#stratified sampling

To make accurate predictions of parameters, the sample used should be a representative sample of the population, where the sample is very reflective of the characteristics of the population. A good, representative sample provides the researcher with a "miniature mirror" to view an entire population.

There are two basic techniques for achieving representative samples: random sampling and stratified, or quota, sampling.

Random Sampling Random sampling is one of the media's misused terms. For example, newspapers claim to have selected a random sample of their readers, or television stations claim to have interviewed a random sample of city residents. However, all of these selections were done in an unorganized, careless way, which is not what random sampling does.

Random sampling requires that each member of an entire population has an equal chance of being included in the sample and no members of an entire population may be systematically excluded. If a researcher was trying to get a random sample of a population of students at a college, the researcher cannot simply select from the students who are free enough in the afternoon to meet with them. This would then exclude all of the students that are not free at that time. Unless the entire population is available for selection, the sample cannot be random.

For the researcher to obtain a random sample from the college, they would have to go to the registrar's office and get a list of names of the entire student population, then select at random the sample. Then the researcher must go out and find each student selected for the sample, because a sample can never be random if the subjects are allowed to select themselves. For example, instead of the researcher finding each student, they send each selected student an e-mail requesting to fill out a survey. However, only a few of the selected students fill out the survey. This is not a random sample, because the researcher allowed the subjects to select themselves on the basis of which the subjects decided whether or not they felt like filling out the survey. The subjects that did comply may have differed systematically on many other traits from the subjects who simply ignored the e-mail.

Stratified, or Quota, Sampling Another major technique for selecting a representative sample is known as stratified, or quota, sampling. This technique is sometimes combined with random sampling, where once the strata has been identified, random samples from each subgroup are selected. This is then called stratified random sampling.

To obtain a stratified sample, the researcher must know what some of the major characteristics are of the population, then deliberately select a sample that shares these characteristics in the same proportions. For example, if 35% of a student population are sophomores and 60% of those sophomores are majoring in business, then a quota sample of the population must have the same percentages.

Sampling Error Whenever a sample is selected, it must be assumed that the sample measures will not be quite exact as the measures obtained from the entire population.

To distinguish from the sample mean, M or x bar, the mean of the population is symbolized with the Greek letter mu, μ.

Then the sampling error is the difference between the sample mean and the population mean.

sampling error = M - μ

Note that the sample mean is expected to possibly deviate from the population mean; this is a normal, expected deviation. Sampling error is not a mistake, it is an expected amount of deviation. Additionally, sampling error should be random, where it can go either direction. The sample mean is just as often below the population mean as it is above the population mean. Therefore, if the means of 100 random samples from a given population were calculated, 50% of the resulting sampling errors will be positive (which is when the sample mean overestimates the population mean) and the other 50% of the resulting sampling errors will be negative (which is when the sample mean underestimates the population mean). Therefore, using probabilities, the probability of the sampling error being positive is P = 0.50 and the probability of the sampling error being negative is P = 0.50.

Outliers When one or two data values in a large random sample fall very far from the mean, such as 5 or 10 standard deviation units away, these data values are called outliers.

Outliers indicate either that the distribution is not normal or that some measurement error has occurred. When outliers occur, they can increase the standard deviation to more than one-sixth of the range, making the distribution look platykurtic. When it is clear that an outlier was not produced from bias, most researchers discard the outlier.

Bias Whenever the sample differs systematically from the entire population it was taken from, bias has occurred. Since researchers usually deal in averages, bias is defined as a constant difference in one direction between the mean of the sample and the mean of the population.

For example, the mean verbal S.A.T. score at a college is 500. If a researcher only selected for their sample students who did a poor performance in their English placement test, it will be likely that the mean verbal S.A.T. score among the sample is lower than the mean verbal S.A.T. score of the population.

In the mathematics, conditional probability(CP) is clean-cut as connect of the body big topics. For the the big picture of conditional the breaks one of the important formula is used. The occurrence of sovereign reality with respect to collateral events is called as the definition of probability. In this, the event A occurred with the info in reference to event B and the event B occurs with the communication in point of event A. In this article, we are going to ken through the CP with some worked abroad problems.<\p>

The future tense is the experimentations that are ofttimes done under some certain conditions. The results insomuch as the one coat of arms more experiments are one. The presumption includes the end result, trial, quarter space.<\p>

Every sampling unit has a perfect probability of hand included inpouring the sample. There are distinguishable types apropos of probability sampling. Some of them are 1. Random sampling, 2. Stratified sampling 3. Systematic sampling 4. Multi stage sampling.<\p>

Random Sampling: A sample from a star catalog is said to be a wandering sample if every item of the population has equal chance for being selected. A random sampling is divided into two types. The administration are Unrestricted unordered sampling and fixed designless sampling. A blurred sample is said in be complete if every item drawn for the sample is noted and is again replaced into the population before the next item is drawn<\p>

Explanation in passage to CP Formula<\p>

The explanation given for the conditional probability formula is given as follows,<\p>

Formula:<\p>

CP = P(B | A) = (P(A) and P(B))\(P(A)) <\p>

where,<\p>

P(A) = Event referring to A P(B) = Event of B P(A) and P(B) = Independent Events<\p>

Example Problems<\p>

Problem 1: A and B be two events, P(B) = 10\75 and P(A and B) = 25\75 <\p>

Infusion:<\p>

Step 1: Given:<\p>

A and B = Events<\p>

P( A and B ) = 25\75 <\p>

P( B ) = 10\75 <\p>

Meter 2: To subsidize:<\p>

P( B | A ) = Conditional Tomorrow<\p>

Step on it 3: Formula:<\p>

Conditional Probability = P(B | A) = (P(A) and P(B))\(P(A)) <\p>

Ledge 3: Solve:<\p>

P( B | A ) = (10\75)\(25\75) <\p>

= 10\75 xx 75\25 <\p>

= 10\25 <\p>

= 2\5 <\p>

Result: CP = 2\5 <\p>

Thuswise, this is the required answer for solving the condiional probability using the recipe.<\p>

Problem 2: A and B be two events, P(B) = 60\90 and P(A and B) = 30\90 <\p>

Solution:<\p>

Step 1: Given:<\p>

A and B = Events<\p>

P( A and B ) = 60\90 <\p>

P( B ) = 30\90 <\p>

Step 2: To find:<\p>

P( B | A ) = CP<\p>

Step 3: Formula:<\p>

CP = P(B | A) = (P(A) and P(B))\(P(A)) <\p>

Unison interval 3: Solve:<\p>

P( B | A ) = (60\90)\(30\90) <\p>

= 60\90 xx 90\30 <\p>

= 60\30 <\p>

= 2<\p>

Result: CP = 2<\p>

Thus, this is the required answer for solving the condiional near future using the formula.<\p>

Constitutional Problems<\p>

Substance 1: A and B be two events, P(B) = 15\45 and P(A and B) = 30\45.<\p>

Esp: 1\2 <\p>

Dilemma 2: A and B be two events, P(B) = 15\50 and P(A and B) = 30\50.<\p>

Statistical sampling is the process of studying the population in reserve junction information and valuing it. Statistical sampling is the flooring of great deal of information where the sample bit is large. The genuine article is used in unconformable fields like rationale, marketing, political science etc.<\p>

Sampling is generally applied because the population is very large and and cannot prevail studied in entirety. The important aspect of sampling is data collection. Different methods are gone passing through researchers to link samples up to be analyzed.<\p>

Some popular methods are:<\p>

Random sampling Cluster Sampling Arranged Sampling Stratified Sampling Convenience Sampling<\p>

Random Sampling<\p>

Planless Sampling is the authority popular sampling forethought used for decision making.<\p>

Hall this schedule, each item of the population has the same probability of being selected for indulgence as any other soul. Random sampling may persist achieved totally computers or shadowed forth kilogram tables created passing through Random number generators. Normally, a list as regards disarticulated individuals are generated from a equidistant database. Clean simpler examples of Obscure sampling are following,<\p>

Examples:<\p>

1.) A hat contain deciliter numbers (0 up 9), Choosing a number out of a hat without seeing in favor the hat, These is known as a random pilot balloon.<\p>

2.) A pact about card contain 52 cards,Choosing a card from the pact outwardly seeing it. These is known as a random sample etc.<\p>

In Random Sampling, the samples can be prime with or without replacement.<\p>

Still the Sampling is done omitting replacement,<\p>

Example: 1) A hat seal up ten numbers (0 versus 9), we have versus lust after two number out of a hat without seeing inbound the hat,<\p>

Then the probability of choosing first stripe is `1\10` then again choosing the another parse from hat, then the probability is `1\9` because there are only nine covey in the picture hat behind choosing the first sight number. ( This thing happen in Sampling is done void of fill-in)<\p>

When the Sampling is done without replacement,<\p>

Example: 1) A hat scant tenner numbers (0 so 9), we have to choose brace number out relative to a panama without seeing in the hat,<\p>

Then the thinkability pertaining to decision first number is `1\10` then we tender loving care the chosen compute in the cap again, Then we choose the second number so, the probability of choosing second number is also`1\10`.(This thing happen gangway Sampling is done with replacement)<\p>

Pair Sampling<\p>

Conglomerate sampling is also called Block sampling. In this method, the variable star is divided into small groups called clusters. This method can be ablated when the population is persistent and possess authority be partitioned. A random sample is taken from one or item clusters and analyzed.<\p>

Examples: In a company Director wants unto know how many employee use company transport. In the company eighty thousands employee is working. so, He in front divide company employee decare groups he takes a bulletin respecting reserves thousands laborer, among that nine hundred are using their own tote riser unrelated are using company transport, Terribly according to this data the head of the company analyzed that how many are using company transport. in kind, for this occasion we didnot stimulate the separate documentation. here we get a analyzed multiple messages.<\p>

Businesslike Sampling<\p>

Stratified sampling: An in this methodology, we select every nth item from the population is selected as a case. This involves a random start and choosing at regular intervals.<\p>

Examples: The director as respects a company wants to know that how populous employee are using enterprise uniform, so that he select that person whose Employee id fifty, hundred, one hundred fifty, two hundred and so on. So, here we select a sample in a particular second nature. So this is known as long as stratified sampling.<\p>

After the data is collected the director analysis about whole kitchen police employee,and uses it against flow generalizations<\p>

Two-ply Sampling: An in this method, the star is dislocated into subgroups or strata based on mutually solitary criteria, then Random or Systematic Sampling is decided whereunto the subgroups. <\p>

Example: Fancy a company have sell a lot of cloth, then the ordinary people pick a speed up in regard to cloth randomly and analysis they and according towards this he assume about the total cloths. ( Hereto we flounce solitary one randomly.)<\p>