YSU



Miss DeHaven Explores Test Score Reliability - Pearson Correlation

With Spearman-Brown Correction

Victoria DeHaven, one of the most dynamic new teachers at Hubbard High School, wants to help her 12th grade students to do well on the Ohio Graduation Test (OGT) by integrating test preparation into daily classroom activities. Miss DeHaven decides the first step is to familiarize her students with the format of a standardized test. At the conclusion of a unit about grammar, she creates a test of 50 multiple-choice items and administers it to the 21 students in her Senior English class.

She wondered if the test scores she has obtained show evidence of reliability. She decides to do a split-half reliabilty test. She knows her first step is to split the test into two components (odd and even) and compute a correlation coefficient.

She begins by organizing the test score results using a data table as follows:

|Student’s Name |Total Correct |Odd Numbered Correct |Even Numbered Correct |

|Amy |43 |19 |24 |

|Stephanie |44 |23 |21 |

|Bruce |38 |20 |18 |

|Chris |46 |22 |24 |

|Ava |33 |13 |20 |

|Mandy |48 |24 |24 |

|Gavin |37 |20 |17 |

|Scott |34 |16 |18 |

|Haley |41 |19 |22 |

|Logan |25 |10 |15 |

|Jeron |44 |21 |23 |

|Jayden |42 |18 |24 |

|Sydnie |33 |12 |11 |

|Kelly |48 |23 |25 |

|Madison |41 |21 |20 |

|Michael |42 |23 |19 |

|Adrienne |46 |21 |25 |

|Aleesa |36 |17 |19 |

|Dylan |45 |24 |21 |

|Jaime |36 |17 |19 |

|Meredith |28 |16 |12 |

(Case Study continued on next page)

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Miss DeHaven then moves to the internet calculator and enters the data. She provides the “x” and “y” axis labels and clicks on “compute”. She checks the number of observations box to make sure all the data were counted and there are no blank spaces, then looks at Pearson Correlation value (.65) and the scatter plot. What initial conclusions might she make?

Victoria knows that by using this “split-half” approach we reduced the number of items in the test (from 50 to 25) and that this reduction will automatically reduce the reliability of the test scores. So, she must now plug this Pearson Correlation value (.65) into the Spearman Brown Split-Half “correction” Formula to estimate the reliability of the whole test.

rsb = 2rxy /(1+rxy)

where rxy is the old Pearson reliability coefficient

where rsb is the new Spearman Brown correction reliability coefficient

rsb = 2 x .65 / 1 + .65 =

rsb = 1.30 / 1.65

rsb = .787

What is you final conclusion about the reliability of the test scores?

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PERFORMANCE TASKS POINT TABLES

ROLL OF THE DICE - STATISTICS PERFORMANCE DEMONSTRATION

In demonstrating your understanding of the Pearson Correlation statistic, the 20 points are divided as follows:

01-03 Data are keyed into internet calculator correctly

01-03 Chart Options are provided (the Scatter Plot’s look: label X-axis and Y-axis)

01-04 Instructor asks about the concepts of positive and negative correlation; explained correctly

01-04 Instructor asks why Pearson “r’”, not Spearman “r”, is used with the data; explained correctly

01-03 Instructor asks about Spearman Brown Split-Half “correction”; reasonable answer provided

01-03 Instructor asks about conclusions from the data analysis; reasonable conclusions provided

EXTRA CREDIT - SCENARIO CREATION PERFORMANCE DEMONSTRATION

In creating your own Pearson Correlation exercise, the 15 points are divided as follows:

01-03 Realistic and appropriate scenario related to school teaching

01-03 Data are created accurately

01-03 Data are keyed into internet calculator correctly

01-02 Instructor asks about the concepts of positive and negative correlation; explained correctly

01-02 Instructor asks why Pearson “r’”, not Spearman “r”, is used with the data; explained correctly

01-02 Instructor asks about conclusions from the data analysis; reasonable conclusions provided

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