Chapter 5 Description of categorical data

Content Rate 、 proportion and ratio Application of relative numbers Standardization of rate Dynamic series and analysis index

Section 1 Relative Numbers 1 、 Rate 2 、 Proportion 3 、 Ratio

1 、 Rate Rate ： To describe the frequency or intension of some phenomenon.  Number of individual occurred some thing within a period of time Rate The whole number of likely to occurred some thing in the same period

Example1 To investigate 8589 old people in some city in 1998, and 2823 people had hypertension. Morbidity rate ： 2823 / 8589  100% = 32.87%

2 、 Proportion Proportion: To describe the ratio of number of one part and the whole number in the same thing. Formula: 100%  Number of individuals in one part Proportion The whole number of individuals

Example2 Calculate the patients proportion of 5 diseases in one hospital in 1990 and 1998.

Example2 Calculate the patients proportions of 5 diseases in one hospital in 1990 and 1998.

Characteristics: （ 1 ） Summation of proportions in one thing is 100%. （ 2 ） Proportions in the same thing are interactional.

3 、 Ratio Ratio: the quotient of two related indexs Formula:

(100%) A index Ratio= B index

Example3 There are 370 male newborns and 358 female newborns in a hospital in one year, then The sex ratio of newborn babies: 370/358 × 100 = 103

Section 2 Application of relative numbers 1 、 The denominator of relative number should not be too small. 2 、 Proportion should not substitute rate. 3 、 To calculate the total rate correctly. 4 、 Comparison of relative numbers 5 、 Comparison of sample rate （ proportion ） should do hypothesis test.

Section 3 Standardization of rate 1 、 Definition To calculate standard rate by uniform interior constitute. Standardization (or adjustment) of rates is used to enable the valid comparison of groups that differ regarding an important health determinant (most commonly age). It is in fact a specific application of the general methods to control for confounding factors.

2 、 Calculation Method Direct standardization Indirect standardization

Approach 1.Choose the correct method by condition of data. 2.Choose standard composing. 3.Calculate standard rate.

Formula Direct standardization

Indirect standardization

Example4 To calculate standard cure rate of two therapeutics.

Approach: 1 ） Disease cure rate of two therapeutics is known- Direct standardization 2)Choose total patients number of two therapeutics as standard. 3 ） Calculate anticipated cure number. 4 ） Calculate standard cure rate.

%47.5% 800   Standard cure rate of A %53.4% 800   Standard cure rate of B

Example 5 A research investigated old women, 776 in the city and 789 in Countryside. Among them, 322 and 335 suffered from primary osteoporosis. The total morbidity rates are 41.5 and 42.5 respectively. Because the proportions of age in urban and rural areas of this investigation forms are different, so we need to standardize the two morbidity rate.

SMR  Urban standard morbidity ratio 42.1% 1.05=44.2%   Urban standard morbidity rate SMR  Rural standard morbidity ratio 42.1% 0.95=40.0%   Rural standard morbidity rate After standardization, urban morbidity rate is higher than rural.

3 、 Application 1.The Standardization only adapt to that interior forms are different in two groups, and may influence the comparison of rate. 2.Because of different chosen standard population, standardized rates are different too. So, while comparing several standardized rates, should adopt the same standard population.

3. Standardized rate is no longer the local real level at that time, it only shows the relative level among the comparing materials. 4. The standardized rates of two samples are sample values, the sampling error exists. When comparing the standardized rates of two samples, we should do hypothesis test if the sample size is small.

Section 4 Dynamic series and analysis index Dynamic series ： A series of statistical index arranged in the order of time. To observe and compare changes and development trends in time series. The index is as follows, absolutely increasing amount, development speed and growth rate, average development speed and average growth speed.

Two important elements ： time ： Statistic index ： base line reported time the end

Example 6 Table 6 shows the statistic data of outpatients amount in one hospital from 1991 to 1999.To analyse by dynamic series.

Table 6 Dynamic changes of outpatients amount

1 、 Absolutely increasing amount the increasing amount totally the increasing amount year by year Absolutely increasing amount explains the absolute value that the thing increases in a regular period.

2 、 Development speed and growth speed ① Relative ratio with fixed base ： a 1 /a 0 ， a 2 /a 0 ， …., a n /a 0 ② Ring ratio ： a 1 /a 0 ， a 2 /a 1 ， …., a n /a n-1 ③ Growth speed = development speed –1 （ 100% ）

3 、 Average development speed and average growth speed Average development speed a 0 base line index a n index in the n period average growth speed= average development speed-1