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User’s Guide Table of Contents Poster Copy Download Information Installation Information Usage Survey Menus Definitions Z-test Single Sample t-test Dependent t-test Average standard deviation denominator example Standard deviation of differences denominator example Independent t-test Hedge’s g example Glass’s delta example Correlation 1 2 3 4 5 6 8 9 11 13 15 16 17 20 21 22 2 Download MOTE Go to http://www.aggieerin.com/mote. Click download on the left hand side of the screen. Copy the program to somewhere you can find the file on your computer. 3 Install MOTE Make sure you have at least JAVA 6.0 by verifying your version here. Link: http://java.com/en/download/installed.jsp That’s it! Double click MOTE.jar to get started. Double click to go! 4 Survey Please note you can fill this survey out online here or email the lab directly here. Link: http://aggieerin.com/mote/survey.php Email: [email protected] Not at all 1 1 1 1 1 1 1 How helpful is the user’s guide? How readable is the user’s guide? How complete is the user’s guide? How easy is MOTE to download/install? How easy is MOTE to use? How applicable is MOTE to what you do? How useful would MOTE be for teaching? Overall, I think MOTE is: I would use MOTE to: I would suggest for MOTE: I experienced errors (please explain): I found incorrect calculations (please explain): 5 2 2 2 2 2 2 2 Somewhat 3 3 3 3 3 3 3 4 4 4 4 4 4 4 Very 5 5 5 5 5 5 5 Menus The edit menu contains the reset button to clear out your data. The measures menu contains the different options for effect sizes listed by effect size and type of test. 6 The help menu contains links to the user’s guide and an about window (coming soon!). 7 User’s Guide Cohen’s d Cohen’s d is one of the most well-known calculations for effect size. The general formula gives the standardized distance between the two population means, or how much the two populations do not overlap. The formula for d is very adaptive and can be used for many different between samples and within samples tests. As such, each test is listed, followed by the formula for d for that test, as well as how to find the information for the calculation in both SPSS and SAS. Related effect sizes: Hedge’s g As Cohen’s d tends to be positively biased, Hedge’s g corrects for this to create an unbiased calculation. Glass’s delta Glass’ delta is a form of effect size found by dividing the difference of the two groups by the standard deviation of only the control group. 8 Z-test Cohen’s d can be found in two ways for a Z-test: 1. By using the means of the populations: 𝑀−𝑢 (1) 𝑜 2. By using the z-statistic: 𝑍 (2) √𝑁 The values for the mean of the population (µ) and the standard deviation of the population (σ) should already be known. The mean for the sample and number of people in the sample can be found in your SPSS output as follows: Descriptive Statistics N Mean KnowlOfES 30 Valid N (listwise) 30 12.8000 Number of individuals in the sample Examples for SAS output as follows: Number of individuals in the sample Sample mean 9 Sample mean Example: So, let us assume that the population has a mean of 10 on our “knowledge of effect size” scale, with a standard deviation of 2. Given the information above, we know that we have a sample mean of 12.8 with 30 people in our sample. Through the program: By putting this in MOTE we come up with an effect size of 1.4 with a lower 95% confidence limit of -2.52, and an upper 95% confidence limit of 5.32. 10 Single Sample t-test Cohen’s d can be found in two ways for a single sample t-test: 1. By using the means of the populations: 𝑀− 𝜇 (3) 𝑆𝐷 2. By using the t-statistic: 𝑡 (4) √𝑁 The value for the mean of the population (µ) should already be known. The mean and standard deviation for the sample as well as the number of people in the sample can be found in your SPSS output as follows: Number of individuals in the sample Sample mean Sample standard deviation t-statistic The same information can be found in your SAS output as follows: Number of individuals in the sample Sample standard deviation Sample mean t-statistic 11 Example: If you have a known population mean of 7 and want to know the difference between the population and your sample, you would input your information into MOTE and get an effect size of -0.43, with a lower 95% confidence limit of -0.77, and an upper 95% confidence limit of -0.08. 12 Dependent Samples t-test Cohen’s d can be found in three ways for a dependent samples t-test: 1. By using the average standard deviation: 𝑀𝑑𝑖𝑓𝑓 (5) (𝑆𝐷1+𝑆𝐷2)⁄2 2. By using the difference of the standard deviations: 𝑀𝑑𝑖𝑓𝑓 (6) 𝑆𝐷𝑑𝑖𝑓𝑓 3. By using the t-statistic: 𝑡 √𝑁 (7) The necessary information can be found in your SPSS output as follows: Sample standard deviation time 1 Sample standard deviation time 2 Number of individuals in the sample Mean difference Standard deviation of the difference scores t-statistic 13 The same information can be found in your SAS output as follows: Sample standard deviation time 1 Number of individuals in the sample Mean difference Standard deviation of the difference scores Sample standard deviation time 2 t-statistic 14 Example: If we are looking for a difference on a measure between time one and time two, we can either use our Dependent t (Averages) page with the following information to produce an effect size of -0.06, with a lower 95% confidence interval of -0.35, and an upper 95% confidence limit of 0.23. 15 Or, we can use our Dependent t (SD Difference) page with the following information to produce an effect size of -0.07, with a lower 95% confidence interval of -0.36, and an upper 95% confidence limit of 0.22. 16 Independent Samples t-test Cohen’s d can be found in three ways for an independent samples t-test: 1. By using the pooled standard deviation: 𝑀1−𝑀2 (8) 𝑆𝑝𝑜𝑜𝑙𝑒𝑑 Where Spooled is found by: (𝑛−1)𝑆𝐷2 +(𝑛−1)𝑆𝐷2 √ (9) 𝑛+𝑛−2 2. By using the t-statistic and the degrees of freedom: 2𝑡 (10) √𝑑𝑓 3. By using the t-statistic and number of individuals in the sample: 𝑛+𝑛 𝑡 √( 𝑛∗𝑛 )( 𝑛+𝑛 ) (11) 𝑛∗𝑛−2 Additionally, Hedge’s g can be calculated by multiplying your d found above by a correction factor for independent samples t-tests: 1−( 3 4(𝑛+𝑛)−9 ) (12) Also, you can calculate Glass’s delta for independent samples t-tests, by using the standard deviation of the control group: 𝑀−𝑀 (13) 𝑆𝐷𝑐𝑜𝑛𝑡𝑟𝑜𝑙 17 The necessary information can be found in your SPSS output as follows: Mean of group 1 Number of individuals in group 1 Mean of group 2 Standard deviation of group 1 Standard deviation of group 2 Number of individuals in group 2 t-statistic Degrees of freedom The same information can be found in your SAS output as follows: Mean of group 1 Number of individuals in group 1 Number of individuals in group 2 Mean of group 2 Standard deviation of group 1 Standard deviation of group 2 Pooled standard deviation t-statistic Degrees of freedom 18 Example: If you are looking for differences between two independent groups, for instance a control group (group 1) and a treatment group (group 2), you can input the information into the Independent t Test page to produce an effect size of -0.71, with a lower 95% confidence interval of -1.21, and an upper 95% confidence limit of -0.20. 19 Similarly, you can input the information into the Hedge’s g - Independent t Test page to produce an effect size of -0.70, with a lower 95% confidence interval of -1.21, and an upper 95% confidence limit of -0.20. 20 You could also input the information into the Glass’s delta - Independent t Test page to produce an effect size of -0.87, with a lower 95% confidence interval of -1.21, and an upper 95% confidence limit of -0.20. 21 Correlation Cohen’s d can be found with the information for r in one way: 1. By using the obtained value of r: 2 4𝑟 √ ⁄(1 − 𝑟 2 ) (14) The necessary information can be found in your SPSS output as follows: Correlations DataA DataB Pearson Correlation 1 .451** Sig. (2-tailed) .001 N 50 50 ** DataB Pearson Correlation .451 1 Sig. (2-tailed) .001 N 50 50 **. Correlation is significant at the 0.01 level (2-tailed). DataA Correlation coefficient (r) Number of individuals in the sample The same information can be found in your SAS output as follows: Number of individuals in the sample Correlation coefficient (r) 22 Example: Suppose a researcher is trying to identify if a relationship exists between two variables that we will designate DataA and DataB. To determine if these two variables are correlated we will run a bivariate correlation and use the output in MOTE page to produce an effect size of 1.01, with a lower 95% confidence interval of 0.20, and an upper 95% confidence limit of 0.79. 23