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Tuesday 25 December 2012

RM- Basic Statistics for Research in Management(Uploaded for BMS students for project work statistical analysis part)

1. Population:  The word 'population' or Universe denotes aggregate or group of individual objects of any nature whose general characteristics are studied by a statistical investigation. The population may finite or infinite.

2. Sample : Sample is a finite sub set of the population and the number of items in a sample is called size of a sample. It may be large or small sample.

3. The standard deviation of sampling distribution of statistic is known as standard error.

4.  Statistical constants of population namely mean (μ) and variance (s2) etc, which are usually referred as parameter.  The statistical measures from sample observation are known as mean (x) and S.D (S), variable (S2).

5.  "A hypothesis in statistics is simply a quantitative statement about a population". It is based an assumptions.

6.  Null hypothesis is the hypothesis, which is tested for possible rejection under the assumption that it is true and is denoted as Ho

7. Alternative hypothesis is the statement about the population, which gives an alternative to the null hypothesis and is denoted by H1.

8.  Type I and Type II error:  Rejection of the hypothesis when it should be accepted is known as Type I error. Acceptance of a hypothesis when it should be rejected is known as Type II error.
                                        Accept Ho                                Reject Ho
Ho is true                         Correct decision                         Type I error
Ho is false                        Type II error                              Correct decision
9.  In testing a given hypothesis, the maximum probability with which we could be willing to risk is called level of significance of the test.

10. critical value:  The value of the test statistic, which separates the sample space into rejection region and the acceptance region, is called the critical value.

11. Procedure for testing of hypothesis:  1. Set up the Null hypothesis: Ho     2. Set up the alternative hypothesis: H1                3. Choose an appropriate level of significance             4. Calculate the test statistic Z= t-e(t)/ s.e(t)             5. Compare the computed value with the table value.  if Z > table value : Reject the Null ;  Z < table value: Accept the Null

12. One-tailed test: In any test, the critical region is represented by a portion of the area under the probability curve of the sampling distribution of the test statistic. A test of any statistical hypothesis where the alternative hypothesis is one tailed (right or left tailed) is called a one-tailed test.

13.Two-tailed test: A test of statistical hypothesis where the alternative hypothesis is two tail. Ho:
μ = μo against the alternative hypothesis H1: μ >μo and H1: μ< μo is known as two tailed test in such case the critical region is given by the portion of the area lie in both the tails of the probability curve of the test statistic.

14. non-parametric test: The tests, which do not depend upon the population parameters such as mean and the variance, they are called non-parametric tests. Non-parametric statistics is a collection of tools for data analysis that offers a different approach to many of the decision problems. Non-parametric tests are distribution free. That is they do not require any assumption to be made about population. They are simple to understand and easy to apply when the sample sizes are small. Non-parametric test make fewer and less stringent assumptions than do the classical procedures. It is less time consuming.  The following are the methods used in non-parametric tests. They are: 1. The sign test 2. A Rank sum test 3. The one sample Runs Test 4. The kruskal wallis or H test 5. The spearman's Rank correlation procedure

15.  Correlation analysis deals with the association between two or more variables. The following are the significances of correlation: There are some kinds of relationship between variables. For example relationship between price and supply, income and expenditure etc. The two variables are closely related. That is the estimate the value of one variable given the value of another. The effect of correlation is to reduce the range of uncertainty.  If two variables tend to move together in the same direction. That is an increase in the value of one variable is accompanied by an increase in the value of other variable.  If two variables tend to move together in opposite directions so that an increase or  decrease in the value of one variable is accompanied by a decrease or increase in the value of other variable then the correlation is called negative or inverse correlation.

16. Rank correlation coefficient:  In 1904, Charles Edwin Spearman a British psychologist found out the method by determining the coefficient of correlation by ranks. This measure is useful in dealing with qualitative characteristics such as intelligence, beauty, morality, character etc. Features of spearman's correlation coefficient : 1. The sum of the difference of ranks between two variables shall be zero
That is d = o 2. Spearman's correlation coefficient is distribution free.

17.  "Regression is the measure of the average relationship between two or more variables in terms of the original units of data". Uses of regression analysis: 1. Regression analysis provides estimates of value of the dependent variable from values of the independent variable. 2. With the help of regression coefficients, we can calculate the correlation coefficient (r) and the coefficient of determination (r2). 3. The regression analysis is highly useful and the regression line equation helps to estimate the value of dependent variable, when the values of independent variables are used in the equation

18. A time series may be defined as a collection of readings belonging to different periods of some economic variable or composite of variables.  The following are the various components of time series. 1. Trend
2. Seasonal charges 3. Cyclical charges 4. Irregular or Random fluctuations. The changes in the value of variable in different periods of time are due to so many factors. These factors are called the components of a time series.

(Source: Text book by S.P.Gupta, Indira Gupta, Notes given by Girija vallaban sir, IGNOU study material)


RM-Statistical analysis in excel few tips

Excel Central Tendency and Variability Functions
FunctionWhat It Calculates
AVERAGEMean of a set of numbers
AVERAGEIFMean of a set of numbers that meet a condition
AVERAGEIFSMean of a set of numbers that meet one or more conditions
HARMEANHarmonic mean of a set of positive numbers
GEOMEANGeometric mean of a set of positive numbers
MODEMode of a set of numbers
MEDIANMedian of a set of numbers
VARPVariance of a set of numbers considered to be a population
VARVariance of a set of numbers considered to be a sample
STDEVPStandard deviation of a set of numbers considered to be a population
STDEVStandard deviation of a set of numbers considered to be a sample
STANDARDIZEA standard score based on a given mean and standard deviation
  
Excel Relative Standing Functions
FunctionWhat It Calculates
RANKRank of a number in a set of numbers
PERCENTRANKRank of a number expressed as a percent
PERCENTILEThe indicated percentile in a set of numbers
QUARTILEThe 1st, 2nd, 3rd, or 4th quartile of a set of numbers
Excel Correlation and Regression Functions
FunctionWhat It Calculates
CORRELCorrelation coefficient between two sets of numbers
PEARSONSame as CORREL. (Go figure!)
RSQCoefficient of determination between two sets of numbers (square of the correlation coefficient)
SLOPESlope of a regression line through two sets of numbers
INTERCEPTIntercept of a regression line through two sets of numbers
STEYXStandard error of estimate for a regression line through two sets of numbers



ToolWhat it Does
Anova: Single FactorAnalysis of variance for two or more samples
Anova: Two Factor with ReplicationAnalysis of variance with two independent variables, and multiple observations in each combination of the levels of the variables.
Anova: Two Factor without ReplicationAnalysis of variance with two independent variables, and one observation in each combination of the levels of the variables.
CorrelationWith more than two measurements on a sample of individuals, calculates a matrix of correlation coefficients for all possible pairs of the measurements
CovarianceWith more than two measurements on a sample of individuals, calculates a matrix of covariances for all possible pairs of the measurements
Descriptive StatisticsGenerates a report of central tendency, variability, and other characteristics of values in the selected range of cells
Exponential SmoothingIn a sequence of values, calculates a prediction based on a preceding set of values, and on a prior prediction for those values
F-Test Two Sample for VariancesPerforms an F-test to compare two variances
HistogramTabulates individual and cumulative frequencies for values in the selected range of cells
Moving AverageIn a sequence of values, calculates a prediction which is the average of a specified number of preceding values
Random Number GenerationProvides a specified amount of random numbers generated from one of seven possible distributions
Rank and PercentileCreates a table that shows the ordinal rank and the percentage rank of each value in a set of values
RegressionCreates a report of the regression statistics based on linear regression through a set of data containing one dependent variable and one or more independent variables
SamplingCreates a sample from the values in a specified range of cells
t-Test: Two SampleThree t-test tools test the difference between two means. One assumes equal variances in the two samples. Another assumes unequal variances in the two samples. The third assumes matched samples.
z-Test: Two Sample for MeansPerforms a two-sample z-test to compare two means when the variances are known

RM-Tools for statistical analysis

1)      ANOVA: ANOVA can be uses to examine differences among the means of several different groups at once. It is a statistical technique for assessing how nominal independent variables influence a continuous dependent variable.
2)      Correlation analysis: The correlation is the study of finding the relationship between the variables. If there are only 2 variables in the study of correlations there it is called simple correlation. Otherwise the study will be in either partial or multiple correlations. In this study the simple inter-correlations analysis is performed between the selected variables and the results are presented in the form of correlation matrix. Further the significance of correlation was tested for is significance at 5% level of significance.
3)      Multiple regression analysis: The multiple regressions analysis is a functional relationship between a dependent variable and a set of independent variables. In this section the results of multiple regressions analysis is presented between the dependent variable and other independent variables.
4)      Chi square analysis: The Chi square test is used in any study on social science and management for testing the independence of two attributes. Each of the Personal factors is compared with the study fact and chi square test is applied and describes the results in terms of personal factors, chi-square values (c2), p values and their significance(S/NS) on the factor studied and the results are presented with suitable hypothesis and relevant interpretations.
5)      Average Score analysis: The Average score analysis is mainly used in any study is to assess the level of opinion/awareness/satisfaction of the different category of respondents on the various aspects relating to the study. First the opinion of the respondents are assessed through a scaling technique and then based on the consolidated opinion of the respondents, the average score is calculated.
6)  Percentage Analysis: It is the simple and common method to represent raw streams of data as a percentage for better understanding of collected data. Percentages are used in making comparison between two or more variables to find the efficacy of each variable.

Basics of statistical analysis

Statistical analysisThis term refers to a wide range of techniques to. . . 1. (Describe) 2. Explore 3. Understand 4. Prove 5. Predict . . . based on sample datasets collected from populations, using some sampling strategy.

Why?1. We want to summarize some data in a shorter form  2. We are trying to understand some process and possible predict based on this understanding  • So we need model it, i.e. make a conceptual or mathematical representation, from which we infer the process. • But how do we know if the model is “correct”? * Are we imagining relations where there are none? * Are there true relations we haven’t found? • Statistical analysis gives us a way to quantify the confidence we can have in our inferences.
Populations and samples• Population: a set of elements (individuals)  * Finite vs. “infinite” • Sample: a subset of elements taken from a population * Representative vs. biased • We make inferences about a population from a sample taken from it. • In some situations we can examine the entire population; then there is no inference from a sample. Example: all pixels in an image.
Types of Variables                                                       1. Nominal  2. Ordinal 3. Interval 4. Ratio
Data analysis strategy1. Posing the research questions  2. Examining data items and their support  3. Exploratory non-spatial data analysis 4. Non-spatial modelling  5. Exploratory spatial data analysis
6. Spatial modelling 7. Prediction 8. Answering the research questions

RM-MM sample example

Marketing1. Consumers outlook1. Towards department stores in ________ city1. Type of research 2. Sampling area: 3. population 4. sample size 5. sampling design 6. primary data 7. secondary data 8.  Research instruments 9. Research analytical tools1. To find out consumer opinion towards department store in______CRMAnalysis of Relationship betweenGender, age, martial status, montly income, family size, class, locality, Customer support, price, satisfaction, feel good, budget, quality, time pass,  easeness, availability, fast, value for money, pride, respect, point benefits, gifts, product range, neatness, tidy, good CRM, parking, easy availability, promotional schemes, wide product range
2. To find out the reasons for purchasing in department store
3. To know consumers satisfaction level towards department
stores

RM-FM selection one sample example

Finance1. Mututal fundsPerception of investors1. Type of research 2. Sampling area: 3. population 4. sample size 5. sampling design 6. primary data 7. secondary data 8.  Research instruments 9. Research analytical toolsThe basic objective of the study is to analyze the quality of financial institutions
in ____________giving the investment expertise to the mutual fund
investors.
Factors impacting investmentThere is no significant difference about investor’s  perception and financial expertise of the mutual fund services providers amongst investors classified by
gender/Age/Qualification/Income/
Investment factors1. Technology:   Builds the access to the knowledge portals with increased speed 2. Innovation  : More creative  options of investment created   3. Counseling  Gives the security to the investor   developed  4. Motivation  Builds the positive attitude  5. Quality information Builds the empowerment
6. Collaboration  Increases the learning and networking  7. Commercialization  Use of knowledge in the industry  8. Information technology Builds the virtual teams and makes the investor emop  9. Marketing strategies Connects to the society and builds the faith  10. Globalization Exposure to the international environment    11. Government support  Builds the quality and faith with better assurance  12. Certification  Increases the credibility
To determine the impact of mutual fund investment on investor’s perceptions
and satisfaction
Impact of MF investmentThere is no significant difference about investor’s  perception and mututal fund performance classified by
gender/Age/Qualification/Income/
Impact of MF investment1. contribution to owners : growth, profitability, realization of objectives and goals, development and innovation of new facilities, and cources 2. to investors: value added services, optimum cost, build loyalty, trust and faith, safe and secured returns 3. to society: giving liquidity for companies for business performance, building pool of savings, better r&d to new products of investments
To frame   the suggested strategy for providing the quality investment
products through the mutual funds.  
Risk assessmentThere is no significant difference about investor’s  perception and mututal fund risks classified by
gender/Age/Qualification/Income/
Risks Country risk ,  Credit risk , Currency risk , Interest rate risk,Liquidity risk , Market risk 
2. Stock marketPerception of investors1. Type of research 2. Sampling area: 3. population 4. sample size 5. sampling design 6. primary data 7. secondary data 8.  Research instruments 9. Research analytical tools     
Perception of Brockers     
3. Investment analysis/Portfolio mangementInvestors attitude     
Invetment objectives     
impact of market movements     
Financial statement fraud     
Towards commodity derivatives-Futures, forward, swaps etc     
Peoples preference as to investment     
Peoples preference as to portfolio     
Peoples preference as to industry     
Corproate governance     
CSR