VIEWS: 10 PAGES: 41 POSTED ON: 8/1/2011
Analyzing Quantitative Research Data The purpose of this session is to FAMILIARIZE you with some base data analysis techniques, NOT to make you an expert statistician. Purpose of Data Analysis Describe or summarize data clearly Search for consistent patterns or themes among data Enable you to answer your research questions Why Use Statistics? Statistics are powerful tools that help people understand interesting phenomena. “Whether you are a student, a researcher, or just a citizen interested in understanding the world around you, statistics can offer one method for helping you make sense of your environment” (Urdan, 2001). Options for Calculating Statistical Analysis Technological advances have made the process of statistically analyzing data easy enough for non-statisticians to do. While there are numerous statistical analysis programs available, most educators have easy access to Microsoft Excel which is capable of calculating even advanced statistical analysis. Hands On-Activities In the slides that follow, you will have directions and see examples of how to actually analyze your data using Microsoft Excel. While reading these slides may be meaningful, I encourage you to work through the examples actually using Excel rather than just reading about how to do it. Types of Statistical Analysis Descriptive Used to describe and summarize data Inferential Used to make inferences or predictions about the similarity of a sample to the population which from which the sample is drawn. Common Types of Descriptive Statistics Percentage (and usually the Frequency) The number per 100 individuals who achieved a certain score. Mean The arithmetic average of a distribution of scores Standard Deviation The average deviation between the individual scores in the distribution and the mean for the distribution Descriptive Analysis Our Scenario: RQ: How do teachers feel about Supervisor support? Our Task: We will use this example to do a few things: Generate Frequency and Percentage data Calculate the Mean Calculate the Standard Deviation The Layout The Task Step-by-Step Movie demonstrating how to complete the steps. Raw Data – Supervisor Questionnaire Question 1 only Frequency and Percentage From the raw data in the previous slide, we now need to summarize the frequency and percentage of responses for Item 1 on your questionnaire. Calculating the Frequency in Excel Click in the cell where you want the percentage to be displayed. Click the fx to open up the Functions box. Select ALL from the SELECT a CATEGORY Dropdown Menu Select SUM from the SELECT a FUNCTION list (list is in alphabetical order) Select the cells you want to include in the sum calculation. Click OK. How to Calculate the Frequency How to Calculate the Frequency Right click the link above and select OPEN URL. This will attempt to launch Windows Media Player OR Real Player so you can view the movie. Calculating the Percentage in Excel Click in the cell where you want the percentage to be displayed. Click the fx to open up the Functions box. Select STATISTICAL from the SELECT a CATEGORY Dropdown Menu Select AVERAGE from the SELECT a FUNCTION list (list is in alphabetical order) Select the cells you want to include in the average calculation. Click OK. How to Calculate Percentages How to Calculate Percentages Right click the link above and select OPEN URL. This will attempt to launch Windows Media Player OR Real Player so you can view the movie. Frequency and Percentage Frequency & Percentage Table for Item 1 Strongly Agree Agree Disagree Strongly Disagree # % # % # % # % Item 1 0 0 1 3% 24 75% 7 22% Warning!!!!! Your book provides an example which calculates the mean and standard deviation for questionnaire items that use a likert scale. Given the attitudinal nature of the responses, it is really NOT appropriate to report such responses using a mean or standard deviation. Such responses are most appropriately reported as frequencies and percentages. Scenario - Mean You are teaching 6th grade math and are interested in examining the effect of using the Wii Big Brain Academy to reinforce basic math and problem solving skills. H1: Use of the Wii Big Brain Academy will increase the basic math skills for 6th grade students at XYZ Middle School. The Design A One-Group pre-test/post-test design will be used determine if the use of the Wii improves student performance. All 20 students in your 2nd period 6th grade math class will take a pre-test that measures their basic math and problem solving skills. You will then implement the use of the Wii for 10 minutes each day for 1 week to reinforce the math and problem solving skills. All 20 students will then take a post test that measures their math and problem solving skills. When to Use Mean When you want to determine the “typical” or average level of performance for a group. As we prepare to ultimately analyze data to prove or disprove our hypothesis, we must first find the average scores on the pre-test and post-test for both 6th grade classes. Calculating the Mean in Excel Click in the cell where you want the mean to be displayed. Click the fx to open up the Functions box. Select the AVERAGE Function from the SELECT a FUNCTION List. Select the cells you want to average. Click OK. Movie of How to Calculate the Mean How to Calculate the Mean Right click the link above and select OPEN URL. This will attempt to launch Windows Media Player OR Real Player so you can view the movie. When to Use Standard Deviation When you need to determine how much a set of scores vary from each other. For the purpose of this scenario, Let’s determine the standard deviation among the student’s scores on the pre-test and then on the post-test. Calculating Standard Deviation in Excel Click in the cell where you want the standard deviation to be displayed. Click the fx to open up the Functions box. Select STATISTICAL from the SELECT a CATEGORY Dropdown Menu Select STDEV from the SELECT a FUNCTION list (list is in alphabetical order) Select the cells you want to include in the standard deviation calculation. Click OK. How to Calculate Standard Deviation How to Calculate Standard Deviation Right click the link above and select OPEN URL. This will attempt to launch Windows Media Player OR Real Player so you can view the movie. Inferential Statistics Cheat Sheet Descriptive Research Descriptive Statistics Design (mean, standard deviation, percentages) Correlational Research Correlation Coefficient Design Experimental & Quasi- t-test, sign-test, Mann- Experimental Whitney U-test, ANOVA, ANCOVA Correlation Coefficient Used to examine relations between two or more variables. Strength of the Correlation -1.0 – 1.0 (closer the number is to -1 or +1 the stronger the relationship) Types of Correlation Positive Correlation Negative Correlation No Correlation Pearson Product Moment Correlation Coefficient = r Scenario In this example, we are interested to know if there appears to be a relationship between the number of hours students study for a test and their test scores. Example 1 Raw Data Participants Hours Studying Exam Score Participant 1 2 80 Participant 2 3 85 Participant 3 1 70 Participant 4 8 90 Participant 5 9 95 Calculating the Correlation Coefficient Click in the cell where you want the standard deviation to be displayed. Click the fx to open up the Functions box. Select ALL from the SELECT a CATEGORY Dropdown Menu Select CORREL from the SELECT a FUNCTION list (list is in alphabetical order) Select the cells you want to include in the standard deviation calculation. (Array 1 = 1st group of numbers # of hours studying, Array 2 = 2nd group of numbers exam scores) Click OK. How to Calculate the Correlation Coefficient How to Calculate the Correlation Coefficient Right click the link above and select OPEN URL. This will attempt to launch Windows Media Player OR Real Player so you can view the movie. Negative Correlation Negative Correlation Example Right click the link above and select OPEN URL. This will attempt to launch Windows Media Player OR Real Player so you can view the movie. No Correlation No Correlation Example Right click the link above and select OPEN URL. This will attempt to launch Windows Media Player OR Real Player so you can view the movie. Group Comparison Data Analysis Strategies Sign Test t-Test Mann-Whitney U-Test Sign Test Used to determine whether posttest scores are different from pretest scores for one group (single variable = test scores). Determines significance of difference between means of one group. Used with One-Group Pretest/Posttest design Scenario Going back to our previous example of the 6th grade match class using a one-group pre/post test design… Our directional hypothesis was: Use of the Wii Big Brain Academy will increase the basic math skills for 6th grade students at XYZ Middle School. Preparing for the Sign Test Note the pretest score for each participant Note the posttest score for each participant Indicate whether there is a POSITIVE difference (+), a NEGATIVE difference (-), or NO difference (0) in the pretest / posttest scores for each student. Calculating the Sign Test Note the total number of participants (N=) Count the number of students whose scores were not the same (all students with a + or -) Change the N= to be the total number of students whose scores changed. Count the number of Pluses Count the number of Minuses Which number is smaller? Assign that number to X = _____ Calculating the Sign Test Cont. Using the N= and the X=, refer to a “Sign Table” to determine the probability Typical level of significance = .05 (means there is a 5% chance error factor Sign Test uses .10 level of significance which is less stringent Determine if the number on your Sign Test Table is greater than or less than .10. If less than .10 the scores are significantly different, if greater than .10 the scores are NOT significantly different. How to Calculate the Sign Test How to Calculate the Sign Test Right click the link above and select OPEN URL. This will attempt to launch Windows Media Player OR Real Player so you can view the movie. Next Steps In part 2 we will examine how to determine a t-test, the Mann-Whitney U-test, and how to analyze qualitative data. In Vista, click on the Analyzing Data Website and then click on Analyzing Data PPT (part 2).