# ANOVA Homework

ANOVA

StudentID | Major | Exam 1 (x_{i}) | ()^{2} | Exam 2 (y_{i}) | ()^{2} | () () | ||

001 | Art | 85 | 5 | 25 | 80 | 0 | 0 | 0 |

002 | Science | 70 | -10 | 100 | 75 | -5 | 25 | 50 |

003 | Science | 90 | 10 | 100 | 92 | 12 | 144 | 120 |

004 | Humanities | 65 | -15 | 225 | 75 | -5 | 25 | 75 |

005 | Art | 90 | 10 | 100 | 72 | -8 | 64 | -80 |

006 | Humanities | 80 | 0 | 0 | 84 | 4 | 16 | 0 |

007 | Science | 74 | -6 | 36 | 80 | 0 | 0 | 0 |

008 | Art | 73 | -7 | 49 | 67 | -13 | 169 | 91 |

009 | Science | 95 | 15 | 225 | 92 | 12 | 144 | 180 |

010 | Humanities | 78 | -2 | 4 | 83 | 3 | 9 | -6 |

N=10 | 80 | 864 | 80 | 596 | 430 |

ANOVA for Exam 1

**1) Find the group means**

Mean for Art students

Mean for Science students

Mean for Humanities Students

**2) Compute the Between Group Variance**

**a. subtract each group mean from the overall mean,**

**b. square the difference**

**c. multiply by number of group members**

**d. repeat for each group**

Art Students: 21.39

Science Students:

Humanities Students:96.45

**e. Sum the 3 values from above (the result is the between group sums of squares)**

**f. Divide between group sums of squares by number of groups minus 1 (the result is the between group variance)**

__3. Find Within Group Variance__

**a. Subtract each score from its group mean, square the difference**

Art Students:

Science Students:

Humanities Students

**b. sum the resulting values (the result is the within group sums of squares)**

**Art:**

**Science:**

**Humanities:**

**Totals=**

**c. divide within group sums of squares by number of cases minus number of groups (the result is the within group variance)**

__3. Compute F:__

__a. Divide the between group variance by the within group variance__

__4. Find the degrees of freedom and test the null hypothesis of no association__

__5. Find the variance explained__

SS_{between}/ SS_{total= } Variance Explained

**a. Find the total sums of squares, this value is the sum of the between and within group sums of squares, and the sums of squares for Y**

**b. divide between group sums of squares by total**.

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