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## Quantitative Data Analysis

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**Quantitative Data Analysis**JN602 Week 10 Veal Ch 13 & 14, SLT Chapter 11**Objectives**• edit questionnaire and interview responses • set up the coding key for the data set and code the data • categorise data and create a data file • use SPSS, Excel or other software programs for data entry and data analysis • get a ‘feel’ for the data using univariate analysis • test the goodness of data • statistically test each hypothesis using bivariate analysis • interpret the computer results and prepare recommendations based on the quantitative data analysis**Quantitative Data Analysis Process**• Data Preparation • Data Cleaning • Familiarisation – Frequencies, Means, Recoding • Data Analysis – Crosstabs, Statistics • Answering research questions • Graphics • Interpretation • Discussion and recommendations**Data Preparation**Getting Data Ready for Analysis • Editing data • Handling blank responses • Coding • Categorising • Entering data • Cleaning**Errors in the analysis process**• Recording errors • Misreading of questionnaire • Multiple responses • Entry errors • Deliberate • Accidental: keying errors; misreading of responses**Entering data**• Enter data from answer sheets directly into computer • Enter raw data through any software programme, eg SPSS Data Editor, Excel, text programme • Assign meaningful names to columns • Save regularly**Cleaning data**• Possible code cleaning • Check that the distribution of the item is within the possible range of responses • If possible, computer program should not permit invalid entries • Contingency cleaning • Cleaning based on prior responses • E.g. males should not have responses regarding giving birth**Data entry:SPSS Variables specification**• For each variable in the questionnaire, specify: • Name • Type – numeric or string • Width – max. no. of characters • Decimal places • Label – longer version of name • Values • Missing – blanks, no answer, etc. – see note • Columns – in Data View • Alignment – left, right, centre • Measure/data type – nominal, ordinal, scale – see note**A note on Measure/Data type**• Nominal data = non-quantitative data: even if numerical codes are used, data cannot be added, multiplied etc. • Ordinal data = ranks: 1, 2, 3 etc. = first, second, third etc. • Scale data = fully numerical: can be added, multiplied, etc. • The type of data has implications for types of analysis which can be undertaken for individual variables**A note on ‘Missing’ values**• If a no value response is entered for a variable (ie. = blank), SPSS treats this as a ‘Missing value’ • Not included in percentages etc. • You can specify other values as ‘Missing’ • eg. 0 could be specified as ‘No answer’ or ‘Not applicable’**Introduction to SPSS**• SPSS uses two ‘windows’: • Variable View window • Data View window • User can ‘toggle’ between the two windows using the tabs at the bottom of the screen**Types of research and approaches to analysis**Starting an SPSS analysis session Analysis procedures Frequencies – one variable Frequencies – multiple variables Missing values Analysis procedures (continued): Checking for errors Multiple response Recode Means Attitude/Likert scales Crosstabulation Weighting Graphics Analysing Questionnaire Survey Data**Starting an SPSS analysis session**• Click on SPSS icon to start session OR select START, then PROGRAMS then SPSS • Select file from recently used files dialog box … or select MORE FILES and locate file, OR • Select FILE from menu bar, then OPEN, select FILES OF TYPE SPSS (.sav), then locate your file. • ‘Variable View’ and ‘Data View’ windows should appear.**The statistics approach**• Concepts/terms/ideas used in statistics: • Forms of analysis • Measures of central tendency and dispersion • The idea of probabilistic statements • The normal distribution • Probabilistic statement formats • Significance • The null hypothesis • Dependent and independent variables**Forms of quantitative analysis**• Univariate - simplest form,describe a case in terms of a single variable. • Bivariate - subgroup comparisons, describe a case in terms of two variables simultaneously. • Multivariate - analysis of two or more variables simultaneously.**Probabilistic statements**It is only possible to estimate the probability that results obtained from a sample are true of the population – therefore statements on findings are probabilities.**Basis of probabilistic statements**• Probability is based on the idea of drawing many random samples • Most results would be close to the population value • Some would be larger or smaller • A few would be very much larger or smaller • This distribution can be estimated using statistical theory • See Figure 14.1 – ‘bell-shaped’ Normal distribution**Probabilistic statement formats**• So far we have used 95% probability • this is sometimes expressed as 5% • and sometimes expressed as 0.05 • 99% probability is also used • also expressed 1% or 0.01 • 99.9% probability is occasionally used • Also expressed as 0.1% or 0.001 • Note particularly in correlation and ANOVA output**Significance**• A finding which is unlikely to have happened by chance (ie. is ‘highly probable’) is described as ‘significant’ • Denoted by the probability of it occuring by chance (e.g. 0.05, 0.01, 0.001) • The larger the sample the greater the likelihood that a finding will be significant • But NB: small differences or weak relationships may not be socially or managerially significant – even when they are statistically significant**Univariate Analysis**• Describing a case in terms of the distribution of attributes that comprise it. • Examples: course of study, sex, age Goals: • Provide reader with the fullest degree of detail regarding the data. • Present data in a manageable form.**Measures of central tendency and dispersion**• Central tendency • The mean is the sum of scores in a distribution divided by the number of scores. • The mode is the most frequent score in a distribution. • The median is the mid-point or mid-score in a distribution • Dispersion • The range is: the highest score in a distribution minus the lowest score in the same distribution. • The variance is: the mean of the squared deviation scores about the mean of a distribution. • The standard deviation is: the square root of the variance**Frequency tables**• For presentation of CATEGORICAL data • Nominal or ordinal responses • Eg. Day of week, sex • Present the distribution of a small number of categories**Bivariate Analysis**• Describe a case in terms of two variables simultaneously. • Aim is to test the relationship between the independent (explanatory) variable and the dependent variable • Example: • Gender • Amount of exercise**Fig. 14.2 Dependent & independent variables**Does this look familiar?**Null hypothesis**• Setting up two mutually incompatible hypotheses: • if one is true the other must be false • The ‘null’ hypothesis and the alternative hypothesis • H0 = Null hypothesis: there is no difference/relationship • H1 = Alternative hypothesis: there is a difference/relationship**Data file**• To demonstrate SPSS statistical procedures: • Data from student background survey • Data from online diary survey • PDA survey data available next week**Chi-square**• Testing the relationship between two variables presented in a frequency crosstabulation. • Null/alternative hypotheses: • H0 - there is no relationship between exercise activity and gender in the population • H1 - there is a relationship between exercise activity and gender in the population. • SPSS - procedures p. 260 - Figure 14.4**Interpreting Chi-square output - 1**• Degrees of freedom • (Number of rows -1) x (Number of columns -1) • Expected counts rule: • Expected count = cell frequency if there was no relationship at all between the variables • Should be: no more than one fifth of cells with expected counts of less than 5 • Should be: no cells with expected count of less than 1 • If rule is violated: try combining rows or columns • Presentation of Chi-square results – See Fig. 14.7**Interpreting Chi-square output - 2**• Value of chi-square: • If value is in the 5% zone (ie. Probability is less that .05) it is an unlikely value and Null Hypothesis is rejected. • Value is 6.588 and probability is 0.037 or 3.7%, so Null Hypothesis is rejected • there is a significant difference in enrolment pattern between men and women. • Presentation of Chi-square results – See Fig. 14.7**Comparing two means: t-test**• Situation 1: two variables applying to all members of the sample • Eg. Compare time spent on exercise and time spent on study • Paired samples t-test • Situation 2: sample is divided in two • Eg. Compare average happiness levels in different activities • Independent samples t-test**Compare 2 means: Independent samples t-test**• Reading t-tests • Example 1: Enjoyment and happiness by activity • Happiness: in class mean 2.53, at work 2.73 • H0 Null hypothesis: there is no difference between these two • t value = -0.712; Probability = 0.478 (which is > 0.05) • Accept the null hypothesis – there is no significant difference**Compare 3+ means: One-way Analysis of Variance (ANOVA)**• Comparing a range of means – see Fig. 14.11 • SPSS – see procedure pp. 243-44 • H0 Null hypothesis: each of the group means is equal to the overall mean • H1 Alternative hypothesis: there is a difference between group means**One-way Analysis of Variance (ANOVA)**• SPSS - procedure p. 271 – see Fig. 14.13