Lab Exercise

Measuring Migration from 1851 to 1861: Distribution, Center and Spread

The purpose of this exercise is twofold: to gain understanding of the statistical concepts of distribution, center, and spread; and to familiarize yourself with two variables that measure migration. In this exercise, use the data in the attached spreadsheet on migration from 1851 to 1861 for selected census registration districts of England and Wales.

1. Create a dot plot. On a piece of graph paper, create a display that shows the distribution of values for the variable "Total Migration" for the decade 1851-1861. Start by drawing a line that encompasses the minimum and maximum values. Then place dots on the line to indicate the positions of each value in the distribution. Your line should look something like this, with a zero near the center to permit your plotting of positive and negative values and a proper label.

Minimum 0 Maximum

Dot Plot of Total Migration 1851-1861

Recall the definition of this variable: for each census Registration District, the change in population from 1851 to 1861 that is attributable to migration. Negative values indicate a decline in the size of the population due to (out) migration; positive values, an increase due to (in) migration.

2. Briefly describe the distribution of values for each variable. What is the range of the distribution, i.e., the difference between the maximum and the minimum? Are the values spread out evenly? Do they cluster?

3. In a sentence or two describe what you think your plot indicates about the pattern of migration during the decade 1851 to 1861.

4. Create a table showing the Center and Range of the distribution you just studied. Calculate the mean, the median, and the range for the same variable, i.e., "Total Migration" for the decade 1851-1861 among your sample of districts

Decade	Mean	Median	Range
1851-1861

5. What do these measures indicate about the distribution and change of the population in your sample districts that was due to migration?

6. Are the mean and the median similar or different? If different, what is it about the distribution that accounts for the difference?

7. If the mean and median are different, which statistic would you use to indicate the "average" or "central" value of this distribution? Why? (Hint: consider the effect of extreme values.)

8. Using the statistic you selected in b), write a sentence or two that describes what the "average" or "central" value and the range indicate about the pattern of migration for the decade 1851-1861.

Standardization: From Counts to Ratios/Rates

9. Counts. Return to your dot plot showing the distribution of total migration from 1851 to 1861. This variable is records the number of individuals who were added or subtracted from the population in 1851 by means of migration into or out of a district. It measures this change by recording counts of individuals.

Place this plot of counts next to the spreadsheet that contains all the sample data. Choose one of the larger values on the dot plot; then locate on the spread sheet the registration district which has this value. Now, compare the value of Total Migration with the Total Population in 1851. Repeat this comparison for at least five values of differing size.

10. What, if any, pattern seems to emerge from this comparison? Do the large values of Total Migration tend to correspond with large values of Total Population? Or do the large values of Total Migration tend to correspond with small values of Total Population?

11. On the basis of this inspection describe in a sentence or two the limitations of using the count variable Total Migration to compare and gauge migratory movements across your sample of Registration Districts.

12. Rates or Ratios. For each Registration District in your sample, calculate the percentage change in population due to migration from 1851 to 1861. [(Total Migration/Total Population in 1851) x 100]. This new variable records a rate or percentage based on the change due to migration in relation to the size of the population at the beginning of the decade of observation. As you discovered above there is considerable variation among the sample Registration Districts in terms of their population size in 1851. This variation makes it difficult to make a judgement about the significance of any given population change due to migration because it's more than likely that districts with small beginning populations will go hand in hand with small changes due to migration, while the opposite is likely for districts with large beginning populations. The use of percentages has the effect of creating values which are measured by the same "yard stick" or "standard," which for each district is the size of its population in 1851.

Study the percentage values that you've calculated and explain in a sentence or two why the conversion of counts to rates/ratios (percentages in this case) facilitates your ability to compare and gauge migratory movements across the Registration Districts in your sample.

13. Create a dot plot showing the distribution of the new variable that you've created above: the percentage change in population due to migration from 1851 to 1861.

14. Compare this dot plot with the dot plot of the count variable Total Migration which you constructed in step 1. Describe the pattern you see in the distribution of the percentage change due to migration.

15. Explain why the variable measuring the percentage change due to migration facilitates the task of comparing and measuring variations in migratory movements across census Registrations Districts.

With the exception of the density of rail coverage, these data are courtesy of Professor Humphrey Southall and Ian Cameron of the Geography Department at Queen Mary and Westfield College, London. The comprise a small sample of data from the Great Britain Historical Data Base.

				Migration				Changes in Population Segment due to Migration						Density of Rail Coverage [Kilometers of rail lines per square kilometer of area]
District	County	Start Date of Decade	Total Pop. at Decade Start	Total Female	Total Male	Total	Percent Change due to Migration	Females 15-24	Females 25-34	Females 45-54	Males 15-24	Males 25-34	Males 35-44		1845	1854	1876	1914
Alton	Hampshire	1851	13360	-446	22	-424	-3.17	-55	-32.8	1	-5	71.3	-34			4	61	161
Alton	Hampshire	1861	14724	-697	-1193	-1890	-12.84	-103	-45	-75	-532	-295.5	-39			4	61	161
Alton	Hampshire	1871	14999	-865	-1037	-1902	-12.68	-207	-40.5	-10	-397	-100	-65			4	61	161
Alton	Hampshire	1881	15198	-947	-936	-1883	-12.39	-154	0	-14	-371	8.5	-33			4	61	161
Alton	Hampshire	1891	15146	-232	-322	-554	-3.66	87	42.5	-1	-153	121	19			4	61	161
Alton	Hampshire	1901	16345	577	3994	4571	27.97	436	203	1	882	430	27			4	61	161
Barton Upon Irwell	Lancashire	1851	31585	1610	78	1688	5.34	217	129	49	-116	55.5	27		82	174	328	547
Barton Upon Irwell	Lancashire	1861	39038	2716	1505	4221	10.81	437	246	60	433	350.5	67		82	174	328	547
Barton Upon Irwell	Lancashire	1871	51571	4715	3451	8166	15.83	852	577	307	1009	745	160		82	174	328	547
Barton Upon Irwell	Lancashire	1881	72815	2881	3549	6430	8.83	479	71.5	47	1226	852	71		82	174	328	547
Barton Upon Irwell	Lancashire	1891	93470	4152	2358	6510	6.96	1308	277	41	840	500.5	-84		82	174	328	547
Barton Upon Irwell	Lancashire	1901	114773	5281	4321	9602	8.37	1775	684.5	109	1465	1260.5	-31		82	174	328	547
Bootle	Cumberland	1851	5973	-311	-399	-710	-11.89	-118	-40.7	0	-197	-48.2	-35			62	90	90
Bootle	Cumberland	1861	5846	386	702	1088	18.61	74	77.7	43	148	155.2	36			62	90	90
Bootle	Cumberland	1871	8475	563	628	1191	14.05	191	100.1	26	175	66.2	34			62	90	90
Bootle	Cumberland	1881	12154	32	-156	-124	-1.02	16	28.1	15	-148	-82.4	-4			62	90	90
Bootle	Cumberland	1891	14790	-631	-655	-1286	-8.70	-89	-63.4	-43	-276	-72.4	-4			62	90	90
Bootle	Cumberland	1901	15800	-1395	-1787	-3182	-20.14	-398	-231	-84	-636	-322	-113			62	90	90
Haltwhistle	Northumberland	1851	7286	-459	-821	-1280	-17.57	-144	-71.5	-7	-198	-261	-40		45	90	90	90
Haltwhistle	Northumberland	1861	6693	-186	-373	-559	-8.35	-97	-24	4	-114	-67.5	-2		45	90	90	90
Haltwhistle	Northumberland	1871	6987	-159	-68	-227	-3.25	-62	17.5	-20	-33	4.5	-21		45	90	90	90
Haltwhistle	Northumberland	1881	7902	-363	-451	-814	-10.30	-142	-59	-34	-196	-70.5	-17		45	90	90	90
Haltwhistle	Northumberland	1891	7746	-198	-171	-369	-4.76	-50	-44.5	-32	-34	-1.5	-19		45	90	90	90
Haltwhistle	Northumberland	1901	4789	-400	-436	-836	-17.46	-104	-50.5	-16	-161	-74.5	-29		45	90	90	90
Haslingden	Lancashire	1851	52822	4411	3143	7554	14.30	728	525.8	188	329	489.0	177			108	108	167
Haslingden	Lancashire	1861	72166	732	-826	-94	-0.13	-421	-52.0	-129	-842	-297.7	-132			108	108	167
Haslingden	Lancashire	1871	83049	1342	246	1588	1.91	-22	-109.6	-74	-288	-43.8	-41			108	108	167
Haslingden	Lancashire	1881	98184	-1245	-2123	-3368	-3.43	-641	-602.4	-201	-842	-426.2	-239			108	108	167
Haslingden	Lancashire	1891	105777	220	-349	-129	-0.12	-160	-386.5	-143	-362	-131.5	-79			108	108	167
Haslingden	Lancashire	1901	115223	-2356	-2567	-4923	-4.27	-760	-1081.5	-391	-815	-722	-298			108	108	167
Hatfield	Hertfordshire	1851	8499	-458	-630	-1088	-12.80	-36	-120	-40	-342	-74.5	-13			80	214	214
Hatfield	Hertfordshire	1861	8400	-369	-466	-835	-9.94	-14	-79	-36	-150	-34.5	-18			80	214	214
Hatfield	Hertfordshire	1871	8631	-504	-529	-1033	-11.97	-48	-59.5	-44	-139	-46	-37			80	214	214
Hatfield	Hertfordshire	1881	8802	-354	-340	-694	-7.88	9	-54.5	-49	-93	-44.5	-29			80	214	214
Hatfield	Hertfordshire	1891	9309	-394	-436	-830	-8.92	48	-26.5	-76	-92	-38.5	-36			80	214	214
Hatfield	Hertfordshire	1901	9816	-82	-84	-166	-1.69	83	2.5	-23	14	67.5	-30			80	214	214
Knaresborough	West Riding	1851	9826	2443	1983	4426	45.04	546	432.9	257	408	427.0	265			364	177	177
Knaresborough	West Riding	1861	17176	211	-199	12	0.07	-28	-15.5	40	-157	-13.5	-7			364	177	177
Knaresborough	West Riding	1871	19088	897	-115	782	4.10	15	122	82	-117	68	27			364	177	177
Knaresborough	West Riding	1881	22635	1479	160	1639	7.24	108	129	112	12	125	95			364	177	177
Knaresborough	West Riding	1891	27158	4926	3484	8410	30.97	1111	526.5	367	970	683.5	332			364	177	177
Knaresborough	West Riding	1901	40504	2500	-106	2394	5.91	197	-71.5	193	-241	75	124			364	177	177
Lexden	Essex	1851	22429	-848	-1321	-2169	-9.67	-187	-60.7	-23	-420	-69.8	-37		55	85	103	137
Lexden	Essex	1861	23678	-1283	-1510	-2793	-11.80	-240	-89.8	-72	-450	-76.1	3		55	85	103	137
Lexden	Essex	1871	24734	-2744	-2413	-5157	-20.85	-537	-333.1	-234	-703	-142.6	-127		55	85	103	137
Lexden	Essex	1881	21775	-1292	-1314	-2606	-11.97	-175	-80	-69	-431	-9.5	-40		55	85	103	137
Lexden	Essex	1891	21590	-1132	-1466	-2598	-12.03	-135	-49.5	-75	-535	-45.5	-52		55	85	103	137
Lexden	Essex	1901	21146	-740	-588	-1328	-6.28	-48	121	-63	-283	147.5	-48		55	85	103	137
Newton Abbot	Devon	1851	52306	867	-1157	-290	-0.55