1. Lecture 1 Chapter 1. Stats Starts Here
Week 1
Lecture 1 Chapter 1. Stats Starts Here

2. What do we need to bring to an intro statistics course?
Growth Mindset: The belief that abilities can be developed (Dr. Carol Dweck)
(Duration: 3:06 minutes)
The Power of believing you can improve. Watch a TED Talk by Dr. Carol Dweck:
(Duration: 10:20 minutes)

3. Why study statistics?
Statistics helps us:
make sense of the world in everyday life.
For example, in health, politics, economics, education, environment, and social issues.
For example, help managers evaluate employee performance using statistics and determine factors that help predict sales of products.
become informed citizens by giving you the tools to understand, question, and interpret data.
Articles published in scientific research journals and reports prepared in government agencies and private industries exemplify the role of statistics:
Which factors have the greatest impact on student performance in school
Which factors affect people’s quality of their health care
Which factors affect people’s decision to retire
Various careers requires:
The use statistical methods
Employees to read reports that contain statistics.
Watch a short video that will tell us why statistics is important:
Video: Improving Human Welfare in 2013 International Year of Statistics

4. What is Statistics?
Statistics is a way of reasoning, along with collection of tools and methods designed to help us understand the world.
Statistics is about variation.
Variation is the of statistics.
Statistical methods helps explain the variation in the data.
We model the variation in the data.
E.g., Students’ university GPA.
There is student to student GPA variation.
Different GPA for different students.
What could explain the variation (differences) in students’ university GPA?
E.g., Hours of study, High School GPA, Hours watching TV, etc.

5. Data Data is plural. Datum is singular.
Data are values along with their context.
Data help us understand and model variation.
Data help us see the underlying truth and pattern.
A useful data has a context.
Nowadays data mostly come in an excel form.
Data are presented in a table (rows and columns).

6. Data
Individual Cases (Individuals) are the objects described by a set of data.
Cases can be people, animals, things.
The cases are sample of cases selected from some larger population that we would like to understand.
A variable is any characteristic of an individual case (or an individual).
A variable can take different values on different cases.
Example: An undergraduate student’ data base.
Individuals: Students of the university.
Variables: Date of birth, gender, GPA, etc.

7. Context of Data Answers the Five W’s
When you plan a statistical study or explore data from someone else’s work, ask your self the following questions:
Who will be the cases in my study? How many individuals will be in my study?
Why conduct this study? What purpose do the data have? Do we hope to answer some specific questions? Do we want to draw conclusions about individuals other than the ones actually have data for?
What? How many variables do the data contain? Exact definitions of these variables? In what unit of measurement is each variable recorded?
Where can I conduct my study?
When is an appropriate time to conduct my study?
In addition to the five W’s:
How can I conduct my study? (e.g. survey instrument)

8. Example
I study students’ attitudes about statistics. Who: Undergraduate students Why: By understanding attitudes about statistics I aim to improve teaching and learning of statistics What: Students’ attitudes, their mathematics related experiences and achievement, their gender, their program of study, their year of study, and their statistics course outcome. Where: University When: At the beginning and at the end of an introductory statistics course How: By administrating the Survey of Attitude Towards Statistics (SATS-36©) and linking students’ responses to students’ repository record from the Office of Registrar. Since I was the instructor for the course, I had a research assistant who assigned a participant number to each student who participated into the study. The participant number is an “Identifier Variable”, which identifies individual cases.

9. Example
I collected data (with ethic approval) on attitude about statistics from a sample of students who took an introductory statistics course in the summer of I assessed students’ attitudes toward statistics. I then grappled with the data (students’ responses) I collected and analyzed data. The statistics that I obtain from my data analyses need to be explained in the context of the study. For instance, I obtained a statistic (average) about students’ willingness to spend a great deal to learn statistics as 5.88 on a 7-point Likert scale (“1” indicates a strong disagreement to “4” neutral to “7” strong agreement). With the value 5.88, since it is above 4 (neutral response) I can report that on average, students reported a great deal of effort to learn statistics (this was by the end of their introductory statistics course).

10. Distribution of Students’ Effort to Learn Statistics

11. Logical Approach A complete solution need to: Explain the context
Show reasoning and calculation
State the conclusion

12. Classify Variables: Quantitative or Categorical
Quantitative variable:
When the measurement scale has numerical values.
These variables accompany with their unit of measurement.
E.g., University GPA: (range form 1.0 to 4.0)
E.g., Hours of study: (0 to infinite!?)
Categorical variable:
When the measurement scale is set of categories.
Often called qualitative variables: Distinct categories differ in their qualities not in their numerical magnitude.
E.g., Gender: Male or Female
E.g., Canadian Provinces: Ontario, British Columbia, Alberta, and so on.

13. Why Classify Variables as Quantitative or Categorical?
For application of different statistical methods.
For obtaining appropriate graphs and summary statistics.
Example of a Quantitative Variable:
Income of Canadian Citizens (in thousands of dollars).
We might be interested in average income of all Canadian Citizens.
Example of a Categorical Variable:
Canadian Provinces.
We might be interested in the number of Canadians living in each province (Count).

14. Scales of Measurement Interval Scales:
For quantitative variables intervals are equal distances.
Example: Annual income (in thousands of dollars).
The interval (distance) between $30,000 to $40,000 is $10,000.
Purpose: We can compare outcomes are how much larger or how much smaller one is than the other (e.g., in which interval should an annual income go to).
Nominal Scales
For categorical variables no level (category) is greater or smaller than any other level (category).
Example: Primary mode of transportation to work.
Categories: automobile, bus, subway, bicycle, walk.

15. Scales of Measurement: Ordinal Scales
Between nominal and interval scales.
Consists of categorical scales having a natural ordering of values.
The levels form an ordinal scale.
Example: Social Class
Categorical scale: upper, middle, lower.
Example: Political philosophy
Categorical scale: Very liberal, moderately liberal, slightly liberal, very conservative, moderately conservative, slightly conservative

16. Quantitative Aspects of Ordinal Scales
The position of ordinal scales on the quantitative-qualitative(categorical) classification is fuzzy.
Often methods used for their statistical analysis is the same as nominal (categorical) variables.
In some cases, they could closely resemble interval scales for quantitative variables.
Each level has a greater or smaller magnitude than another level.
We can conduct a sensitivity analysis and check if conclusions would differ in any significant way of other choices of scores.
Example: Survey of Attitude Towards Statistics (SATS-36©):
SATS-36© items are ordinal (e.g., strongly disagree, strongly agree)
We might want to treat them as a quantitative variable (1, 2, 3, 4, 5, 6, 7; interval scale: distance is 1) to compute a mean score for an item (e.g., I will like statistics).

19. Nice to meet you and see you soon 