Social Web Analytics

Question 1 –Chi Square, Confidence Interval

The table below shows the counts of reach by age group and gender for a particular facebook page.

13–24 | 25–34 | 35–44 | 45+ | Total |

F | 7 | 19 | 42 | 7 | 75 |

M | 24 | 44 | 45 | 12 | 125 |

Total | 31 | 63 | 87 | 19 | 200 |

The owner of this page is interested in determining whether the age profile of reach varies by gender.

(a) Find expected counts for each entry in the table assuming gender and age group

are independent.

Expected Count = (Column Total*Row Total)/Total in sample (n)

Eg. Females 13-24

(31*75)/200=11.63

EXPECTED COUNTS FOR EACH CATEGORY (PART A) |

| 13-24 | 25-34 | 35-44 | 45+ | Total |

Female | 11.63 | 23.63 | 32.63 | 7.13 | 75 |

Male | 19.38 | 39.375 | 54.38 | 11.88 | 125 |

Total | 31 | 63 | 87 | 19 | 200 |

(b)Calculate a X2 statistic for testing whether the age profile varies by gender, and

state its degrees of freedom.

OBSERVED COUNTS VS (EXPECTED COUNTS) (PART B) |

| 13-24 | 25-34 | 35-44 | 45+ | Total |

Female | 7(11.63) | 19(23.63) | 42(32.63) | 7(7.13) | 75 |

Male | 24(19.38) | 44(39.375) | 45(54.38) | 12(11.88) | 125 |

Total | 31 | 63 | 87 | 19 | 200 |

To calculate the X statistic (X2) you have to do the (O-E)^2/E bit of the formula for each expected value and add them all together:

O= Observed count

E= Expected count

Eg. On Calc of Female 13-24

Eg. On Calc of Female 13-24

X2 statistic = 8.70

Degree of freedom = (Rows-1)*(Columns-1) = (2-1)*(4-1) = 3

(c)Computea95%confidenceintervalfortheproportionoffemales. (Recallthat

z0.025=1.960)

p=75/200 (0.375)(proportion of sample)

n=200 (number in sample)

z=1.960 (95%)

Formula:

∆ = z * √(p(1-p)/n)

∆ = 1.960 * √(0.375*(1-0375)/200) = 0.067

Confidence Interval = p±∆ = 0.375±0.067 = (0.308, 0.442)

Question 2 –Stopwords, Document-Term Matrix, Cosine Similarity, TF-IDF Weight

Using the three documents:

i. Go dog, go!

ii. Stop cat, stop

iii. The dog stops the cat and...