1.2 types of data
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The document discusses different types of data that can be collected in statistics including categorical vs. quantitative data, discrete vs. continuous data, and different levels of measurement for data including nominal, ordinal, interval, and ratio scales. It also discusses key concepts such as parameters, statistics, populations, and samples. Potential pitfalls in statistical analysis are outlined such as misleading conclusions, nonresponse bias, and issues with survey question wording and order.
1.2 types of data
- 1. Elementary Statistics Chapter 1: Introduction to Statistics 1.2 Types of Data 1
- 2. Chapter 1: Introduction to Statistics 1.1 Statistical and Critical Thinking 1.2 Types of Data 1.3 Collecting Sample Data 2
- 3. Population: It consists of all subjects (human or otherwise) that are studied. Sample: It is a subset of the population. Census: The collection of data from every member of a population 3 1.1 Statistical and Critical Thinking, Key Concept • Voluntary Response Sample Voluntary Response Sample or Self-Selected Sample is one in which the respondents themselves decide whether to be included. Statistics: The science of planning studies and experiments, obtaining data, and organizing, summarizing, presenting, analyzing, and interpreting those data and then drawing conclusions based on them. Data: Collections of observations, such as measurements, genders, or survey responses
- 4. The final step in our statistical process involves conclusions, and we should develop an ability to distinguish between statistical significance and practical significance. • Statistical Significance Statistical significance is achieved in a study if the likelihood of an event occurring by chance is 5% or less. Getting 98 girls in 100 random births is statistically significant because such an extreme outcome is not likely to result from random chance. Getting 52 girls in 100 births is not statistically significant because that event could easily occur with random chance. 4 1.1 Statistical and Critical Thinking, Conclude • Practical Significance It is possible that some treatment or finding is effective, but common sense might suggest that the treatment or finding does not make enough of a difference to justify its use or to be practical.
- 5. • Misleading Conclusions When forming a conclusion based on a statistical analysis, we should make statements that are clear even to those who have no understanding of statistics and its terminology. • Sample Data Reported Instead of Measured When collecting data from people, it is better to take measurements yourself instead of asking subjects to report results. • Loaded Questions If survey results are not worded carefully, the results of a study can be misleading. • Order of Questions Sometimes survey questions are unintentionally loaded by the order of the items being considered. • Nonresponse A nonresponse occurs when someone either refuses to respond or is unavailable. • Percentages Some studies cite misleading percentages. Note that 100% of some quantity is all of it, but if there are references made to percentages that exceed 100%, such references are often not justified. 5 1.1 Statistical and Critical Thinking Analyzing Data: Potential Pitfalls
- 6. A major use of statistics is to collect and use sample data to make conclusions about populations. 1.2 Types of Data, Key Concept Parameter & Statistic • Parameter a numerical measurement describing some characteristic of a population • Statistic a numerical measurement describing some characteristic of a sample 6
- 7. Quantitative Data & Categorical Data • Quantitative (or numerical) data consists of numbers representing counts or measurements. Example: The weights of supermodels Example: The ages of respondents • Categorical (or qualitative or attribute) data consists of names or labels (not numbers that represent counts or measurements). Example: The gender (male/female) of professional athletes Example: Shirt numbers on professional athletes uniforms - substitutes for names 1.2 Types of Data 7
- 8. Discrete & Continuous types: • Discrete data result when the data values are quantitative and the number of values is finite, or “countable.” Example: The number of tosses of a coin before getting tails • Continuous (numerical) data result from infinitely many possible quantitative values, where the collection of values is not countable. Example: The lengths of distances from 0 cm to 12 cm 1.2 Types of Data, Quantitative Data 8
- 9. 1.2 Types of Data, Quantitative Data Data Qualitative Categorical Quantitative Numerical, Can be ranked Discrete Countable 5, 29, 8000, etc. Continuous Can be decimals 2.59, 312.1, etc. 9
- 10. • Nominal level of measurement characterized by data that consist of names, labels, or categories only, and the data cannot be arranged in some order (such as low to high). Example: Survey responses of yes, no, and undecided • Ordinal level of measurement involves data that can be arranged in some order, but differences (obtained by subtraction) between data values either cannot be determined or are meaningless. Example: Course grades A, B, C, D, or F • Interval level of measurement involves data that can be arranged in order, and the differences between data values can be found and are meaningful. However, there is no natural zero starting point at which none of the quantity is present. Example: Years 1000, 2000, 1776, and 1492 • Ratio level of measurement data can be arranged in order, differences can be found and are meaningful, and there is a natural zero starting point (where zero indicates that none of the quantity is present). Differences and ratios are both meaningful. Example: Class times of 50 minutes and 100 minutes 1.2 Types of Data, Levels of Measurement: Another way of classifying data: 4 levels of measurement: nominal, ordinal, interval, and ratio. 10 • Nominal - categories only (Names) • Ordinal - categories with some order ( nominal, plus can be ranked (order)) • Interval - differences but no natural zero point (Ordinal, plus intervals are consistent) • Ratio - differences and a natural zero point(Iinterval, plus ratios are consistent, true zero)
- 11. 1.2 Types of Data, Levels of Measurement: 11 Example 1: Determine the measurement level. Variable Nominal Ordinal Interval Ratio Level Hair Color Yes No Nominal Zip Code Yes No Nominal Letter Grade Yes Yes No Ordinal ACT Score Yes Yes Yes No Interval Height Yes Yes Yes Yes Ratio Age Yes Yes Yes Yes Ratio Temperature (F) Yes Yes Yes No Interval
- 12. 12 Example 2:
- 13. 13 Example 3: Parameter or Statistic? Statistic Parameter
- 14. 14 Example 4: Discrete or Continuous? Continuous Discrete
- 15. 15 Example 5: Determine the measurement level. Nominal Ordinal Interval Ratio
- 16. 16 Example 6: Determine the measurement level & what’s wrong with the conclusion?