Chapter 1 Getting Started

1. Chapter 1 Getting Started What is Statistics?

2. Individuals vs. Variables Individuals Variables Characteristic of the individual to be measured or observed • People or objects included in the study

3. Quantitative vs. Qualitative Quantitative Variables Qualitative Variables Describes an individual by placing the individual into a category or group, such as male or female • Have value or numerical measurement for which operations such as addition or averaging make sense

4. Population vs. Sample Population Data Sample Data The data are from only some of the individuals of interest Sample Statistics are numerical measures that describe an aspect of a sample • Data is from every individual of interest • Population Parameters are numerical measures that describe an aspect of a population

5. Levels of Measurement • Nominal – Names, Labels, Categories • Ordinal – Arranged in meaningful mathematical order • Interval – Differences are meaningful • Ratio – Division or percentage comparisons make sense; zero point

7. Chapter 1 Getting Started 1.2 Random Samples

8. Simple Random Sample (SRS) • A simple random sample of n measurements from a population is a subset of the population selected in such a manner that every sample of size n from the population has an equal chance of being selected.

9. Random Number Tables (RNT) • Used to help secure a SRS • Steps: • Number all members of the population sequentially. • Drop a pin on the RNT to pick a starting point • Pull digits n at a time, discarding non-used numbers • Repetition?

10. Do Now • With a partner, discuss how a Random Number Table or Random Number Generator could be used to generate the answer key for a multiple choice test (assume 10 questions on quiz and 5 choices per question). • Rephrased: How can a RNT or RNG be used to determine next to which letter the correct answer to each question should be placed?

11. Other Methods to Secure a Sample • Systematic • Stratified • Cluster • Multistage • Convenience

12. Systematic Sampling • Population is numbered • Select a starting point at random and pick every kth member

13. Convenience Sampling • Create sample by selecting population members which are easily available

14. Stratified Sampling • Divide population into distinct subgroups based on specific characteristics • Draw random samples from each strata

15. Cluster Sampling • Divide population into pre-existing segments or clusters (often geographic). • Make a random selection of clusters. • All members of cluster are chosen.

16. Multistage Sampling • Use a variety of sampling methods to create successively smaller groups at each stage. • Final sample is made of clusters.

17. Do Now • Copy the Blue Box from page 21 into your notebooks. This is the beginning of Section 1.3 “Introduction to Experimental Design”

18. Census vs. Sample • Census – measurements from observations from the entire population are used. • Sample – measurements from observations from part of the population are used

19. Observational Study vs. Experiment • Observational Study – observations and measurements of individuals are conducted in a way that doesn’t change the response or the variable being measured • Experiment – a treatment is deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured

20. Within Experiments: • Placebo Effect – occurs when a subject receives no treatment but (incorrectly) believes he or she is in fact receiving treatment and responds favorably • Control Group – those who receive the placebo treatment • Treatment Group – those who receive the actual treatment • Completely Randomized Experiment – one in which a random process is used to assign each individual to one of the treatments

21. Completely Randomized Experiment • C.R.E. – is one in which a random process is used to assign each individual to one of the treatments

22. Characteristics of a Well-Designed Experiment • Block – a group of individuals sharing some common features that might affect the treatment • Randomized Block Experiment – individuals are first sorted into blocks, and then a random process is used to assign each individual in the block to one of the treatments

23. Characteristics of a Well-Designed Experiment • Control Groups – used to account for the influence of other known or unknown variables that might be an underlying cause of change in response in the experimental group. • Lurking or Confounding Variables – such variables

24. Characteristics of a Well-Designed Experiment • Randomization – used to assign individuals to the two treatment groups. Helps to prevent bias in selecting members to the groups • Replication – on many patients reduces the possibility that the differences in occurred by chance alone.

25. Potential Pitfalls of Surveys • Nonresponse • Truthfulness of Response • Faulty Recall • Hidden Bias • Vague Wording • Interview Influence • Voluntary Response

26. Data Collection Techniques (Summary) • Census • Samples • Observational Studies • Experiments • Surveys • Simulations (previously)

27. The Birthday Paradox States… • In a room full of 23 randomly selected people, the probability that at least two share a birthday is around 50%...

28. Believe it or not… • The probability is very close to 99% if there are 57 people in the room.

29. Do Now • Open a blank Excel document • Write your name A1 • Type =randbetween(1,365)in the second cell assigned to you in your column. • Pull down to secure a sample of 23 birthdays. (You will have data in row 24) • Check for repetition and write Yes for repetition or No for none in row 25