EDUC7011 Lesson 21 - Introduction (Quantitative Variables) (cont'd)

A comparison between the Percentile Ranking for "Not assuming normality" and "Assuming Normality":

According to the textbook (p154):
Variables with distributions that are substantially non-normal will have greater discrepancies between percentile ranks compared computed using the two methods, and variables with relatively normal distributions will yield similar percentile ranks.

collgpa	Rank_CollGPA	PerRank_CollGPA (Not assuming Normality)	PerRank_CollGPA (Standardised) (Assuming Normality)	Difference in Rank (Not assuming Normality - Assuming Normality)	Zcollgpa
1.17	1	1	0	1	-2.92232
1.48	2	2	1	1	-2.23451
1.58	3	3	2	1	-2.01264
1.71	4	4	4	0	-1.7242
1.75	6	7	5	2	-1.63545
1.75	6	7	5	2	-1.63545
1.79	7	8	6	2	-1.5467
1.84	8	9	8	1	-1.43577
1.91	9	10	10	0	-1.28045
1.94	10	11	11	0	-1.21389
2	11	12	14	-2	-1.08077
2.01	12	13	14	-1	-1.05858
2.05	15	17	17	0	-0.96983
2.05	15	17	17	0	-0.96983
2.05	15	17	17	0	-0.96983
2.06	17	19	17	2	-0.94765
2.06	17	19	17	2	-0.94765
2.08	18	20	18	2	-0.90327
2.1	20	22	20	2	-0.8589
2.1	20	22	20	2	-0.8589
2.13	21	23	21	2	-0.79233
2.15	22	24	23	1	-0.74796
2.18	23	26	25	1	-0.6814
2.19	24	27	25	2	-0.65921
2.2	25	28	26	2	-0.63702
2.22	26	29	28	1	-0.59265
2.24	27	30	29	1	-0.54827
2.25	28	31	30	1	-0.52609
2.26	29	32	31	1	-0.5039
2.27	30	33	32	1	-0.48171
2.32	32	36	36	0	-0.37077
2.32	32	36	36	0	-0.37077
2.34	33	37	37	0	-0.3264
2.36	34	38	39	-1	-0.28203
2.37	36	40	40	0	-0.25984
2.37	36	40	40	0	-0.25984
2.38	37	41	41	0	-0.23765
2.41	38	42	43	-1	-0.17109
2.44	40	44	46	-2	-0.10453
2.44	40	44	46	-2	-0.10453
2.45	41	46	47	-1	-0.08234
2.46	42	47	48	-1	-0.06015
2.47	43	48	48	0	-0.03796
2.48	44	49	49	0	-0.01578
2.56	45	50	56	-6	0.16172
2.57	47	52	57	-5	0.18391
2.57	47	52	57	-5	0.18391
2.58	48	53	58	-5	0.2061
2.59	50	56	59	-3	0.22828
2.59	50	56	59	-3	0.22828
2.6	51	57	60	-3	0.25047
2.61	52	58	61	-3	0.27266
2.62	54	60	62	-2	0.29484
2.62	54	60	62	-2	0.29484
2.64	58	64	63	1	0.33922
2.64	58	64	63	1	0.33922
2.64	58	64	63	1	0.33922
2.64	58	64	63	1	0.33922
2.65	59	66	64	2	0.36141
2.66	60	67	65	2	0.38359
2.67	62	69	66	3	0.40578
2.67	62	69	66	3	0.40578
2.69	63	70	67	3	0.45016
2.72	64	71	70	1	0.51672
2.74	65	72	71	1	0.56109
2.75	67	74	72	2	0.58328
2.75	67	74	72	2	0.58328
2.79	68	76	75	1	0.67203
2.8	69	77	76	1	0.69422
2.81	70	78	76	2	0.7164
2.82	71	79	77	2	0.73859
2.85	72	80	79	1	0.80515
2.86	73	81	80	1	0.82734
2.93	75	83	84	-1	0.98265
2.93	75	83	84	-1	0.98265
2.94	77	86	84	2	1.00484
2.94	77	86	84	2	1.00484
2.95	78	87	85	2	1.02703
3.03	80	89	89	0	1.20452
3.03	80	89	89	0	1.20452
3.06	81	90	90	0	1.27109
3.07	82	91	90	1	1.29327
3.09	83	92	91	1	1.33765
3.13	84	93	92	1	1.4264
3.14	85	94	93	1	1.44859
3.25	86	96	95	1	1.69265
3.31	87	97	97	0	1.82577
3.34	88	98	97	1	1.89233
3.37	89	99	97	2	1.95889
3.45	90	100	98	2	2.13639