Ch. 6 Correlation

1. Introduction

- A. Uses

1. First step in determining cause-effect

2. Evaluation of tests

2. Scatter plot: defined as the graph of paired X and Y values.

a. How to

STUDENT | STATS GRADE | ANXIETY SCORE |

1 | 7 | 3 |

2 | 5 | 4 |

3 | 2 | 9 |

4 | 6 | 4 |

5 | 10 | 1 |

b. Linear Relationship vs. Curvilinear Relationship

3. Equation of a straight line:

- i. find slope:

- ii. Find a=Y-bX

- iii. Substitute values

4. Types of relationships

a. Positive

b. Negative

c. Perfect

d. Imperfect

5. Correlation/Correlation coefficient

A. Magnitude, Direction of correlation coefficient

B. Link between scatter plot and correlation coefficient

3.Pearson r

A. Definitions 1: Pearson r measures the extent to which paired scores occupy the same or opposite position within their own distributions

TEST | MEAN | STANDARD DEVIATION | RAW SCORE |

Assignment | 15 | 2.5 | 16(80%) |

Test | 36 | 6 | 48(80%) |

B. Qualities

1. Independent of scale units, number of subjects, differences in variability

4. Calculation of Pearson r

5. Pearson r and explained variability

A. coefficient of determination

6. Other correlation coefficients

A. Spearman Rho

Chair Rankings (X) | Agency Rankings (Y) |

2 | 4 |

1 | 3 |

3 | 1 |

4.5 | 2 |

4.5 | 5 |

7 | 10 |

8 | 7 |

6 | 7 |

9 | 7 |

10 | 9 |

6. Effect of range on correlation

A. Restricted range

7. Correlation and causation

- A. correlation does not imply causation

- a. Accident of sampling

- . X -> Y

- Y -> X

- . Z

X Y