Statistic and probability

Statistic and probability

1. CONTEXT CASE STUDY

   • It involves an analysis details of a case particular, whether a event, a person, an organization or some other phenomenon, with the objective of understand it in depth

2. POPULATION, SAMPLE AND INDIVIDUAL

   • INDIVIDUAL
     • Individuals are the minimum unit of analysis
   • SAMPLE
     • The sample it's a subgroup of individuals of the population to study, The main reasons for studying samples instead of populations are: Save research time and costs, Increase the quality of the study, Selection of specific samples
   • POPULATION
     • The population is a set of individuals that have a series of defining characteristics of their group.

3. PROBABILITY

   • Probability is a numerical measure of the chance of an event occurring. It is used to quantify the uncertainty associated with random events or processes.
     • Multiplicative principle
       • refers to the idea that the probability of two independent events occurring simultaneously is the product of their individual probabilities. This principle applies in situations where two events do not have a direct influence on each other.
         • 𝒏𝟏 ∗ 𝒏𝟐 ∗ … ∗ 𝒏𝒑 possible ways
     • Additive principle.
       • The additive principle in probability refers to the probability that at least one of two events will occur. This principle applies when events are mutually exclusive, meaning they cannot occur simultaneously
         • M + N + W = possible ways or forms.
     • Combination
       • Combinations are formed with a selection of elements from a set of n elements, taking into account that the order in which they are placed does not matter or choose.
     • Permutation
       • It is any arrangement of elements in which we are interested in the place or position occupied by each of the components that make up the arrangement.
         • Elements are not repeated.
         • If all elements enter
         • Order does matter
         • • Pn = n!

4. SAMPLING TYPES

   • Non-probabilistic
     • By convenience
       • The study units that are available at the time of data collection are selected. Its advantage is that it is easier, cheaper, and more accessible
     • By consecutive cases
       • Consists of choosing each patient who meets the selection criteria within a specific time interval or until a defined number of patients is reached.
     • By quotas
       • From each of the subgroups that make up the population, units are selected of study in a predetermined quota. It guarantees that a certain number of sampling units of different categories appear in the sample to that everyone is represented.
     • if the sample is chosen by means of a subjective or arbitrary process so that the probability of selection of each unit of the population is not known and can be:
   • Probabilistic
     • when the method of sample selection allows all elements of the population to have the same probability of being selected in the sample and can be:
       • Simple random
         • Everyone has the same probability of being selected for the study. It requires having a numbered list of all the units in the sample frame, deciding the sample size, selecting the sample at random using random number tables, calculator, or computer
       • Systematic
         • All the individuals they select intervals regular, every element K. Choose dividing the total population by The number of items desired, what will give us the interval in which are selected. He risk of bias is elderly.
       • Stratified
         • The population is first divided into relevant strata (subgroups) and then the random sample is selected from each stratum
       • Clustering
         • It's about the group selection of units of study, instead of study units individual. His main advantage is it is not necessary the sampling frame of the units of study individual
       • Multistage
         • Its main advantages are that it does not require a list of study units, initially the cluster list is enough and then only the cluster list is required selected and the sample of units.

5. SIMPLE LINEAR REGRESSION

   • In a simple linear regression model we try to explain the relationship that exists between the response variable Y and a single explanatory variable X.

6. LAW OF LARGE NUMBERS

   • Describes the behavior of the average of a large number of observations of a random phenomenon. This law suggests that, as the number of observations increases, the mean of those observations tends to approach the expected value or theoretical average of the phenomenon.
     • Representative
       • It implies having all the important characteristics of the population from which it was taken, in similar proportions, i.e., that it can cover one of the requirements to transpose the results of its sample to the population from which it was obtained
     • Adequate
       • This refers to its size and is calculated with different formulas established According to whether the study is looking for an existing proportion in a population, differences between the means or proportions of two populations, correlation between two or more factors, risk factors,
     • Cost
     • Feasibility
     • Accuracy
     • Speed

7. Statistics is a science that is dedicated to systematizing, collecting, ordering and presentation of data referring to a phenomenon that presents variability or uncertainty due to its methodical study

Images and files in the map