Q.1 Lift Analysis. Chips&Burgers.

Sausages 
^Sausages 
Burgers 
600 
400 
1000 
^Burgers 
200 
200 
400 

800 
600 
1400 
Lift(Burgers, Chips) = (600/1400)/ ((800/1400)*(1000/1400)) = 1.05
Lift(Burgers, Chips)>1 → Positive Correlation.
Lift(Burgers, ^Chips) = (200/1400)/ ((800/1400)*(400/1400)) = 0.875
Lift(Burgers, ^Chips) <1 → Negative Correlation.
Lift(^Burgers, Chips) = (200/1400)/ ((800/1400)*(400/1400))= 0.875
Lift(^Burgers, Chips) <1→ Negative Correlation.
Lift(^Burgers, ^Chips) = (200/1400)/ ((60/1400)*(200/1400)) = 2.3
Lift(^Burgers, ^Chips) >1 → Positive Correlation.
2. Lift Analysis. Ketchup&Shampoo.

Shampoo 
^Shampoo 
Ketchup 
100 
200 
300 
^Ketchup 
200 
400 
600 

300 
600 
900 
Lift(Ketchup, Shampoo)= (100/900)/ ((300/900)*(300/900)) = 1 →
→ Independent correlation.
Lift(Ketchup, ^Shampoo) = (200/900)/ ((600/900)*(300/900)) = 1 →
→ No correlation.
Lift(^Ketchup, Shampoo) = (200/900)/ ((300/900)*(600/900)) = 1 →
→ No correlation.
Lift(^Ketchup, ^Shampoo) = (400/900)/ ((600/900)*(600/900)) = 1 →
→ Independent.
Q.3. Chi Squared Analysis. Burgers&Chips.

Chips 
^Chips 
Burgers 
900 (800) 
100 (200) 
1000 
^Burgers 
300 (400) 
200 (100) 
500 
Total Column 
1200 
300 
1500 
χ^2=((900800)^2)/800 + ((100200)^2)/200 +
+((300400)^2)/400 + ((200100)^2)/100 = 187.5
χ^2 >0 → There is correlation.
Burgers and Chips: 900 sold, 800 expected → positive correlation.
Burgers and Not Chips: 100 sold, 200 expected → negative correlation.
Chips and Not Burgers: 300 sold, 400 expected → negative correlation.
Not Chips and Not Burgers: 200 sold, 100 expected→ positive correlation.
Q.4. Chi Squared Analysis. Burgers and Sausages.

Sausages 
^Sausages 
Burgers 
800 (800) 
200 (200) 
1000 
^Burgers 
400 (400) 
100 (100) 
500 

1200 
300 
1500 
χ^2=((800800)^2)/800 + ((200200)^2)/200 + ((400400)^2)/400 + ((100100)^2)/100 =0 χ^2=0 → There is no correlation.
Each paired combination got the same value observed and expected.
Q.5. When is Lift and Chi Squared a poor algorithm?
When you are using really large numbers, there is going to be a huge swing in the Lift value which will result in great limitation. Nullinvariant measures were invented for this purpose, for example, Jaccard Coefficient, Kulczynski measure.