Chi-squared Flashcards
1
Q
RECAP
A
- CONTINUOUS variable COMPARED between 2 UNRELATED (BETWEEN) GROUPS=WRS (Wilcoxon Rank Sum)
- CONTINUOUS variable COMPARED between 2 RELATED (WITHIN) GROUPS=WMP (Wilcoxon Matched Pairs)
- COUNTS COMPARED between 2 UNRELATED GROUPS=BT (Binomial Test)
2
Q
CS
A
- CHI-SQUARED=COUNTS COMPARED between 3+ UNRELATED GROUPS (N-BY-1)/COMPARED RELATIONSHIP in COUNTS between 2 DIF categorical variables (CONTINGENCY)
3
Q
NB1
A
- Similar to binomial as asks whether observed freqs are dif to expected via N-by-1 table (ie. N columns/1 row)
4
Q
NB1 1
A
o 1. CALC EXPECTED COUNT o Sum counts/N= o OBS ATTACKS=41, 16, 37=94/N=3 o EXP ATTACKS=31.33, 31.33, 31.33 o Expresses extent of dif between OBS VS EXP under H0 (“goodness-of-fit”) o X^2=E((OBS-EXP)^2/EXP)
5
Q
NB1 2
A
o 2. FOR EACH CATEGORY, OBS-EXP
o OBS-EXP=9.67, -15.33, 5.67
6
Q
NB1 3
A
o 3. SQUARE VALUES
o (OBS-EXP)^2=93.4, 235.1, 32.1
7
Q
NB1 4
A
o 4. SQUARE DIF/EXP
o SQUARE DIF/EXP=2.98, 7.5, 1.02
8
Q
NB1 5
A
o 5. SUM=X^2
o 2.98+7.5+1.02=11.51
9
Q
NB1 6
A
o 7. CALC DF
o N=3; DF=N-1=2
10
Q
NB1 7
A
o 8. COMPARE TO CV IN TABLE o X^2CRIT=5.991 o STATSIG if GREATER than CV o 11.51>5.991; reject H0; prey not attacked equally o STATSIG!
11
Q
NBM (EG)
A
- Ie. (OBS) CO-OP: 3Y=12; 4Y=3
- (OBS) COMP: 3Y=6; 4Y=27
- What affects these infrequencies? Are they independent? Or is one dependant (ie. contingent) on the other?
- Age & play related; how? H0=age & play are independent.
12
Q
NBM 1
A
3Y 4Y TOTAL COOP 12 3 15 COMP 6 27 33 TOTAL 18 30 48 o EXP=(row sum x column sum)/TOTAL o EXP=(15x18)48=5.625 3Y 4Y TOTAL 5.625 9.375 15 12.375 20.625 33 18 30 48
13
Q
NBM 2
A
o 2.EXTENT OF DIF o X^2=E((OBS-EXP)^2/EXP) o X^2=(12-5.625)^2/5.625 o + (3-9.375)^2/9.375=4.335 o + (6-12.375)^2/12.375=3.284 o + (27-20.625)^2/20.625=1.970 o = 7.225 +4.335 + 3.284 + 1.970 o = 16.8
14
Q
NBM 3
A
o 3. COMP W/CV
o DF=1 (remember, multi-tailed as lots of directions for data)
o X^2CRIT=3.841; X^2=16.8; DF=1
o STATSIG!
o Play styles differ sig according to age (more coop at 3; more comp at 4)
15
Q
CS EVA
A
- Chi-squared assumes all EXP is 5; if untrue, may be invalid; E<5 may lead to loss of power/sensitivity rather than increasing risk of incorrect conclusion of relationship.
