Chapter 1 [1.2, 1.4, 1.5]

Chapter 1

[1.2, 1.4, 1.5]

STAT 109 MSU SPRING 2022

Welcome to STAT 109

In this course, you will learn how to use statistics to communicate important information about data sets and use data responsibly to develop and test hypotheses about the world.

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Important Course Information

Important Course Information

Before you dig in, there are some important resources for you to know about:

​- Canvas Navigation: Modules, Assignments, Grades.

- Resources: Free Tutoring (ASC), GA Tutoring Hours, CAPS, DRC

- Contact: [e-mail] (allow for 48-hour response time)

- Homework

- Quizzes and Exams​

- Project and Checkpoints​

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Statistics

Statistics is the study of data. We use statistics to describe the most important features of data sets, identify trends in data, and make inferences or generalizations about the world using data.

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In this course, we will cover topics from two different fields of statistics: Descriptive Statistics and Inferential Statistics.​

Statistics

Statistics

Used to make reasonable inferences (hypotheses) or generalizations about a population based on a sample of data. When we engage in inferential statistics, we use what we know about data to develop new ideas.

Inferential Statistics

Used to summarize important features of data sets. When we engage in descriptive statistics, we determine factual aspects of a data set.

Descriptive Statistics

1.2 Classifying and Storing Data

- Data: Recorded observations, measurements, calculations, etc in context.

- Variables:​ Characteristics that describe the context of collected data.​

- Sample: A set of data collected and grouped together, also called a dataset. A sample a subset of all relevant existing data.

- Population: The set of all relevant existing data from which a sample is taken.

1.2 Classifying and Storing Data

1.2 Classifying and Storing Data

Variables which are categorical in nature and can't be counted, measured, or calculated.

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Comparisons between categorical data points are not objective.

Qualitative Variables

Variables which are numerical in nature and can be observed by counting, measuring, or calculating.

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Comparisons between the values of numerical data points are objective.​

Quantitative Variables

Multiple Choice

Which of these variables is quantitative?

• Hair Color

• Zip Code

• Height

• Phone Number

Multiple Choice

Which of these variables is qualitative?

• Weight

• Blood Type

• Number of Students

• Number of Leaves

1.4 Organizing Categorical Data

- Frequency: The number of times an entry appears in a data set (a count of each possible data entry).

- Relative Frequency: The frequency of a data entry measured as a proportion of the whole data set​. The relative frequency of a data entry can be recorded as a decimal or a percentage.

​ R.F. = F/n (as a decimal)

​ R.F. = (F/n)*100 (as a percentage)

1.4 Organizing Categorical Data

1.4 Organizing Categorical Data

Used to summarize categorical data collected from two distinct groups where exactly two responses were available.

Two-Way Tables

Fill in the Blanks

Fill in the Blanks

Multiple Choice

60% of the men in this sample wear their seatbelt all the time. 70% of women in this sample wear their seatbelt all the time.

Select the most accurate, reasonable statement.

• Women are definitely more likely to wear their seatbelt all the time than men.

• Women could be more likely to wear their seatbelt all the time than men.

• Men could be more likely to wear their seatbelt all the time than women.

• Men are definitely more likely to wear their seatbelt all the time than women.

1.5 Collecting Data to Understand Causality

- Cause and Effect: If the variation in one variable is responsible at least in part for the variation in another, we say that there is a cause and effect relationship between the two variables. The effects we see in the second variable are caused by the first.

- Note that there is no way to prove that a cause and effect relationship exists, and our assumptions regarding cause and effect may often be incorrect. (Correlation does not imply causation).​

1.5 Collecting Data to Understand Causality

When considering cause and effect relationships, we can consider three types of variables.

- The treatment variable and the outcome (response) variable: Our data collection is based around the inference that variation in the outcome variable is caused at least in part by variation in the treatment variable.

- Confounding variables: Some or all of the variation in the outcome variable may be caused by variables other than the treatment variable.

1.5 Collecting Data to Understand Causality

- Observational Studies: researchers have no control over which subjects are placed into the treatment group and which are placed into the control group. Researchers simply observe data with no influence over it. These studies are incredibly vulnerable to the effects of confounding variables.

- Controlled Experiments: researchers assign subjects to either the treatment group or control group (randomly) and then collect data. When done correctly, the two groups are alike in every regard except where the treatment variable is concerned.​ These studies are less vulnerable to the effects of confounding variables.

1.5 Collecting Data to Understand Causality

Multiple Choice

Is the following study an example of an observational study or a controlled experiment?

The New York Times reported on a seven-year study about the eating habits of a sample of 50,000 adults in the United States. The participants were all members of the Seventh Day Adventist religion. According to the report, "breakfast eaters" were more likely to keep their weight down after seven years than were "breakfast skippers."

• Observational Study

• Controlled Experiement

Multiple Choice

Is the following study an example of an observational study or a controlled experiment?

Crohn's disease is a bowel disease that causes cramping, abdominal pain, fever, and fatigue. A study reported in the New England Journal of Medicine tested two medicines for the disease: injections of infliximab (Inflix) and oral azathioprine (Azath). The participants were randomized into three groups: one group received Inflix injections, one group received Azath pills, and a third group received only placebos.

• Observational Study

• Controlled Experiement