Descriptive Statistics becoming familiar with the data

The Strategies Initial Screening Initial Screening Levels of Measurement Levels of Measurement Five Descriptive Questions Five Descriptive Questions Graphical Presentations Graphical Presentations Search for Outliers Search for Outliers

Initial Screening Missing values Missing values Defining labels Defining labels Key punch errors Key punch errors Valid values Valid values Understanding what you have Understanding what you have Understanding the population, sampling frame, and sample Understanding the population, sampling frame, and sample

Levels of Measurement Nominal Nominal Ordinal Ordinal Interval Interval Ratio Ratio Determining what statistics are appropriate Determining what statistics are appropriate

Nominal Naming things. Naming things. Creating groups that are qualitatively different or unique… Creating groups that are qualitatively different or unique… But not necessarily quantitatively different. But not necessarily quantitatively different.

Nominal Placing individuals or objects into categories. Placing individuals or objects into categories. Making mutually excusive categories. Making mutually excusive categories. Numbers assigned to categories are arbitrary. Numbers assigned to categories are arbitrary.

Nominal Sample variables: Sample variables: – Gender – Race – Ethnicity – Geographic location – Hair or eye color

Ordinal Rank ordering things. Rank ordering things. Creating groups or categories when only rank order is known. Creating groups or categories when only rank order is known. Numbers imply order but not exact quantity of anything. Numbers imply order but not exact quantity of anything.

Ordinal The difference between individuals with adjacent ranks, on relevant quantitative variables, is not necessarily the same across the distribution. The difference between individuals with adjacent ranks, on relevant quantitative variables, is not necessarily the same across the distribution.

Ordinal Sample variables: Sample variables: – Class Rank – Place of finish in a race (1 st, 2 nd, etc.) – Judges ratings – Responses to Likert scale items (for example – SD, D, N, A, SA)

Interval Orders observations according to the quantity of some attribute. Orders observations according to the quantity of some attribute. Arbitrary origin. Arbitrary origin. Equal intervals. Equal intervals. Equal differences expressed as equal distances. Equal differences expressed as equal distances.

Interval Sample variables: Sample variables: – Test Scores SAT SAT GRE GRE IQ tests IQ tests – Temperature Celsius Celsius Fahrenheit Fahrenheit

Ratio Quantitative measurement. Quantitative measurement. Equal intervals. Equal intervals. True zero point. True zero point. Ratios between values are useful. Ratios between values are useful.

Ratio Sample variables: Sample variables: – Financial variables – Finish times in a race – Number of units sold – Test scores scaled as percent correct or number correct

Levels of Measurement Review What level of measurement? What level of measurement? – Today is a fall day. – Today is the third hottest day of the month. – The high today was 70 o Fahrenheit. – The high today was 20 o Celsius. – The high today was 294 o Kelvin.

Levels of Measurement Review What level of measurement? What level of measurement? – Student #1256 is: – a male – from Lawrenceville, GA. – He came in third place in the race today. – He scored 550 on the SAT verbal section. – He has turned in 8 out of the 10 homework assignments.

Levels of Measurement Review What level of measurement? What level of measurement? – Student #3654 is: – in the third reading group. – Nominal? – Ordinal? – Interval? – Ratio?

Five Descriptive Questions What is the middle of the set of scores? What is the middle of the set of scores? How spread out are the scores? How spread out are the scores? Where do specific scores fall in the distribution of scores? Where do specific scores fall in the distribution of scores? What is the shape of the distribution? What is the shape of the distribution? How do different variables relate to each other? How do different variables relate to each other?

Five Descriptive Questions Middle Middle Spread Spread Rank or Relative Position Rank or Relative Position Shape Shape Correlation Correlation Descriptive Statistics Answer Sheet Descriptive Statistics Answer Sheet Descriptive Questions in Excel, SPSS, and TI-83 Descriptive Questions in Excel, SPSS, and TI-83

Middle Mean Mean Median Median Mode Mode

Spread Standard Deviation Standard Deviation Variance Variance Range Range IQR IQR

Rank or Relative Position Five number summary Five number summary Min, 25 th, 50 th, 75 th, Max Min, 25 th, 50 th, 75 th, Max Identifying specific values that have interpretive meaning Identifying specific values that have interpretive meaning Identifying where they fall in the set of scores Identifying where they fall in the set of scores Box plots Box plots Outliers Outliers

Shape Positive Skewness Positive Skewness Negative Skewness Negative Skewness Normality Normality Histograms Histograms

Shape - Normality

Shape- Positive Skewness

Shape – Negative Skewness

Correlation Direction of Relationships Direction of Relationships Positive or Negative Positive or Negative Magnitude of Relationships Magnitude of Relationships Weak, Moderate, Strong Weak, Moderate, Strong Scatterplots Scatterplots Outliers Outliers

Outliers

Outliers Boxplot shows middle 50% of scores as the box. Boxplot shows middle 50% of scores as the box. Q3 (75 th ) – Q1 (25 th ) = IQR Q3 (75 th ) – Q1 (25 th ) = IQR Data outside 1.5 IQR rule are outliers Data outside 1.5 IQR rule are outliers Q1 – (1.5*IQR) Q1 – (1.5*IQR) Q3 + (1.5*IQR) Q3 + (1.5*IQR)

Outliers

Outliers

Outliers

Outliers If normality of the population can be assumed, other rules can be used. If normality of the population can be assumed, other rules can be used. Mean +/- 2 SDs or Mean +/- 3 SDs Mean +/- 2 SDs or Mean +/- 3 SDs Empirical Rule Empirical Rule Approximately 68% within +/- 1 SD Approximately 68% within +/- 1 SD Approximately 95% within +/- 2 SD Approximately 95% within +/- 2 SD Approximately 99% within +/- 3 SD Approximately 99% within +/- 3 SD

Outliers You can also look at outliers in the bivariate case. You can also look at outliers in the bivariate case. Examine the scatterplots for values out of the pattern. Examine the scatterplots for values out of the pattern.

Outliers