Here are all 3-mark answers from Park's PSM:
Q18. Record Linkage
Record linkage is the process of bringing together records relating to one individual (or family), the records originating in different times or places. Medical record linkage implies the assembly and maintenance, for each individual in a population, of a file of the more important records relating to his health.
Events commonly recorded: birth, marriage, death, hospital admission and discharge. Other useful data may include sickness absence from work, prophylactic procedures, use of social services, etc.
Uses: Record linkage is particularly suitable for studying associations between diseases - these associations may have aetiological significance.
Limitation: The main problem is the volume of data that can accumulate. Therefore, in practice it has been applied only on a limited scale - e.g., twin studies, measurement of morbidity, chronic disease epidemiology, and family and genetic studies. At the moment, record linkage is beyond the reach of many developing countries.
Q19. Bar Diagram (Bar Charts) and Its Uses
Bar charts present a set of numbers by the length of a bar - the length is proportional to the magnitude represented. They are popular because they are easy to prepare and enable values to be compared visually.
Types of bar charts:
- Simple bar chart - bars may be vertical or horizontal; separated by appropriate spaces. Used to compare one variable.
- Multiple (compound) bar chart - two or more bars grouped together; used to compare more than one variable simultaneously (e.g., population and land area by region).
- Component bar chart - bars divided into two or more parts; each part represents a certain item and is proportional to the magnitude of that item (e.g., India's growth of population 1901-2011).
Uses: Presenting statistical data in newspapers, magazines, and health reports. Diagrams are better retained in memory than statistical tables.
Q20. Histogram
A histogram is a pictorial diagram of frequency distribution. It consists of a series of blocks/rectangles.
- The class intervals are given along the horizontal axis.
- The frequencies are given along the vertical axis.
- The area of each block is proportional to the frequency.
(Example: histogram of frequency distribution of blood pressure in females aged 45-64 years.)
Difference from bar chart: In a histogram, the bars are contiguous (touching each other) with no gaps, as the data is continuous. In a bar chart, bars are separated by spaces.
Frequency polygon is obtained by joining the mid-points of the histogram blocks.
Q21. Pie Chart - Advantages and Disadvantages
In a pie chart, instead of comparing the length of a bar, the areas of segments of a circle are compared. The area of each segment depends upon the angle at the centre. Percentages are often indicated in the segments.
Advantages:
- Simple and visually appealing
- Easy to understand at a glance
- Extremely popular with the laity (non-statisticians)
- Shows proportions clearly as parts of a whole
Disadvantages:
- Not preferred by statisticians - considered inferior to bar charts
- Difficult to compare the areas of segments visually without labelling
- It is often necessary to indicate percentages in segments because it may not be easy to visually compare areas
- Cannot show trends over time
- Becomes confusing when many segments are used
Q22. What is a Spot Map?
A spot map is a type of statistical map used to show the local (geographical) distribution of disease cases. Each case is marked by a dot or spot on a map of the area.
- Inner and outer city variations in disease frequency are best studied with spot maps or shaded maps.
- These maps show at a glance areas of high or low frequency, and the boundaries and patterns of disease distribution.
- If the map shows clustering of cases, it may suggest a common source of infection or a common risk factor shared by all the cases.
Classic example: John Snow of England in his classic investigation of the cholera epidemic of 1854 in the Golden Square district of London used a spot map of fatal cases. He was able to focus attention on the common water pump in Broad Street as the source of infection - based entirely on descriptive mapping.
Q23. Measures of Central Tendency
The word "average" implies a value around which other values are distributed. There are three commonly used measures:
1. Mean (Arithmetic Mean)
- Individual observations are added together and divided by the number of observations.
- Formula: x̄ = Σx / n
- Advantages: Easy to calculate and understand; most useful of the statistical averages.
- Disadvantages: May be unduly influenced by abnormal (extreme) values.
2. Median
- Data is arranged in ascending or descending order; the middle value is the median.
- Advantages: Not affected by extreme values; more representative when extreme values distort the mean.
- Disadvantages: Does not use all values in its calculation.
3. Mode
- The most frequently occurring value in a distribution.
- Advantages: Easy to understand; not affected by extreme items.
- Disadvantages: Exact location is often uncertain and not clearly defined; therefore not often used in biological or medical statistics.
Q24. Standard Normal Curve - Properties / Draw
Although there is an infinite number of normal curves, there is only one standardized normal curve devised by statisticians to estimate easily the area under the normal curve between any two ordinates.
Properties:
- Smooth, bell-shaped, perfectly symmetrical curve.
- Based on an infinitely large number of observations.
- Total area of the curve = 1 (100%).
- Mean = 0; Standard deviation = 1.
- Mean, median and mode all coincide at the centre.
- The curve is asymptotic to the baseline (never touches the x-axis).
- The standard normal deviate (Z) is given by:
Z = (x - x̄) / σ
Area under the curve:
| Range | % of values included |
|---|
| x̄ ± 1σ | ~68% |
| x̄ ± 2σ | ~95% |
| x̄ ± 3σ | ~99.7% |
These limits are called confidence limits.
(Draw a symmetrical bell curve with the centre labelled mean=0, and mark the ±1σ, ±2σ, ±3σ zones with 68%, 95%, 99.7% areas.)
Q25. Sampling Methods/Types
When a large population has to be studied, a sample is taken - it is easier and more economical than studying the whole population. The sample must be representative of the whole population.
Sampling Frame: A listing of members of the universe from which the sample is to be drawn.
Three main sampling methods:
1. Simple Random Sample
- Each unit is assigned a number; a table of random numbers is used to select units.
- Each unit has an equal chance of being drawn.
- Provides the greatest number of possible samples.
2. Systematic Random Sample
- Every 5th or 10th unit is picked at regular intervals.
- Example: to carry out a filaria survey, houses are numbered; a starting number is chosen at random between 1 and 10 (say 4), then every 10th number is selected: 4, 14, 24, 34...
- Each unit has the same chance of selection, but the number of possible samples is reduced.
3. Stratified Random Sample
- The sample is deliberately drawn so that each portion represents a corresponding strata (sub-group) of the universe.
- Useful when one is interested in analysing data by a characteristic - e.g., religion (Hindus, Christians, Muslims), age groups, etc.
- Ensures proportional representation of each subgroup.
Q28. Name the Tests of Significance
Tests of significance are used to determine whether an observed difference is real or merely due to chance. When P < 0.05 (1 in 20), the difference is considered significant; when P < 0.01, it is considered more significant.
The tests include:
-
(a) Standard Error of the Mean - tests whether the sample mean accurately represents the population mean; used to set confidence limits.
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(b) Standard Error of Proportion - tests significance when data is expressed as proportions or percentages.
-
(c) Standard Error of Difference (between two means) - tests whether the difference between means of two groups is significant (i.e., whether the two samples represent different universes).
-
(d) Standard Error of Difference between two Proportions - tests significance of the difference between two proportions or ratios.
-
Chi-square (χ²) Test - an alternate method; used when two or more groups (proportions) are to be compared.
Decision rule:
| Normal Deviate (N.D.) | P value | Conclusion |
|---|
| N.D. > 2 | P < 0.05 | Significant |
| N.D. = 2 | P = 0.05 | Just significant |
| N.D. < 2 | P > 0.05 | Not significant |
Q29. Chi-Square Test (χ²)
Chi-square test is an alternate method of testing the significance of difference between two or more proportions. It has the advantage of being usable when more than two groups are to be compared.
Steps:
(1) Set up Null Hypothesis - assume there is NO difference between the groups, then test this hypothesis quantitatively.
(2) Calculate expected values - pool the results and calculate the expected number in each cell based on the overall proportion.
(3) Apply the χ² formula:
χ² = Σ (O - E)² / E
Where O = Observed value, E = Expected value.
(4) Find Degree of Freedom (d.f.):
d.f. = (c - 1)(r - 1)
Where c = number of columns, r = number of rows.
(5) Refer to χ² probability tables:
- For 1 d.f., χ² value at P = 0.05 is 3.84
- If calculated χ² > 3.84 → result is significant (reject null hypothesis)
- If calculated χ² < 3.84 → result is not significant (accept null hypothesis)
Limitation: The test is valid only if the expected number in each cell is not less than 2.
(Park's Textbook of Preventive and Social Medicine, Biostatistics chapter)