ISDS Chapter 1

The Nominal Scale

- The least sophisticated level of measurement. - Data are simply categories for grouping the data.

The Interval Scale

- Consider the Fahrenheit scale of temperature. - This scale is _____ because the data are ranked and differences (+ or ) may be obtained. But there is no "absolute 0" (What does 0F mean?)

The Interval Scale

- Data may be categorized and ranked with respect to some characteristic or trait. - Differences between interval values are equal and meaningful. - No "absolute 0" or starting point defined. Meaningful ratios may not be obtained.

The Ordinal Scale

- Differences between categories are meaningless because the actual numbers used may be arbitrary. - There is no objective way to interpret the difference between instructor quality.

To do good statistics, you must

- Find the right data. - Use the appropriate statistical tools. - Clearly communicate the numerical information into written language.

Statistics

- Language of data - Study of collecting, analyzing, presenting, and interpreting data - Science of getting useful information from data

Cross- Sectional Data

- Many subjects at same point in time - Without regard to differences in time * Individuals, households, firms, countries

Discrete Quantitative (Numerical) Variables

- Number of children in a family - Number of points scored in a basketball game. - Number of books purchased - Number of classes taken

Time Series Data

- One subject over several time periods - Daily, weekly, monthly, quarterly, annual * Monthly sales, daily price, weekly rate

The Ratio Scale

- The strongest level of measurement. - Ratio data may be categorized and ranked with respect to some characteristic or trait. - Differences between interval values are equal and meaningful. - There is an "absolute 0" or defined starting point. "0" does mean "the absence of ..." Thus, meaningful ratios may be obtained.

Reasons for sampling from the population

- Too expensive to gather information on the entire population - Often impossible to gather information on the entire population

Continuous Quantitative (Numerical) Variables

- Weight - Height - Investment return - Length of time

Qualitative (Categorical) Variables

- Yes/No - Day of Week - Year Classification - Name of Insurance Provider

Descriptive and Inferential

2 Branches of statistice

Sample

A subset of the population.

Nominal, Ordinal, Interval, Ratio

All data measurements can be classified into one of four major categories

Discrete Quantitative (Numerical) Variables

Countable number of distinct values

Continuous Variable

Can take on any value within an interval. Using a sufficient precision of measurement, no two continuous values are identical.

Nominal

Categorical data; data in each group differ by name or label

Descriptive

Characterize data i.e., the sample mean

Descriptive Statistics

Collecting, organizing, and presenting the data.

Population

Consists of all items of interest.

Parameter

Described characteristic of a population - P & P

Statistic

Describes characteristic of a sample - S & S

Quantitative (Numerical) Variables

Discrete and Continuous

Zero Point

Does not reflect a complete absence of what is being measured

Inferential Statistics

Drawing conclusions about a population based on sample data from that population.

Correlation- to- Causation

Even if two variables are highly correlated, one does not necessarily cause the other.

Ordinal Scale

Example: instructors are often evaluated on an ordinal scale (excellent, good, fair, poor).

Values

Expressed in words but coded into numbers for processing purposes

Problem with Conclusion

Incorrect to draw conclusion based on one data point.

Continuous Quantitative (Numerical) Variables

Infinite number of values within some interval

Quantitative Variables

Interval and Ratio

Interval Scale

Is used with Quantitative variables

Arbitrarily Chosen

Main drawback is the value of zero is ______

Qualitative Values

May be converted to quantitative values for analysis purposes.

Descriptive

Methods to help collect, summarize, and analyze set of data. Use when you know all of the data points

Inferential

Methods use data collected from a small population to make inferences, draw conclusions, about a larger population.

Qualitative Variables

Nominal and Ordinal

Scales of Meausure

Nominal and Ordinal > Qualitative Variables Interval and Ratio > Quantitative Variables

Parameter

Numerical measure that describes a characteristic of a population.

Staristic

Numerical measure that describes a characteristic of a sample.

Ordinal Scale

Ordinal data may be categorized and ranked with respect to some characteristic or trait.

Discrete Variable

Takes on individually distinct values.

The Ratio Scale

The following variables are measured on a ratio scale: - General Examples: Weight, Time, and Distance - Business Examples: Sales, Profits, and Inventory Levels

Variable

The general characteristic being observed on an object of interest

Statistics

The methodology of extracting useful information from a data set

Qualitative

Unlike ______ data, arithmetic operations are valid on interval and ratio scaled data.

Inferential

Use when the actual count is not easily obtainable. Often times inferences are made about college students based on data obtained in a sample.

Summarizing

When __________ typically count number or calculate the percentage of persons or objects that fall into each possible category.

Importance of Statistics

With knowledge of statistics: - Avoid risk of making uninformed decisions and costly mistakes - Differentiate between sound statistical conclusions and questionable conclusions.