POPULATION.pptx

Population in statistics means the whole of the information which comes under the preview of statistical investigation.
In other words, an aggregate of objects animate or in animate under study is the population.
It is also known as “Universe”.

1. BIOSTATISTICS AND RESEARCH METHODOLOGY Unit-3: introduction of research PRESENTED BY Himanshu Rasyara B. Pharmacy IV Year UNDER THE GUIDANCE OF Gangu Sreelatha M.Pharm., (Ph.D) Assistant Professor CMR College of Pharmacy, Hyderabad. email: [email protected]

2. POPULATION Population in statistics means the whole of the information which comes under the preview of statistical investigation. In other words, an aggregate of objects animate or in animate under study is the population. It is also known as “Universe”. For population a finished package contains a finite number of tablets, all possible tablets made by a particular process, past, present and future, can be considered infinite in concept. In most of the examples, the population will be considered to be infinite, or at least very large compared to the sample size. A population may consist of all patients with a particular disease(or) tablets from a production batch.

3. SAMPLE A part of the population selected for study is called Sample. (OR) The selection of a group of individual (or) items from a population in such a way that this group represents the population is called a Sample. The sample is only part of the available data. When designing an experiment the population should be clearly defined so that samples chosen are representative of the population. This is important in clinical trials. When the sample drawn is perfectly representative, it is identical with its present population almost in every respect except that it is smaller than the population. Size Of Sample The number of individuals included in the finite sample is called the size of the sample. Population Parameters and Sample Statistics Mean, Median, and Mode, Standard deviation, coefficient of variation etc can be complied both from population/universe data and sample data. Parameter : Any measurable characteristic of the universe is called a “Parameter”. (or) Any statistical measure computed from population data is known as “Parameter”. Parameters are generally denoted by Greek letters.

4. Statistic : Quantities derived from the sample are called “Sample statistics”. (or) Any statistical measure computed from sample data is known as “Statistic”. Notations : Statistical Measure Population Sample Mean μ x̄ Standard Deviation σ s Population P p Size N n Use Of Sampling: The study of relationships existing between a population and the samples drawn from the population is called Sampling. Statistical inference made on the basis of sampling results are of 3 types.

5. Statistical Estimation It helps in estimating an unknown population parameters (such as Population mean, Median, Mode etc.) on the basis of suitable statistic (such as Sample Mean, Mode, Median, Variable etc) computed from the sample drawn from the sample drawn from such present population. Test Of Significance Sampling helps in determining whether observed differences between 2 samples are actually due to chance or weather they are really significant such questions helps us in deciding whether one production is better than the other. The test of significance plays an important role in the theory of decisions. Statistical Inference It means drawing conclusions about some matters on the basis of certain statistical results.

6. SAMPLING METHOD In  Statistics , the sampling method or sampling technique is the process of studying the population by gathering information and analyzing that data. It is the basis of the data where the  sample space  is enormous .  TYPES OF SAMPLING METHOD

7. PROBABILITY SAMPLING The probability sampling method utilizes some form of random selection. In this method, all the eligible individuals have a chance of selecting the sample from the whole sample space. This method is more time consuming and expensive than the non-probability sampling method. The benefit of using probability sampling is that it guarantees the sample that should be the representative of the population. SIMPLE RANDOM SAMPLING: In simple random sampling technique, every item in the population has an equal and independent chance of being selected in the sample. Since the item selection entirely depends on the chance, this method is known as “ Method of chance Selection ”. As the  sample size  is large, and the item is chosen randomly, it is also known as “ Representative Sampling ”. MERITS This method requires minimum knowledge of population in advance which is needed in the case of purposive sampling. This method is free from classification error. DEMERITS This method does not make use of the knowledge about the population which researcher may have. Time and cost of collecting data become too large.

8. STRATIFIED SAMPLING: In a stratified sampling method, the total population is divided into smaller groups to complete the sampling process. The small group is formed based on a few characteristics in the population. After separating the population into a smaller group, the statisticians randomly select the sample. MERITS Increases probability of sample being representative. Assures adequate number of ease for subgroups. DEMERITS Requires accurate knowledge of population. May be costly to prepare stratified lists. Statistics are more complicated. SYSTEMATIC SAMPLING: In the systematic sampling method, the items are selected from the target population by selecting the random selection point and selecting the other methods after a fixed sample interval. It is calculated by dividing the total population size by the desired population size. The steps involved in this sampling is : To obtain a list of the total population (N). The sample size (n) decide. The sampling interval width (k) is determined by (N/n). DEMERITS Samples may be biased if ordering of population is not random. After the first sampling element is chosen, population members no longer have equal chance of being chosen.

9. CLUSTERED SAMPLING: In the clustered sampling method, the cluster or group of people are formed from the population set. The group has similar significatory characteristics. Also, they have an equal chance of being a part of the sample. This method uses simple random sampling for the cluster of population. In cluster sampling we use the following steps: Divide population into clusters. Randomly sample clusters. Measure all the units within sampled clusters. MERITS: Save money and time. Arrangements made with small number of sample units. DEMERITS: Larger sampling errors than other probability samples. Require assignment of each member of population uniquely to a cluster. Statistics are more complicated. NON-PROBABILITY SAMPLING The non-probability sampling method is a technique in which the researcher selects the sample based on subjective judgment rather than the random selection. In this method, not all the members of the population have a chance to participate in the study.

10. CONVENIENCE, ACCIDENTAL OR HAPHAZARD SAMPLING: In a convenience sampling method, the samples are selected from the population directly because they are conveniently available for the researcher. The samples are easy to select, and the researcher did not choose the sample that outlines the entire population. It is referred to as accidental or incidental and involves choosing readily available people or objects for a study. Convenience samples are chosen because of the savings in time and money. PURPOSIVE SAMPLING: In purposive sampling, the samples are selected only based on the researcher’s knowledge. As their knowledge is instrumental in creating the samples, there are the chances of obtaining highly accurate answers with a minimum marginal error. It is also known as judgmental sampling or authoritative sampling. MERITS: It is simple to draw and people often use it in exploratory investigations which precede major survey. It is less costly and involves less field work. DEMERITS: It is not always reliable. It requires from the researcher considerable knowledge about the population which he usually does not posses .

11. QUOTA SAMPLING: In the quota sampling method, the researcher forms a sample that involves the individuals to represent the population based on specific traits or qualities. The researcher chooses the sample subsets that bring the useful collection of data that generalizes the entire population. The term ‘ Quota ’ arises from the researchers establishment of a desired quota or proportion for some population variable of interest. MERITS : Quota sampling is less costly. Quota sampling is administratively easy. Most suitable in a situation where field work has to be done quickly. DEMERITS: In this type the investigator very often selects. It may not provide a representative sample of respondents. Differences between probability and Non probability sampling: Probability (Random) Non- Probability (Authoritative) Complex, time consuming and costly. Conceptually convenient and simple. Every member of a population has a known and equal chance of being selected. Samples selected based on selective judgement of the researcher. Selection is random. Results/Sampling is biased. These are also known as Random sampling methods. These are also called non-random sampling methods. These are used for research which is conclusive These are used for research which is exploratory.

12. HYPOTHESIS Statistical technique to test some hypothesis about the parent population from which the sample is actually drawn. (OR) Hypothesis is an idea that can be tested or it is a claim that we want to test. (OR) A statistical hypothesis is a hypothesis concerning the parameters (or) from the probability distribution for a designated population/ populations or more generally of a probabilistic mechanism which is supposed to generate the observations. Types of Hypothesis:

13. Hypothesis Testing :

14. Procedure: Hypothesis test procedure. To setup the hypothesis. To setup a suitable significant level Selection of appropriate probability distribution for the test[t test, f test]. To calculate or compute the data using the test. Statistical decision or decision making. NULL HYPOTHESIS: A null hypothesis define a test that there is no difference between the assumed value and natural value of parameter. A statistical hypothesis which is written for the possible acceptance is called null hypothesis. The  null hypothesis  is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data. This hypothesis is either rejected or not rejected based on the viability of the given  population or sample It also gives a natural idea about a relationship between the variables under study. It is denoted by H o . Null Hypothesis Principle The principle followed for null hypothesis testing is, collecting the data and determining the chances of a given set of data during the study on some random sample, assuming that the null hypothesis is true .

15. Alternative hypothesis: An alternative hypothesis defines there is a statistically important relationship between two variables. The alternative hypothesis is a statement used in statistical inference experiment. In hypothesis testing, an alternative theory is a statement which a researcher is testing. This statement is true from the researcher’s point of view and ultimately proves to reject the null to replace it with an alternative assumption. It is denoted by H a  or H 1 . Differences between Null and Alternative Hypothesis: Null Hypothesis Alternative Hypothesis It denotes there is no relationship between two measured phenomena. It’s a hypothesis that a random cause may influence the observed data or sample. It is represented by H It is represented by H a  or H 1 . The observations of this hypothesis are the result of chance. The observations of this hypothesis are the result of real effect. The mathematical formulation of the null hypothesis is an equal sign. The mathematical formulation alternative hypothesis is an inequality sign such as greater than, less than, etc.

16. In  statistics ,  asymptotic theory , or  large sample theory , is a framework for assessing properties of  estimators  and  statistical tests . Within this framework, it is often assumed that the  sample size   n  may grow indefinitely; the properties of estimators and tests are then evaluated under the limit of  n  → ∞. In practice, a limit evaluation is considered to be approximately valid for large finite sample sizes too. If the sample size is less than 30 (n<30) , it is known as small sample. For small samples the sampling distributions are t, F and χ 2 distribution. A study of sampling distributions for small samples is known as small sample theory. Sometimes the sample size can be very small. When the sample size is small (n < 30), we use the t distribution in place of the normal distribution. If the population variance is unknown and the sample size is small, then we use the t statistic to test the null hypothesis with both one-tailed and two-tailed, where Large Sample Size Generate for more accurate estimates but large sample size might cause difficulties in interpreting the usual tests of significance, and the same problem may arise in case of very small sample size. Thus, neither too large nor too small sample sizes help research projects.

17. TYPE I ERROR: A type I error appears when the  null hypothesis  (H ) of an experiment is true, but still, it is rejected. It is stating something which is not present or a false hit. A type I error is often called a false positive (an event that shows that a given condition is present when it is absent). The type I error significance level or rate level is the probability of refusing the null hypothesis given that it is true. It is represented by Greek letter α (alpha) and is also known as alpha level. Usually, the significance level or the probability of type i error is set to 0.05 (5%), assuming that it is satisfactory to have a 5% probability of inaccurately rejecting the null hypothesis. TYPE II ERROR: A type II error appears when the null hypothesis is false but mistakenly fails to be refused. It is losing to state what is present and a miss. A type II error is also known as false negative (where a real hit was rejected by the test and is observed as a miss. A type II error is assigned when a true  alternative hypothesis  is not acknowledged. The rate level of the type II error is represented by the Greek letter β (beta) and linked to the power of a test (which equals 1−β). Table of Type I and Type II Error The relationship between truth or false of the null hypothesis and outcomes or result of the test is given in the tabular form :

18. Error Types When H  is True When H  is False Don’t Reject Correct Decision (True negative) Probability = 1 – α Type II Error (False negative) Probability = β Reject Type II Error (False Positive) Probability = α Correct Decision (True Positive) Probability = 1 – β Type I and Type II Errors Example Example:   Null hypothesis- A patient’s signs after treatment A, are the same from a placebo . Type I error (False Positive) Type II error (False Negative) Treatment A is more efficient than the placebo Treatment A is more powerful than placebo even though it truly is more efficient.

20. Standard error of 2 sample mean, x 1 and x 2 drawn from the same population. Standard error (x 1 -x 2 )= n 1 -n 2 = Sizes of 2 samples, which are drawn from same population. Standard error of difference of 2 samples mean x 1 and x 2 from 2 different populations with standard deviations σ 1 and σ 2 respectively S.E (x 1 -x 2 )= Where n 1 and n 2 are the size of samples.