Summary When implementing an intervention, scientists will compare a control group against a group that receives the intervention. Various statistical analyses can help demonstrate whether the groups are significantly different or similar. In this project we will be comparing two data sets by determining several statistics for each of the data sets. Project Objectives This project will further student understanding of the following MATLAB concepts: Using MATLAB Docs math and stats functions arrays usage of mat files the ttest function colon operator output statements assignment statements multiple return values . . Project Setup To set up the project acquire the starter code and the project's main and alternate mat files for testing. 1. Use the project's starter code to create a new script within MATLAB and name it project2.m. 2 Use the project's mat files as the basis for importing variables stored in the mat into your workspace in part 1 of your implementation. You may change the values or create your own mat files for testing, but your final submissions should use the same filename as the one provided. 3. Read through all the project instructions before implementing any steps. It is always good to understand or at least know what the entire project is prior to implementing the first part. This way you know all the pieces and don't accidentally implement an early part that will not play nice with later parts and force you to redo work. Project Implementation Part 1: Importing the.mat Variables The project's mat file has two variables in it, data and N1 N1 is the size of the control group, and data is in a single array containing numerical data collected from both the control and the experimental groups. As mentioned in setup, complete this step by importing the "Project2_PresetVariables.mat" file for use in the remainder of your program. An alternate file is also provided so you can quickly execute a second test without generating your own, but you should perform your own testing in addition to testing with the two provided examples. Part 2: Split the Data Use the N1 variable to split the single array into two arrays named control and experimental. You must use these variable names for the respective data sets. N1 corresponds to the control group data, which is the first N1 elements in the provided data array Part 3: Calculate Per Group Stats You now have two sets of data. For each dataset you must calculate the following items and in the final step you will display the results. For each data set we will calculate the average value, the median or the middle of the data, the mode or the most often repeated value, the standard deviation, and the group size. Each is calculated similarly with a MATLAB function, recall we covered the length function in lecture, Part 3: Calculate Per Group Stats You now have two sets of data. For each dataset you must calculate the following items and in the final step you will display the results. For each data set we will calculate the average value, the median or the middle of the data, the mode or the most often repeated value, the standard deviation, and the group size. Each is calculated similarly with a MATLAB function, recall we covered the length function in lecture. For each dataset use the built-in MATLAB functions to calculate: mean mode median standard deviation . group size . Implementation Constraint: You may store most of your calculations into variables with names of your choosing, but the means and data group sizes must be stored in variables named controlMean, experimentalMean, and N2 (N1 is given). Part 4: Calculate Advanced Comparison Statistics There are many advanced statistical analyses to help compare groups based on the core group stats, and normally you would utilize the stats and the knowledge of the test methodology to inform your decision, but we are going to just use two tests specifically, the t-test to calculate a p-value and Cohen's d to calculate the effect size p-value: One of the methods for determining whether control and experimental groups are significantly different is to compare a p-value against a threshold. Thresholds of 0.01 or 0.05 are often used and the strictness of a threshold may vary by scientific area. One such test that generates a p-value is the student t-test. MATLAB has a built-in functions to perform a t-test named test and test2, but you will be implementing a version of Welch's t-test using the following formula. ( x1-x2) = (51)2 (S2)2 Where: X1 is the control group's mean X2 is the experimental group's mean S1 is the control group's standard deviation S2 is the experimental group's standard deviation N1 is the control group's size N2 is the experimental group's size tis the result (p-value) n1 na Implementation Constraint: Store the Welch's t-test calculation result in a variable named pvalue. Effect Size: Calculating Cohen's dis one method used to determine an effect size value. The effect size can be used to compare experiments done under different circumstances, and is often used in Effect Size: Calculating Cohen's dis one method used to determine an effect size value. The effect size can be used to compare experiments done under different circumstances, and is often used in combination with other analyses. The threshold values can change based on the scientific field, but generally 8.18 is considered a small impact, 0.30 is a medium impact, and 0.58 is a large impact. Implementation Constraint: Store the Cohen's d calculation result in a variable named effectSize. Cohen's d is calculated in two steps. For our evaluation, items with a 1 subscript refer to the control group's data and statistical calculations. 1. Calculate the pooled standard deviation 2. Use the pooled standard deviation and the group means to calculate Cohen's d. SD + SD SD pooled 2 SD pooled d=M, - M o - hp 2 5 8 6 7 00 T Y O [ 3 G H J K. Part 5: Display Results As the final step in your project implementation you should display the results of your calculations. Check the testing section for example executions of the program to provide guidance on what to display and how to display your results. Testing Testing within MATLAB We have provided two sample executions of the program for you to compare to, but you should thoroughly test your program with other possible values. Each corresponds to the mat files we have provided to you. To generate more data sets, try changing the N1 value to easily create different data sets or create your own small data sets. Do not rely on zyBooks to prove and assume correctness as your program will be graded automatically and manually by the TAS. >> project 2 Group Stats The control group has 4 participants. Mean: 71 Median: 86.5 Mode: 89 Standard deviation: 32.7516 >> project2 Group Stats The control group has 160 participants. Mean: 79.4875 Median: 88 Mode: 92 Standard deviation: 22.0528 The experimental group has 7 participants. Meani 82.7143 Mediant 92 Model 92 Standard Deviation: 18.6879 The experimental group has 165 participants. Mean: 74.4303 Median: 87 Mode: 93 Standard Deviation: 28.7071 Advanced Analyses desses Summary When implementing an intervention, scientists will compare a control group against a group that receives the intervention. Various statistical analyses can help demonstrate whether the groups are significantly different or similar. In this project we will be comparing two data sets by determining several statistics for each of the data sets. Project Objectives This project will further student understanding of the following MATLAB concepts: Using MATLAB Docs math and stats functions arrays usage of mat files the ttest function colon operator output statements assignment statements multiple return values . . Project Setup To set up the project acquire the starter code and the project's main and alternate mat files for testing. 1. Use the project's starter code to create a new script within MATLAB and name it project2.m. 2 Use the project's mat files as the basis for importing variables stored in the mat into your workspace in part 1 of your implementation. You may change the values or create your own mat files for testing, but your final submissions should use the same filename as the one provided. 3. Read through all the project instructions before implementing any steps. It is always good to understand or at least know what the entire project is prior to implementing the first part. This way you know all the pieces and don't accidentally implement an early part that will not play nice with later parts and force you to redo work. Project Implementation Part 1: Importing the.mat Variables The project's mat file has two variables in it, data and N1 N1 is the size of the control group, and data is in a single array containing numerical data collected from both the control and the experimental groups. As mentioned in setup, complete this step by importing the "Project2_PresetVariables.mat" file for use in the remainder of your program. An alternate file is also provided so you can quickly execute a second test without generating your own, but you should perform your own testing in addition to testing with the two provided examples. Part 2: Split the Data Use the N1 variable to split the single array into two arrays named control and experimental. You must use these variable names for the respective data sets. N1 corresponds to the control group data, which is the first N1 elements in the provided data array Part 3: Calculate Per Group Stats You now have two sets of data. For each dataset you must calculate the following items and in the final step you will display the results. For each data set we will calculate the average value, the median or the middle of the data, the mode or the most often repeated value, the standard deviation, and the group size. Each is calculated similarly with a MATLAB function, recall we covered the length function in lecture, Part 3: Calculate Per Group Stats You now have two sets of data. For each dataset you must calculate the following items and in the final step you will display the results. For each data set we will calculate the average value, the median or the middle of the data, the mode or the most often repeated value, the standard deviation, and the group size. Each is calculated similarly with a MATLAB function, recall we covered the length function in lecture. For each dataset use the built-in MATLAB functions to calculate: mean mode median standard deviation . group size . Implementation Constraint: You may store most of your calculations into variables with names of your choosing, but the means and data group sizes must be stored in variables named controlMean, experimentalMean, and N2 (N1 is given). Part 4: Calculate Advanced Comparison Statistics There are many advanced statistical analyses to help compare groups based on the core group stats, and normally you would utilize the stats and the knowledge of the test methodology to inform your decision, but we are going to just use two tests specifically, the t-test to calculate a p-value and Cohen's d to calculate the effect size p-value: One of the methods for determining whether control and experimental groups are significantly different is to compare a p-value against a threshold. Thresholds of 0.01 or 0.05 are often used and the strictness of a threshold may vary by scientific area. One such test that generates a p-value is the student t-test. MATLAB has a built-in functions to perform a t-test named test and test2, but you will be implementing a version of Welch's t-test using the following formula. ( x1-x2) = (51)2 (S2)2 Where: X1 is the control group's mean X2 is the experimental group's mean S1 is the control group's standard deviation S2 is the experimental group's standard deviation N1 is the control group's size N2 is the experimental group's size tis the result (p-value) n1 na Implementation Constraint: Store the Welch's t-test calculation result in a variable named pvalue. Effect Size: Calculating Cohen's dis one method used to determine an effect size value. The effect size can be used to compare experiments done under different circumstances, and is often used in Effect Size: Calculating Cohen's dis one method used to determine an effect size value. The effect size can be used to compare experiments done under different circumstances, and is often used in combination with other analyses. The threshold values can change based on the scientific field, but generally 8.18 is considered a small impact, 0.30 is a medium impact, and 0.58 is a large impact. Implementation Constraint: Store the Cohen's d calculation result in a variable named effectSize. Cohen's d is calculated in two steps. For our evaluation, items with a 1 subscript refer to the control group's data and statistical calculations. 1. Calculate the pooled standard deviation 2. Use the pooled standard deviation and the group means to calculate Cohen's d. SD + SD SD pooled 2 SD pooled d=M, - M o - hp 2 5 8 6 7 00 T Y O [ 3 G H J K. Part 5: Display Results As the final step in your project implementation you should display the results of your calculations. Check the testing section for example executions of the program to provide guidance on what to display and how to display your results. Testing Testing within MATLAB We have provided two sample executions of the program for you to compare to, but you should thoroughly test your program with other possible values. Each corresponds to the mat files we have provided to you. To generate more data sets, try changing the N1 value to easily create different data sets or create your own small data sets. Do not rely on zyBooks to prove and assume correctness as your program will be graded automatically and manually by the TAS. >> project 2 Group Stats The control group has 4 participants. Mean: 71 Median: 86.5 Mode: 89 Standard deviation: 32.7516 >> project2 Group Stats The control group has 160 participants. Mean: 79.4875 Median: 88 Mode: 92 Standard deviation: 22.0528 The experimental group has 7 participants. Meani 82.7143 Mediant 92 Model 92 Standard Deviation: 18.6879 The experimental group has 165 participants. Mean: 74.4303 Median: 87 Mode: 93 Standard Deviation: 28.7071 Advanced Analyses desses