Data familiarisation and description

Transcription

1 BUSINESS STATISTICS

2 Data familiarisation and description Week 1 Descriptive Statistics I, Excel I The U.S. Space Shuttle Challenger 28 January 1986, Challenger exploded soon after take-off, killing all 7 crew. Cause: failure of an O-ring in a joint on the solid rocket booster. Prior to the disaster, engineers were aware of in-flight damage to O-rings. the adverse effect of cold weather on O-rings. Nevertheless, Challenger was launched! The presidential commission of investigation criticised the decision-making process leading up to the launch. - Most business decisions rely on data and its analysis - Management accountability requires objective sources of information to support manager s decisions - Managers seek convergent validity for their decisions, requiring relevant data - Convergent validity the degree to which results/evidence from different tests/sources converge on the same conclusion/outcome Background Usually 4 steps 1- Recognise/describe the problem that needs to be solved 2- Gather data to help understand and solve the problem Which concepts to measure? Are appropriate data available? o If so, what is the form of the data? o If not, then data must be collected

3 3- Analyse and present the data How is this best done? 4- Act on the analysis Nature of data - Population all members of a group about which you want to draw a conclusion e.g. all voters in election, all Telstra shareholders, all invoice submitted to Medicare for reimbursement etc. - Sample a subset of the population selection for analysis Often chosen randomly Preferably representative of the population - Parameter a numerical measure that describes a characteristics of a population - Statistic a numerical measure that describes characteristic of a sample - Data set is a rectangular array of data where Each column contains a variable (aka field or attribute Each row contains an observation (aka case or record ) - Variable a characteristic of the members of the population/sample e.g. age, gender - Data are the observations (observed values) of the variables

4 Descriptive statistics Collecting, summarising and presenting data (tables, charts, pivot table and analysis Collect data e.g. a survey Summarise/characterise data Sample mean Present data e.g. tables and graphs Data Types 1- Categorical (qualitative or non-numeric) Nominal Values are simply labels and do not imply any order e.g. Yes/No, Holden/Toyota, Male/Female Ordinal Values are still labels but they have order e.g. HD/D/C/P/N, Satisfied/Neutral/Unsatisfied Categorical data can also be coded numerically e.g. Opinion variable below

5 2- Numerical (quantitative) Discrete Continuous The distinction is whether the data arise from counting or continuous measurement e.g. Children variable discrete counting Age variable continuous measure time It is critical to know the data type because it predetermines the subsequent analysis Variables can be further identified by the level of measurement or measurement of scale Values for a numerical variable are measured on o An interval scale o A ratio scale Data can also be categorised according to the timing of its collection or observation - Snapshot (aka Cross-sectional) Data Variation is across different members of the population at one point in time e.g. age, salary, opinion - Time series data Variation is over time i.e. track one of more variables through time e.g. monthly sales, annual profit etc. - Panel (aka Longitudinal) Data Variation is across different members of the population and time Most commonly, panels are sample units who agreed to answer a set f questions at periodic intervals e.g. households and their monthly purchase behaviour

6 Categorical data - Bar charts and pie charts are often used for qualitative data (categories or nominal scale) - Length of bar or size of pie slice shows the frequency or percentage for each category - Bar charts are preferred for comparing the frequency of occurrence of categories - Pie charts are preferred for observing the proportion of the total which lies in a particular category e.g. market share of various car brands - Summary tables and charts Arithmetic can t be performed on categorical values. So, counting is the primary method to describe categorical variables Counts can be reported as o raw counts o percentages (by performing the raw counts o or both, o depending on the objective

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8 Numerical data - Since arithmetic CAN be performed on numeric variables, we have two descriptive techniques 1- Tables and charts for numerical variables bar charts and histograms 2- Numerical summary measures e.g. mean, median, standard deviation, variation etc. 1. To tabulate numerical data, we use a frequency distribution For any variable, the frequency of a value is the number of data points equal to that value Frequency distribution for discrete data