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# Level of Measurement, Frequency Distribution,Stem & Leaf

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### Level of Measurement, Frequency Distribution,Stem & Leaf

1. 1. “MULTIVARIATE DATA ANALYSIS” PRESENTED BY 1- Faiza Batool 2- Faisal Hafeez 2
2. 2. LIST OF TOPICS 1-Qualitative and Quantitative Data 2- Level of Measurement 3-Frequency Distribution 4- Stem and Leaf Plot 5- SPSS demonstration and interpretation 6- What are Multivariate data analysis and multivariate technique? 7- Why the knowledge of level of measurement is important?
3. 3. DATA is a collection of facts and figures. It can be numbers, words, measurements, observations or even just descriptions of things. 1 Data Qualitative Nominal Ordinal Quantitative Interval Ratio
4. 4. QUALITATIVE DATA Qualitative data can be arranged into categories that are not numerical. These categories can be physical traits, gender, colours or anything that does not have a number associated to it. Example: case studies and interviews. They provide a more in depth and rich description. 2
5. 5. QUANTITATIVE DATA The term quantitative data is used to describe a type of information that can be counted or expressed numerically. This type of data is often collected in experiments, manipulated and statistically analyzed. Quantitative methods are those which focus on numbers and frequencies rather than on meaning and experience. These data may be represented by interval or ratio scales. Examples of quantitative data are scores on achievement tests, number of hours of study, or weight of a subject. 3 1
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7. 7. LEVEL OF MEASUREMENT 5
8. 8. LEVEL OF MEASUREMENT 6 Scale Type Qualitative/quant itative Difference Example Nominal Qualitative Non-metric Gender, Nationality Ordinal Qualitative Non-metric Class ranking Interval Quantitative Metric Temperature, dress size Ratio Quantitative Metric Age, Income, weight
9. 9. FREQUENCY DISTRIBUTION A method of showing the number of occurrences of observational data in order from least to greatest. When a data set with a variable that has numerical values, to make a frequency distribution or more likely, a histogram of the data from that variable in order to explore the shape of the data center, skew, gaps, unusually high or low values, etc. The frequencies command(SPSS) can be used to determine measures of central tendency (mean, median, and mode), measures of dispersion (standard deviation, variance, minimum and maximum), measures of skewness and kurtosis and create histograms. 7
10. 10. FREQUENCY DISTRIBUTION Frequency analysis to answer research question. Frequency analysis is a descriptive statistical method that shows the number of occurrences of each response chosen by the respondents. 8
11. 11. STEM AND LEAF PLOT Stem-and-Leaf Plots: A convenient method to display every piece of data by showing the digits of each number. A table in which data values are divided into either a "leaf" or a "stem." In a stem and leaf plot, the stem values appear on the vertical axis and the leaf values are listed on the horizontal axis. Stem: The digit or digits that remain when the leaf is dropped. Leaf: The last digit on the right of the number. Example: 9 18 2 Stem Leaf =182
12. 12. STEM AND LEAF PLOT 10
13. 13. SPSS DEMONSTRATION AND INTERPRETATION 1-Execution of frequency distribution 2-Executing stem and leaf plot 13
14. 14. MULTIVARIATE DATAANALYSIS When there is analysis of two variables at which statistical techniques are applied on objects under investigation. Multivariate refers to all statistical techniques that simultaneously analyze multiple measurements on the individual or objects under investigation. It is to examine relationships between or among more than two variables. 11
15. 15. MULTIVARIATE TECHNIQUES Dependency Interdependency One Dependent Causal Correlation Simple Regression Multiple Regression Multiple dependents MANOVA MANCOVA Pearson Correlation Spearman Partial 12
16. 16. KNOWLEDGE OF LEVEL OF MEASUREMENT IS IMPORTANT There is metric and non metric data and both treatment can’t be same so important is to identify the level of measurement for correct treatment. Example: Country names ( Canada, Japan, Africa) a non- metric data and if it is used as metric and mean is taken it will be wrong. The measurement scale is also critical in determining which multivariate techniques are most applicable to the data, with consideration made for both independent and dependent variables 13
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19. 19. EXAMPLES : Simple regression is that there is one predictor variable and one dependent variable. Multiple regression When there are several predictor variables and one dependent variable. Some Multivariate techniques e.g. factor analysis, the variates that represent the best represent the patterns of variables (like factor analysis is use to develop questionnaire). Discriminant analysis which differentiates among groups based on the variables. Multivariate analysis of variance (MANOVA) is a statistical test procedure for comparing multivariate (population) means of several groups. Multivariate analysis of covariance (MANCOVA) is a method to cover cases where there is more then one dependent variable and where the control of continuous independent variable. 19 MULTIVARIATE TECHNIQUES
20. 20. 20 Multiple Regression Discriminant Analysis MANOVA Canonical Correlation, Dummy Variables Metric Nonmetric Metric Nonmetric One Dependent Variable Several Dependent Variables Metric Nonmetric Factor Analysis Cluster Analysis Non-metric MDS and Correspond- ance Analysis Metric MDS Metric MDS
21. 21. Multidimensional scaling (MDS) is a set of related statistical techniques often used in information visualization for exploring similarities or dissimilarities in data. Cluster analysis is an exploratory data analysis tool for solving classification problems. Its object is to sort cases (people, things, events, etc) into groups, or clusters, so that the degree of association is strong between members of the same cluster and weak between members of different clusters. In non-metric MDS, only the rank order of entries in the data matrix (not the actual dissimilarities) is assumed to contain the significant information. Dummy variables is one that takes the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. Canonical correlation analysis is used to identify and measure the associations among two sets of variables. Canonical correlation is appropriate in the same situations where multiple regression would be, but where are there are multiple inter correlated outcome variables. 21
22. 22. LEVEL OF MEASUREMENT Nominal Scales - A type of categorical data in which objects fall into unordered categories. Ordinal scales -provide no measure of the actual magnitude in absolute terms ,only the order of values. Interval scale- provides meaningful difference to value. Ratio Scales - captures the properties of the other types of scales, but also contains a true zero 22