3. Data and sampling. Plan for today

Transcription

1 3. Data and sampling Business Statistics Plan for today Reminders and introduction Data: qualitative and quantitative Quantitative data: discrete and continuous Qualitative data discussion Samples and sampling methods Errors and variation Critical evaluation 1

2 Two major types of data Qualitative data: categorize or describe attributes of a population. Examples include: hair color, blood type, ethnicity, the make and model of a car, profession, educational attainment, names of trees, birds, etc. Quantitative data: the values are numerical, and describe the result of measurements or counting. Examples: weight, income, age, mileage, Recall that variables can be classified as numerical or categorical. Quantitative data types Quantitative discrete data: take only specific numerical values. The result of counting always yield discrete data. Example: the number of cars on a parking lot. Quantitative continuous data: usually are the result of measuring, and take values on an interval. Example: the distance traveled by a car in a day. 2

3 Example A study concerns backpacks of school students. In each backpack, among other things are books that the students carry to school. Then the numbers of books in the backpacks are discrete data and the weights of the backpacks are continuous data. Qualitative Data Discussion In a pie chart, categories of data are represented by wedges in a circle and are proportional in size to the percent of individuals in each category. 3

4 Qualitative Data Discussion In a bar graph, the length of the bar for each category is proportional to the number or percent of individuals in each category. Bars may be vertical or horizontal. Qualitative Data Discussion A Pareto chart consists of bars that are sorted into order by category size (usually, largest to smallest). 4

5 Qualitative Data Discussion The percentages do not always have to add up to 100% : There could be missing data: for example when data is not known for some part of the population or the data falls into a non-essential category The data could be overlapping: one person could belong to two or more different categories. Example: percentage of workers traveling to work using car, bus, or bicycle. Both: missing categories and overlapping. Sampling Why do we use samples? Because gathering information about each person in the entire population is very costly (example: national census in Canada) and virtually impossible. A sample has to be representative of the entire population, i.e. have the same characteristics as the population that it is supposed to represent. 5

6 Simple random samples Every member of the population has an equal chance to be included in a simple random sample. If the size of the sample is n, then every sample of size n from the population has an equal chance of being selected. Can be achieved using a generator of random numbers, such as Sampling Random sampling can be done with replacement. That is, once a member is picked, that member goes back into the population and thus may be chosen more than once. In practice, in most populations, simple random sampling is done without replacement. Surveys are typically done without replacement. That is, a member of the population may be chosen only once. 6

7 Sampling Stratified sample: dividing members of the population into homogeneous subgroups and then sampling proportionally. Cluster sample: first, choosing clusters, and then sampling inside the chosen clusters. It is best when most of the variation in the population is within the groups, not between them. Systematic sample: picking every n-th person. The above are examples of random samples. Sampling Convenience sampling: uses results or people that are readily available. For example, conducting a survey among the people who happen to pass by. This sampling is not random. The results may be very biased, that is they favor particular outcomes. For example, telephone surveys that use landline databases favor older demographics. 7

8 Errors Sampling errors: always present, but can be controlled by choosing a large enough random sample. Non-sampling errors: hard to control, such a defective measuring device or false data. Sampling bias: when the sample is definitively not representative. For example, randomly selected sample of voters has 70% men. Variation in samples Three random samples of 1000 voters each. In sample A : 376 people will vote Liberal In sample B : 402 people will vote Liberal In sample C : 388 people will vote Liberal They give different data. But all three samples can be valid and representative. Later on we will quantify these kinds of variability in random samples. 8

9 Critical evaluation Types of sampling bias: Selection from specific groups Self-selection bias (online, phone-in polls) Exclusion bias (only polling in English) Sample size issues: is the sample too small? Undue influence: how the question is formulated and the data are collected. Improperly funded studies, misleading data Homework Final remarks Follow the textbook examples 9