Data Analysis Techniques

Quantitative Research Methods Dr Nripendra P Rana Professor in Digital Marketing Head of International Business, Marketing & Branding Associate Editor : International Journal of Information Management 9 th September 2020 Lecture – Data Analysis techniques: Descriptive and Inferential statistics – Multivariate Data Analysis  What are different tools that can help with data analysis for generating different types of statistics?  What are things to check and correct in data before performing main analysis and generating results?  What descriptive statistics are generally reported in research papers and doctoral theses?  What statistics are generally employed to demonstrate reliability and validities of results reported?  What are examples of inferential statistics? Data Analysis Techniques (Opening Discussion for 10 Minutes) What is SPSS? (Bhattacherjee, 2012) • Statistical Package for the Social Sciences (SPSS) • Used to perform data entry and analysis • Other tools (such as SAS, Excel) can also be used to perform various analyses • Data may be collected from a variety of sources: – mail -in surveys, interviews, pretest or posttest experimental data, observational data – must be converted into a machine -readable, numeric format - spreadsheet or a text file • Coding – how data is specified in variable view – Where the coding process is conducted by different people, to help the coding team code data in a consistent manner, and also to help others understand and interpret the coded data – In case of question with multiple responses, the total number of checked items can be used as an aggregate measure of benefits Preparing a data file (Bhattacherjee , 2012) • Coded data can be entered into a spreadsheet , database , text file , or directly into a statistical program like SPSS • SPSS stores data as . sav files that makes it difficult to share that data with other statistical programs • So it is better to first enter data into a spreadsheet or database, where they can be reorganized as needed, shared across programs, and subsets of data can be extracted for analysis • Look for evidence of bad data - respondent selecting the “strongly agree” response to all items irrespective of content • Open new SPSS file • Save file and save regularly - no automatic saving • Need to define variable names and coding instructions in ‘Variable view’  Each variable name must be unique  Make sure you give each respondent a unique ID number • Once this is done you can enter data in ‘Data View’ Descriptive statistics (Bhattacherjee , 2012) • Descriptive statistics are used to describe the basic features of the data – Helps to simplify large amounts of data in a sensible way – statistically describing, aggregating, and presenting the constructs of interest or associations between these constructs • The Distribution – A summary of the frequency (counts and/or percentages) of individual values or ranges of values for a variable – Frequency distributions can be depicted using either a table or a graph (i.e. bar chart) • The Central Tendency – Mean, Median, Mode • The Dispersion - spread of the values around the central tendency – Can be measured using the range (the highest value minus the lowest value) and the standard deviation – SD corrects for outliers limitation of range by considering how close or how far each value from the distribution mean Descriptive statistics (Bhattacherjee, 2012) • The square of the standard deviation is called the variance of a distribution • It is seen that 68% of the observations lie within one standard deviation of the mean ( μ + 1 σ ), 95% of the observations lie within two standard deviations ( μ + 2 σ ), and 99.7% of the observations lie within three standard deviations ( μ + 3 σ ) • Univariate analysis refers to a set of descriptive statistical techniques: – frequency distribution; central tendency; dispersion • The most common bivariate statistic is the “correlation”, should vary between -1 and +1 denoting the strength of the association – Cross -tab and Chi Square also used for bivariate • Found in the ‘ Analyze ’ drop down • Check for data entry errors  Check for minimum and maximum values • Get a feel of your respondents’ characteristics Missing Value Analysis (Bhattacherjee , 2012) • Need to check whether the data is missing at random or not • ‘Analyze ’ then ‘Missing Value Analysis’ • As a good researcher you should not just delete cases missing less than 10% of data • Listwise deletion and Imputation – In most software programs is to simply drop the entire observation containing even a single missing value – Software programs allow the option of replacing missing values with an estimated value via a process called imputation – If the missing value is one item in a multi -item scale, the imputed value may be the average of the respondent’s responses to remaining items on that scale – If the missing value belongs to a single -item scale then use the average of other respondent’s responses to that item as the imputed value – the maximum likelihood procedures and multiple imputation methods can produce relatively unbiased estimates for imputation Outliers • Outlying responses are either inconsistent with, or particularly dissimilar to, the rest of the dataset • Outliers on Likert scale questions need to be assessed with caution – they might only detect those who have strongly agreed/disagreed, for example • Compute standard scores (z scores) for each variable (through ‘Descriptive’ function) • Outliers are those with z scores ± 3.29 Normality ( Bhattacherjee, 2012) • Most observations are clustered toward the center of the range of values, and fewer and fewer observations toward the extreme ends of the range • Normality is a fundamental assumption of many statistical techniques, thus violation can seriously invalidate test statistics • ‘Analyze’  ‘Descriptive Statistics’  ‘Explore’ • Kolmogorov -Smirnov statistics needs to be non -significant ( > .05 ) to suggest normal distribution • If the K -S statistics is significant then examine Skewness and Kurtosis values – so long as these are ≤ 2 and ≤ 7 respectively then you’re OK • Reverse coded items – should be reversed before they can be compared or combined with items that are not reverse coded. • Creating scale measures by averaging individual scale items of observed measures – This help to collapse multiple values into fewer categories Data transformation (Bhattacherjee, 2012) • Inferential statistics employed to draw conclusions from the results that extend beyond the immediate data alone – Statistical testing of hypotheses (theory testing) – Inferences from data samples to more general conditions – For example, comparing the average performance of two groups on a single measure to see if there is a difference • Examples – The t -test – Analysis of Variance (ANOVA) – Regression analysis – Factor analysis – Cluster analysis – Discriminant function analysis Inferential Statistics • The significance level is the maximum level of risk that we are willing to accept as the price of our inference from the sample to the population. – If the p -value is less than 0.05 or 5%, it means that we have a 5% chance of being incorrect in rejecting the null hypothesis or having a Type I error. – If p>0.05, we do not have enough evidence to reject the null hypothesis or accept the alternative hypothesis. • A sample is never identical to the population, every sample always has some inherent level of error, called the standard error . – If this standard error is small, then statistical estimates derived from the sample (such as sample mean) are reasonably good estimates of the population. – The precision of our sample estimates is defined in terms of a confidence interval (CI). – A 95% CI is defined as a range of plus or minus two standard deviations of the mean estimate. • what we mean is that we are confident that 95% of the time, the population parameter is within two standard deviations of our observed sample estimate. – Jointly, the p -value and the CI give us a good idea of the probability of our result and how close it is from the corresponding population parameter. Inferential Statistics (Bhattacherjee, 2012) • Regression analysis is for predicting changes in DV based on changes in IV. – A line that describes the relationship between two or more variables is called a regression line, β0 and β1 (and other beta values) are called regression coefficients – The process of estimating regression coefficients is called regression analysis • A predictor variable may represent an independent variable or covariates (control variables). – They are are not of theoretical interest but may have some impact on the dependent variable – Should be controlled in order to so detect the residual effects of the independent variables more precisely. • Covariates capture systematic errors in a regression equation while the error term captures random errors. Inferential Statistics (Bhattacherjee, 2012) • Some predictor variables may even be nominal variables (e.g., gender: male or female) – can be coded as dummy variables – Such variables can assume one of only two possible values: 0 or 1 (in the gender example, “male” may be designated as 0 and “female” as 1 or vice versa). • If comparing the effects of the two levels (0 and 1) of a dummy variable on the outcome variable - analysis of variance (ANOVA) • When doing ANOVA while controlling for the effects of one or more covariate - An analysis of covariance (ANCOVA) • When multiple outcome variables are modeled as being predicted by the same set of predictor variables - multivariate regression • Doing ANOVA or ANCOVA analysis with multiple outcome variables - a multivariate ANOVA (MANOVA) or multivariate ANCOVA (MANCOVA) respectively Inferential Statistics (Bhattacherjee , 2012) • Logistic regression (or logit model) when the outcome variable is binary (0 or 1 ) – An example is predicting the probability of heart attack within a specific period, based on predictors such as age, body mass index, exercise regimen, and so forth . – Logistic regression is extremely popular in the medical sciences . • Probit regression (or Probit model) – When the outcome variable can vary between 0 and 1 (or can assume discrete values 0 and 1 ). – A popular technique for predictive analysis in the actuarial science, financial services, insurance, and other industries for applications such as credit scoring based on a person’s credit rating, salary, debt and other information from her loan application . • Path analysis – When analyzing directional relationships among a set of variables – Where the dependent variable in one equation is the independent variable in another equation Inferential Statistics (Bhattacherjee, 2012) • t-test is for comparing the average performance (or any other differences) between two groups • Factor analysis is for describing variability among observed, correlated variables and their categorisation on a fewer unobserved variables k/a factors or components • Cluster analysis is for grouping a set of similar objects in the same group • Discriminant analysis is for predicting a categorical dependent variable (for example, adoption – Yes/No) by one or more continuous or binary independent variables Inferential Statistics (Bhattacherjee , 2012) Independent samples T Test • Independent samples t-tests are used to assess statistically significant differences between two groups, e .g . males/females • ‘Analyze’  ‘Compare Means’  ‘Independent -Samples T Test’ 1. If Levene’s value is significant then use first t-value ; if non - significant then use second t-value 2. If the two -tailed significance value is ≤ .05 then it suggests significant differences between the two groups exist Factor analysis • Condenses variables that are highly interrelated into a smaller number of factors • ‘Analyze’  ‘ Dimension Reduction’  ‘Factor … ’ • Use KMO (needs to be > .6 ) and Bartlett’s test of sphericity (needs to be significant) to ensure suitability for factor analysis • Use principal components analysis with Varimax rotation • Factor loadings need to be > .5 and cross -loadings need to be < .4 Reliability test • Assesses the internal consistency of the measures deduced through factor analysis • ‘Analyze’  ‘Scale’  ‘Reliability’ • Cronbach’s alpha values ≥ .90 = excellent reliability • Cronbach’s alpha values .70 -.90 = high reliability Computing a variable • Based on factor analysis results you can create a new variable from existing variables • ‘Transform’  ‘Compute Variable’ • Name your new variable in ‘Target Variable’ • Add the variables into parentheses in ‘Numeric Expression’ and divide by the number of variables you include E.g. (PE1 + PE2 + PE3)/3 Regression • Used to predict the value of a variable based on the value of another variable • Used to answer hypothesis such as H1: Perceived risk negatively affects behavioural intention – ‘Analyze’ then ‘Regression’ then ‘Linear’ – ‘Model Summary’ - Adjusted R Square = variance of dependent variable explained by independent variable(s) – ‘Coefficients’ – Standardized Coefficients = strength of effect of independent variable on dependent variable Help and guides • Bhattacherjee , A . (2012 ), "Social Science Research : Principles, Methods, and Practices “, Textbooks Collection . Book 3. Available at http ://scholarcommons .usf .edu/oa_textbooks/ 3 • Pallant , J. (2013 ). SPSS Survival Manual : Step by Step Guide to Data Analysis Using IBM SPSS (5th ed .). Berkshire : Open University Press . • Gefen , D ., Straub, D . & Boudreau, M . (2000 ). ‘Structural equation modelling and regression : Guidelines for research practice’, Communications of AIS , 4(7), 1-79 . • Hinton, P., Brownlow, C ., McMurray, I. & Cozens, B . (2004 ). SPSS explained , East Sussex : Routledge Inc . • McDaniel, C . & Gates, R . (2010 ). Marketing Research with SPSS (8th ed .), Asia : John Wiley & Sons . • Straub, D ., Boudreau, M -C ., & Gefen, D . (2004 ). ‘Validation guidelines for IS positivist research’, Communications of the Association for Information Systems , 13 (1), 63 . • https ://www .socialresearchmethods .net/kb/statdesc .php Thank you! Questions?