICE
Another Test of Independence
Chi Square Procedures (PPT)
Chi Squares and Confidence Intervals Calculator (good for checking if Chi is within a selected CI)
Chi Square Demonstration
The Chi square Test Tutorial
COURSE ASSIGNMENTS
The assignments include one Group Qualitative Analysis project and Five Quantitative Worksheets. Click on the link below for Assignment software and other resources.
ONLINE SOFTWARE & RESOURCES FOR ASSIGNMENTS
Downloading Files
Most files are in PDF, DOC, or RTF format. If you have trouble viewing them online,
try right-clicking on the link, and select "Save Target as". Remember which folder you saved the file in.
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