Lab 1: Data Summaries

Background

Categorical Data

A variable is classified as categorical when the outcomes fall into groups. The groups have no inherent order. When summarizing categorical data the typical numerical summary is reporting percentages and modes, where the graphical summaries are pie charts and bar charts.

Numerical Data

A variable is classified as numerical when the outcome fall into a range of values. The numbers specify an order. Continuous data can have any value in the range (fractions or decimals). Discrete data has to be a whole number. When summarizing numerical data there are two main options. The mean and standard deviation or the median and inter-quartile range (IQR). The mean and standard deviation are the best choice for symmetrical (non-skewed) data set, where the median and IQR are more representative of typical values in a skewed data set. The graphical summaries include histograms and box plots.

Lab

The lab today consists of two different data sets for which we will work on a data exploration. For each set you will describe the data with both graphical and numerical summaries and then make conclusions based on the findings. Both sets are linked below with a brief description. Be sure to use the correct set when answering lab questions.

Elderly Health

A study examined the medical records of elderly patients to determine whether there are difference between men and women in their calcium or inorganic phosphorous blood levels (both in millimoles per liter, mmol/L). Note: for the variable 'sex' male = 1 and female = 2

Observation	Age	Sex	Lab	Calcium	InorgPhosph	agegroup
1	78	2	4	2.53	1.07	3
2	72	2	4	2.5	1.16	2
3	72	2	4	2.43	1.13	2
4	73	2	4	2.48	0.81	2
5	73	2	4	2.33	1.13	2
6	73	2	4	2.13	0.84	2
7	65	2	4	2.55	1.26	1
8	68	2	4	2.45	1.23	1
9	89	1	4	2.25	0.65	5
10	84	1	4	2.43	0.84	4
11	71	1	4	2.4	1.1	2
12	80	2	5	2.25	1.1	4
13	80	2	5	2.18	1.49	4
14	76	2	5	2.55	1.23	3
15	70	2	2	2.38	1.42	2
16	70	2	5	2.3	1.16	2
17	71	2	4	2.6	1.32	2
18	70	2	5	2.2	1.07	2
19	70	2	5	2.38	1.13	2
20	66	2	5	2.63	1.13	1
21	76	1	5	2.2	0.9	3
22	76	1	5	2.18	0.84	3
23	68	1	5	2.15	0.52	1
24	69	1	5	2.3	1.36	1
25	76	2	3	2.53	1.07	3
26	70	2	3	2	0.97	2
27	71	2	3	2.23	0.94	2
28	70	2	3	2.43	1.42	2
29	74	2	3	2.5	0.87	2
30	74	2	3	2.33	0.94	2
31	74	2	3	2.4	1.16	2
32	70	2	3	2.5	1.23	2
33	69	2	3	2.5	1.07	1
34	82	1	3	2.35	0.9	4
35	84	1	3	2.25	0.94	4
36	70	1	3	2.45	0.84	2
37	68	1	3	2.33	0.87	1
38	84	2	2	2.33	0.94	4
39	76	2	2	2.43	1.29	3
40	76	2	2	2.38	1.03	3
41	75	2	2	2.4	1.18	3
42	75	2	2	2.28		3
43	71	2	2	2.35	1.32	2
44	72	2	2	2.28	1.07	2
45	73	2	2	2.48	1	2
46	72	2	2	2.48	1.42	2
47	70	2	2	2.35	1.03	2
48	74	2	2	2.63	1.23	2
49	71	2	2	2.45	1.26	2
50	73	2	2	2.75	0.9	2
51	72	2	2	2.4	1.19	2
52	71	2	2	2.48	1.13	2
53	69	2	2	2.45	1.19	1
54	65	2	2	2.45	1.13	1
55	69	2	2	2.33	0.97	1
56	68	2	2	2.43	1.1	1
57	69	2	2	2.6	1.29	1
58	67	2	2	2.45	1.19	1
59	88	1	2	2.35	0.87	5
60	77	1	2	2.4	1.26	3
61	76	1	2	2.4	1.39	3
62	76	1	2	2.38	1	3
63	76	1	2	2.33	1	3
64	77	1	2	2.35	1	3
65	78	1	2	2.58	1.1	3
66	78	1	2	2.23	0.87	3
67	75	1	2	2.43	1.23	3
68	75	1	2	2.4	1.19	3
69	70	1	2	2.48	0.87	2
70	74	1	2	2.33	1.23	2
71	71	1	2	2.5	0.97	2
72	70	1	2	2.35	1.13	2
73	70	1	2	2.53	1.42	2
74	73	1	2	2.55	1.13	2
75	67	1	2	2.45	1.26	1
76	69	1	2	2.33	1.16	1
77	68	1	2	2.43	0.97	1
78	67	1	2	2.38	0.97	1
79	82	2	1	2.33	1.61	4
80	79	2	1	2.28	1.23	3
81	78	2	1	2.13	1.19	3
82	75	2	1	2.4	1.26	3
83	79	2	1	2.48	0.97	3
84	75	2	1	2.2	1.23	3
85	78	2	1		1.19	3
86	75	2	1	2.5	1.29	3
87	73	2	1	2.2	0.94	2
88	71	2	1	2.5	1	2
89	73	2	1	2.35	0.94	2
90	74	2	1	2.7	1.19	2
91	71	2	1	2.5	1	2
92	73	2	1	2.2	0.94	2
93	72	2	1	2.45	1.58	2
94	70	2	1	2.25	1.16	2
95	71	2	1	2.5	1.26	2
96	74	2	1	2.38	1.26	2
97	73	2	1	2.3	1.32	2
98	72	2	1	2.2	0.94	2
99	69	2	1	2.65	1.29	1
100	69	2	1	2.33	1.07	1
101	66	2	1	2.3	1.13	1
102	65	2	1	2.53	1.07	1
103	66	2	1	2.3	1.13	1
104	68	2	1	2.4	0.97	1
105		2	1	2.25	1.36	1
106	65	2	1	2.28	1.1	1
107	68	2	1	2.3	1.19	1
108	86	1	1	2.25	0.9	5
109	80	1	1	2.48	0.77	4
110	80	1	1	2.48	1.23	4
111	81	1	1	2.18	0.97	4
112	78	1	1	2.3	1.16	3
113	77	1	1	2.25	1.07	3
114	79	1	1	2.55	1	3
115	79	1	1	2.25	1.23	3
116	75	1	1	2.28	1	3
117	75	1	1	2.48	1.13	3
118	78	1	1	2.18	1.13	3
119	75	1	1	2.1	1.1	3
120	79	1	1	2.15	1.26	3
121	79	1	1	2.28	1.13	3
122	77	1	1	2.18	1.16	3
123	73	1	1	2.38	0.84	2
124	72	1	1	2.2	0.77	2
125	74	1	1	2.25	0.94	2
126	70	1	1	2.35	0.84	2
127	70	1	1	2.45	0.84	2
128	72	1	1	2.3	0.87	2
129	71	1	1	2.33	1	2
130	70	1	1	2.33	1.23	2
131	72	1	1	2.1	1.29	2
132	74	1	1	2.35	0.84	2
133	71	1	1	2.25	0.97	2
134	71	1	1	2.15	1	2
135	70	1	1	2.33	1.07	2
136	71	1	1	2.33	0.87	2
137	72	1	1	2.28	1	2
138	74	1	1	2.38	1.03	2
139	68	1	1	2.18	1.13	1
140	67	1	1	2.35	0.97	1
141	65	1	1	2.35	0.77	1
142	69	1	1	2.23	1.23	1
143	69	1	1	2.2	1.32	1
144	66	1	1	2.33	1.23	1
145	67	1	1	2.25	1.26	1
146	67	1	1	2.35	1.26	1
147	67	1	1	2.5	0.84	1
148	68	1	1	1.9	1.32	1
149	65	1	1	2.05	1.19	1
150	68	1	1	2.4	1.19	1
151	66	1	1	2.3	0.97	1
152	69	1	1	2.23	1.03	1
153	68	1	1	2.3	1.13	1
154	68	1	1	2.43	1.16	1
155	69	1	1	2.25	1.07	1
156	68	1	1	2.4	1.42	1
157	67	1	1	2.25	1.07	1
158	67	1	1	2.28	1.32	1
159	67	1	1	2.18	0.97	1
160	68	1	1	2.5	1.36	1
161	66	1	1	2.4	1.29	1
162	65	1	1	2.28	1.16	1
163	65	1	1	2.1	1.16	1
164	69	1	1	2.3	1	1
165	67	1	1	2.38	0.84	1
166	68	1	1	2.43	1.16	1
167	80	2	6	2.35	1.1	4
168	76	1	6	2.23	1.16	3
169	66	2	6	2.4	1.19	1
170	72	2		2.3	1.36	2
171	73	2	6	2.48	1.36	2
172	72	2	6	2.4	1.19	2
173	74	2	3	2.2	1.19	2
174	72	2	3	2.45	1.07	2
175	71	2	3	2.18	1.1	2
176	67	2	6	2.3	1.26	1
177	77	2	4	2.65	0.97	3
178	70	2	4	2.5	0.97	2

Question 1

Using the Elderly Health Data set:

Make an appropriate graphical summary (you pick one, there are several options) of the 'sex' variable and paste it here (be sure to label it well).

sentence or two about why you chose this graph and what it tells us about the study.

Question 2

Using the Elderly Health Data set:

Make a pie chart of both 'agegroup' and 'age' (upload them here).

Which one is better and why?

For the one that isn't very useful, what would be a better way to display that data?

Question 3

Using the Elderly Health Data set:

Make side-by-side box plots to compare the calcium or the inorganic phosphorous by sex; (upload it)

Describe notable features of the graph. (What features do we discuss in boxplots?)

Regarding the research question: Is there a difference between the sexes for the calcium and inorganic phosphorous levels? What would you conclude and why?

Question 4

Using the Everglades Water Data set:

Pick one of the variables. Make a histogram and calculate summary statistics for it. (upload it here)

For each, describe the shape of the distribution and the whether the 5 number summary or mean and standard deviation describe it better; and why.

Question 5

Using the Everglades Water Data set:

Make a time plot of one of the variables. (Include it here)

Are there any noticeable trends?