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Introduction Basic Definitions and Concepts Nilesh Kulkarni • • • • • • Contents: Defination of variables. Types of variables. Sampling & population & different types. Population parameter and sample statistics. Precision, Accuracy, bias. Nilesh Kulkarni • Objective: To know about the proper variables and how to identify it properly. • By this we will know that how to select thing in a proper manner . • By this study some confusions might be clear about systematic . Nilesh Kulkarni • VARIABLES: A Variable is defined as anything that varies or changes in value. Variables take on two or more value.variable generally is anything that may assume different numerical or categorical value. • Variable it may be increase or decrease. • For eg:like weight, height or income i.e family income is a variable it can take on value from zero to billion of rupees. • Gender is a variable it can take two value male and female. • Marital status is a variable it can on value of never married,single, married, divorced. • Variables it can be in the production batch. • ake on two or more values. Variable generally is anything that may assume different numerical or categorical Nilesh Kulkarni TYPES OF VARIABLES 1)Continuous Variables & Discrete Variables . 2)Dependent Variables &Independent Variables. 3)Moderating Variables. 4)Intervening Variables. 5)Extraneous Variables. 1) Continuous Variables & Discrete Variables: Values of variable can be divided into fraction we call it as a continuous variables. • Value even in decimal point are called continuous variables. • Variables can take infinite number of value • For eg:age,income, temprature. • • • • • • • Nilesh Kulkarni • Discrete Variables: It is also called as non-continuous • • • • • variables or categorical variables or discontinuous variables. Variables that has a limited number of distinct value & which cannot divided into fraction is a called discontinuous variable. Variables that are not continuous they can expressed in integral value they are non-continuous variables. For eg: number of children is an ex. of not –continuous. Some variable has only 2 value i.e. Male-female,presence or absence,employed- unemployed.such variable are refered as dichotomous variable Eg:same class 2 students are selected Nilesh Kulkarni • 2)Dependent Variables &IndependenVariables: • Independent variables: variable which are in the hand of researcher . • Dependent Variables: outcome of manipulation is dependent • Eg:Reduction particle size improve solubility. • For eg:Height depend upon age. Height is dependent variable &age is independent • Ingredients & Tablet. Ingredients is independent ,tablet is dependent. • Cipla launch new medicine & market share increase. New medicine is independent & market share is dependent. Nilesh Kulkarni • 3)Moderating Variables: The presence of third variable(the moderating variable) that modifies relationship between the independent& the dependent variable. • For eg:library facilities(x)& performance of the students(y)…… in this facilities is independent & performance is dependent & interest and inclination of student is 3rd variable and i.e. hard afford and strength of student. • 4)Intervening Variables: It comes between the independent &dependent variables and shows the mechanism between them. • Certain variable that cannot be controlled or measured directly may have & important effect on the out come. These modifying variables intervene between the cause and effect. • For eg:Mobile,simcard,network. Mobile-dependent ,simcardindependent,network-mechanism • Married people are less likely to suicide than single. • API,Tablet,excipient. • Coiumn,HPLC,Pressure. Nilesh Kulkarni • Particle size,solubility,Temprature. (5)Extraneous Variable: Extraneous variables are those uncontrolled variables(i.e,Variables are not manipulated by the experimenters) that may have a significant influence on the result of a study. Many research conclusion are questionable because of the influence of the extraneous variables. Nilesh Kulkarni Sample and population • Population: A population is defined as a group of individual which at least one common characteristic which distinguishes that group of individuals. • Eg.Learning disabilities If we want to select then Go to narrow Population in that narrow population. Select Specific area, After selecting specific area select specific place and from that we can select. • eg.group of population suffering from diabetics Nilesh Kulkarni Sample • • A sample is a small proportion of the population that is selected for observation and analysis. By observing the characteristics of sample one can make certain inferences about the characterics of the population from which it was drawn One can also infer changes observed in the sample. changes that would likely have occurred in the population. Contrary to population sample are not selected haphazardly, they stare chosen in a systematically random way. so that chance or the operation of probability is utilized. Where random selection is not possible other systematic methods are used. Nilesh Kulkarni Sampling Method • • • • • • Randomness. Simple Random sample. Random number. Systematic sample. Stratified random sample. Area or cluster sample. Nilesh Kulkarni • 1)Randomness:It is based on the assumption that while individual events cannot be predicted with great accuracy aggregate. • Although it may not predict with great accuracy an individual academic achievement .it will predict accurately the average academic performance of a group. • It has two important application:1)selection of group of individuals for observation who are representative of the population. • 2)Assigning individuals by random assignment i.e each of individual has equal chance. Nilesh Kulkarni • Sampling error: A small difference in conclusion or a small variation in conclusion. • 2)Simple Random Sample: Probability sampling is also known as Random sampling or Chance sampling. • Each has an equal & independent chance of being selected. • In this entire population have equal chance of being included in the sample • This applies to sampling without replacement i.e once an item is selected for the sample ,it cannot appear in the sample again. Nilesh Kulkarni • 2)Simple random sample are: • a)It gives each element in the population an equal probability of getting into the sample & all choice are independent of one another. • b)It gives each possible sample combination an equal probability. • 1) sample random sample from the finite population as a sample which can chosen such a way that each of the N Cn Possible sample has same probability 1/ N Cn being selected • for more clear we take certain finite population comsisting 6 elements (say a,b,c,d,e,f) i. e N=6 & sample size n=3, then there are 6C3 = 20 • possible distinct sample of required size element consist abc,abd,abc,abd,abe,abf,acd,ace,acf,ade,adf,aef,bcd,bce,bcf,bde, bdf,bef,cde,cdf,cef,def.If we chose one of the samples in such a way that each has the probability 1/20 of being chose. • 2)eg:on a cheat write a no & put it into one pot & see the cheat which no as for the requirement of the sample . Nilesh Kulkarni • 3) Random Number: A more convenient way of • • • • • selecting a random sample or assigning individuals to experimental & control groups so that they are equated is by the use of a table of random numbers. Many such tables have been generated by computers producing a random sequence of digitals. This random number selected from left,right,top,bottom. For eg: assume that sample of 30 is selected from serially numbered population of 835, table of random no produce 30 In this 3 digit no are selected by reading from left,right,up down. The sample comprises 30 no members of population .the group are divided into 2 groups 15 in one group and 15 in other group Nilesh Kulkarni The Sample 503 426 197 161 590 913 449 931 337 422 530 234 408 669 333 802 381 820 457 497 092 050 242 660 273 939 982 090 897 699 161 117 074 383 234 744 407 893 In selecting this sample 8 no.were deleted number 931 ,982,897,893,939,913 were deleted because they were larger than the population of 835 no. 234 and 161 were deleted because duplicate previous selection. Nilesh Kulkarni • 4)Systematic Sample:The most practical way of sampling is to select every or nth term from a list sampling of this type is known as systematic sampling . • Systematic sampling has plus point. • For eg:Sample of 200 were to be selected from a telephone director 20,000 listings .one would selected the first name by random selecting page. • Then every thousand name would selected until the 200 name & if the last page were reached before desired no then again start from first & complete 200 • Eg: BSNL Nilesh Kulkarni • 5)Stratified Random sample: Stratified random sample is that subdivided the population into smaller group more accurate representation. • Eg:If an new setup of industry is done an employ is appointed over there i.e 60 worker then properly subdivided them category wise like education skilled,unskilled person. Nilesh Kulkarni • 6) Area or cluster sample: The total area of intrested happen to be a big one a convenient way in which a sample can be taken is to divided the area into a smaller area & then select is with the ultimate sample consisting of all units in these small area or clusters. • For eg:for the purpose of servey researchers wanted to select a sample from all public elementary teacher in the united states • From 50 states a random sample of 20 could be selected • From 20 state all countries could be listed random sample of 80 countries selected • From 80 countries all the school districts are listed • 30 school where selected • Now from 30 school random selected 500 teachers, • Successive random sampling of states,countries,school districts ,finally individuals would involve Nilesh Kulkarni • For eg: best school. Population parameter & sample statistics • statistics is to understand the difference between populations and samples. Populations consist of everything or everybody you want to measure. • for example, “all women in the Bay Area between the ages of 18 and 54.” • “The light bulbs we are manufacturing in this plant.” “Every human being on planet earth.” These are all populations. Populations have parameters .” • The science of statistics is based on measuring these samples; in other words, samples have statistics. Hypothesis testing is done by testing the sample statistics against assumptions about the population parameters. Nilesh Kulkarni Variation: • The act ,process, or result of varying. • Something slightly different from another of the same type. • Variation in quality, amount or variation in temperature. • Eg: Variation of the needle ,compass , height. Nilesh Kulkarni • The mean and variance of a population are population parameter: • Population mean=(μ) the average value • Sample mean =Y estimates μ • Population median-middle value. • Sample mean estimate population median. • Population variance. • Sample variance. • Standard deviation. • Standard error of mean. • Coefficient of variance. Nilesh Kulkarni Precision and Accuracy: • Precision:Pression is defined as the closeness of agreement between series of measurement obtained from multiple sampling of the same homogeneous sample under prescribed condition. • Accuracy: defined as closeness of agreement between the value which is accepted either as a conventional true value or an accepted reference value and the found value. Nilesh Kulkarni Bias: • The different between a population mean of the measurement of test results & accepted reference or true value. • Therefore bias leads to an under or overestimate of the true value. • Measurement bias usually does not disappear with ↑sed sample effect as all measurement are systematically bias away from true value. • Eg:observed no. of species is a negatively bias estimator of the total species richness whoes bias ↓ses with ↑sing sample effect. Nilesh Kulkarni • • • • • Significant figures Non-zero digits are always significant. All zeros between other significant digits are significant. The number of significant figures is determined starting with the leftmost non-zero digit. The leftmost non-zero digit is sometimes called the most significant digit or the most significant figure. For example, in the number 0.004205 the '4' is the most significant figure. The left-hand '0's are not significant. The zero between the '2' and the '5' is significant. The rightmost digit of a decimal number is the least significant digit or least significant figure. Another way to look at the least significant figure is to consider it to be the rightmost digit when the number is written in scientific notation. Least significant figures are still significant! In the number 0.004205 (which may be written as 4.205 x 10-3), the '5' is the least significant figure. In the number 43.120 (which may be written as 4.3210 x 101), the '0' is the least significant figure. If no decimal point is present, the rightmost non-zero digit is the least significant figure. In the number 5800, the least significant figure is '8'. Nilesh Kulkarni Conclusion • In this we find the best way to distinguish large population to small one in simple way. • All work carried in properly • No confusion occur . Nilesh Kulkarni Reference • 1)Research in Education Tenth edition. By John W.Best,JamesV.Khan. • 2)Research Methodology Methods and Techniques. Second revised edition.C.R.Kothari. • 3)Moor DS, McCabe GP & Craig BA. Introduction to the Basic practice of Statistic. New york:W.H.Freeman & CO, Fifth edition. • 4)B.A .Walter Zool museum univ,of Copenhagen. • 5) Significant Figures in Measurements and Calculations By Anne Marie Helmensline,ph.D. Nilesh Kulkarni Jackson L. S.; Lee K. (1991-01-01). "Microencapsulation and the food industry". Lebensmittle–WissenschaftTechnologie. http://cat.inist.ft/?aModele=afficheN&cpsidt=5014466. Retrieved 1991-02-02. Nilesh Kulkarni