Chapter one: The Nature of Probability and Statistics

What are statistics? Statistics is the science of conducting studies to collect, organize, summarize, analyze and draw conclusions from data. Always ask the 3 w’s: Who, what and why?

1-1: Descriptive and inferential statistics  Variable: is a characteristic or attribute that can assume different values.  Data: Are the values (measurements or observations) that the variables can assume.  Random Variables: Variables whose values are determined by chance.  Data set: Collection of data values  Data value (Datum): each value in the data set.

Two types of statistics  Descriptive statistics: consists of the collection, organization, summarization and presentation of data.  Inferential statistics: consists of generalizing from samples to populations, performing estimations and hypotheses tests, determining relationships among variables, and making predictions.  (Inferential statistics uses probability(the chance of something occurring)

Sample vs Population  Population: consists of all subjects (human or otherwise) that are being studied.  Sample: is a group of subjects selected from a population.

Hypothesis testing  An area of inferential statistics that is used in decision making process for evaluating claims about a population based on information obtained from a process from samples.

1-2 Variables and types of Data  Two types of data: Qualitative vs quantitative  Qualitative variables can be placed into distinct categories, according to some characteristic or attribute  Quantitative variables: are numerical and can be ordered or ranked.  Two types of quantitative:  Discrete variables: assume values that can be counted  Continuous variables: can assume an infinite number of values between any two specific values. They are obtained by measuring. They often include fractions and decimals.  Boundaries see handout

Levels of measurement  Nominal  Ordinal  Interval  Ratio

Nominal (sounds like names)  Categorical/qualitative  Consists of a set of categories that has different labels  Often dichotomous (ie. Biological sex or yes of no questions)  Another example: country of residency  ADVANCED: What kind of statistics use nominal scales? Pearson chi-square (both independent and dependent are measured on a nominal scale like handedness and dyslexia)

Ordinal: (sounds like order)  Categorical/qualitative  A set of categories organized in an ordered sequence. Ranks; Likert scale (An order exists but unknown quantitative differences: ie: name your five closest friends)  ADVANCED: Spearman correlation(Likert items)

Interval (numerical scale with a meaningful order)  Quantitative difference between numbers within the scale reflect equal differences in magnitude.  Limitations: no zero (ie: Celsius (zero is not the absence of temp) Calendar (zero is not absence of time), SAT (lowest score 200) IQ (lowest is 40)  ADVANCED: Pearson Correlation (IQ and SAT scores), (TEMP and SAT)

Ratio(interval + natural zero point)  Can express differences between two values as a ratio (can multiply or divide values) {with interval you can add and subtract but cannot multiple or divide} ie: height or weight, # of times out of the country, # of items recalled on a memory test, reaction time..  ADVANCED: Pearson Correlation ***note many statisticians do not differentiate between ratio and interval.

1-3 Data Collection and Sampling techniques  Name and define the four basic sampling methods:  Random: selected by using chance (think of the rectangles)  systematic: Selecting every kth subject (students entering the classroom)  Stratified: Dividing the population into groups (called strata) think of Freshmen, Sophomore, Junior, Senior.  Cluster: Geographic area of schools in a large school district.  Another popular technique convenience sample.

1-4 Observational and experimental studies  An observational study: the researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations.  An experimental study: the researcher manipulates one of the variables and tries to determine how the manipulation influences other variables. [Quasi- experimental study: using intact groups]  WATCH Brown eyes BLUE eyes (

Variable review  Independent variable also called the explanatory variable is the one being manipulated  Dependent variable also called the outcome variable is the resultant variable.  (dependent is the one that is studied to see if it has changed significantly due to the manipulation of the independent variable)  Treatment group and the control group  Confounding variable is one that influences the dependent or outcome variable but was not separated from the independent variable.

1-5 Uses and misuses of statistics Recall the 3 w’s  Suspect samples  Ambiguous averages  Changing the subject  Detached statistics  Implied connections  Misleading graphs  Faulty survey questions

Suspect Samples  Too small of a sample  Bad selection of sample  (convenience sampling)

Ambiguous Averages  Measures of central tendency are mean, median, mode and midrange. When someone says average what are they talking about.  Real estate example

Changing the subject  Different values are used to represent the same data.  Using percentages vs actual numbers for wow factor

Detached Statistics  Advil works 3 times faster.  1/3 fewer calories  Low fat

Implied Connections  “Eating fish may help to reduce your cholesterol”  Studies suggest that using our exercise machine will reduce your weight  Taking calcium will lower blood pressure in some people.

Misleading graphs

Faulty survey questions  Do you feel that the school should build a new football stadium?  Vs Do you favor increasing school taxes for a new athletic field?