LESSON 9

UNIT 9: INFERENTIAL STATISTICS: SAMPLING AND ESTIMATION

1. STATISTICAL INFERENCE

When we propose a study in the health field to establish relations between variables, our interest is usually not exclusively in the specific patients to whom we have access, but rather in all patients similar to these.

In inferring you never have the sure data of the entire population on which you deduce the results of a study carried out previously on the population that interests us, to infer always there is random error.

• To the group of patients about whom we want to study some question (draw conclusions) we call it study population.

• To the set of concrete individuals that participate in the study we call it sample.

• The number of individuals in the sample is called the sample size.

• To the set of statistical procedures that allow us to pass from the particular, the sample, to the general, the population, we call it statistical inference.

• To the set of procedures that allow to choose samples in such a way that they reflect the characteristics of the population we call Sampling techniques, this is done to avoid bias.

Whenever we work with samples, even if they are representative, we must assume a certain error.

• If the sample is chosen by a random procedure, that error can be evaluated. The sampling technique in this case is called probabilistic or random sampling and the error associated with that sample chosen at random is called a random error.

• In non-probabilistic sampling, it is not possible to evaluate the error.

• The larger the sample size, I favor the reduction of random error by probability.

2. STATISTICAL INFERENCE PROCESS

We have a study population, and the measure we want to get is called a parameter.

We make a random selection and obtain a sample, the measure of the study variable obtained in the sample, is called the estimator.

The process by which from the estimator, I approach the parameter is called inference.

3. STANDARD ERROR.

It is the measure that tries to capture the variability of the values ​​of the estimator.

The standard error of any estimator measures the degree of variability in the estimator values ​​in the different samples of a given size that we could take from a population.

The smaller the standard error of an estimator, the more we can rely on the value of a particular sample

STANDARD ERROR CALCULATION

It depends on each estimator:

- Standard error for a mean:

- Standard error for a ratio (relative frequency):

From both formulas, it follows that the larger the sample size, the lower the standard error.

4. THE CENTRAL THEOREM OF THE LIMIT

For estimators that can be expressed as the sum of sample values, the distribution of their values ​​follows a normal distribution with population mean and standard deviation equal to the standard error of the estimator in question. If you follow a normal distribution, follow the basic principles of this:

± 1S 68.26% of observations.

± 2S 95.45% of observations.

± 1.95S 95% of observations

± 3S 99.73% of observations.

± 2.58S 99% of observations.

5. INTERVALS OF CONFIDENCE:

·         They are a means of knowing the parameter in a population by measuring the error that has to do with chance (random error).

·         It is a pair of numbers such that, with a certain confidence level, we can ensure that the value of the parameter is greater or less than both numbers.

·         It is calculated considering that the sample estimator follows a normal distribution, as established by the central limit theory.

The greater the confidence we want to give to the interval, the longer it will be, ie the lower and the upper end of the interval will be more distanced, and therefore the interval will be less precise.

You can calculate confidence intervals for any parameter: arithmetic means, proportions, relative risks, odds ratio ...

In formulas each time we use proportion we express in the formula in as many as 1 and not in as many as 100 (%)

6. SAMPLE PROCEDURE. (Sampling Technique).

- A sampling is a method such that when choosing a small group of a population we can have a degree of probability that this small group has the characteristics of the population that we are studying.

- The general population of the we want to obtain conclusions we will choose random (random), to obtain the sample and from this make inference of the entire population.

7. TYPES OF SAMPLING.

• ·         PROBABILISTIC SAMPLING.

It is the method of extracting a part (or sample) from a population, so that all possible samples of fixed size have the same possibility of being sel

- Simple Random. (It is the most reliable and equitable)

1. It is characterized because each unit has the equitable probability of being included in the sample:

• Lottery or raffle: We assign a number to each member of the population, calculate the sample size and randomly select that number. This type of method is not easy when the population is very large.

• Random number table: more economical and less time consuming. It is done when we have a computerized list in a database of the study population.ected.

- Systematic Random.

Similar to the simple random, where each individual has the same probability of being selected.

- Stratified.

It is characterized by the subdivision of the study population into subgroups or strata, since the main variables to be studied have some known variability or distribution that may affect the results.

- Conglomerate.

1. It is used when there is not a detailed and enumerated list of each of the units that make up the sample and it is very complex to elaborate it. In selecting the sample, the subgroups or sets of units, conglomerates, are taken.

2. In this type of sampling the researcher does not know the distribution of the variable.

NON-PROBABILISTIC SAMPLING.

- The random process is not followed.

- The sample can not be considered representative of a population.

- It is characterized because the researcher selects the sample following some criteria identified for the purposes of the study that performs.

-Types:

1. By quotas: in which the researcher selects the sample considering some phenomena or variables to study, such as: Sex, race, religion, etc. (There is no randomness)

2. Accidental: is to use for the study the people available at any given time, depending on what is interesting to study. Of the three is the most deficient.

3. For convenience or intentional. In which the investigated, decides according to its objectives, the elements that integrate the sample.

8. SAMPLE SIZE.

The size of the sample to be taken will depend on

- Standard error.

- Variations of the variable to be studied.

- The size of the study population.