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Statistics

STATS 120A

James Hull

Fall

Description

Chapter 1 Objectives: Statistical Imagination
• Explain the meaning of the core concepts of statistics, statistical imagination, statistical norms and ideals, and data
This is a fine example of a statistical norm(in the year 2003, about 7 out of every 1,000 infants in the United States died before the age of 1.)as
defined on pages 4 and 5 the average rate of occurrence of a phenomenon. We often express statistical norms as rates, fractions, ratios, or percentages,
as in thexample of the infant mortality rate. A social norm, in contrast is a shared idea of the behavior that is appropriate
or inappropriate in a given situation in a given culture.
When Ritchey says, "To have the statistical imagination is to understand that most events are predictable," what
does he mean by predictable? That even if we can’t predict precisely when an event will occur, in many cases we can
predict how often it will occur over time.
-the data show” or “the data say” singular form is datum plural is data
Not political
• List the differences between descriptive and inferential statistics
Inferential statistics: The branch of the statistics field that deals with understanding cause and consequence and also
with making predictions based on data
Descriptive statistics: statistics field that deals with counting and calculating how often a certain type of event occurs
A variable is any measurable phenomena that can change or vary over time, across space, or from individual to
individual.A constant is, well, constant. It will not vary from study subject to study subject.
Constant: person's age in years at the time they earn th e right to vote in the US, person's age in years at
the time they were born.
Variable: A measurement of a person's age in years at the time they graduate from college.
-The phrases "predictor variable" and "independent variable" refer to the same measure of a concept in a statistical
model (they are synonymous).
-SYMBOL = UNEVALUATED FORMULA = EVALUATED FORMULA = FINAL ANSWER
-A statistic includes small errors that derive from sampling and other sources, while a parameter includes no errors by
definition. Also Parameters describe all members of a population, Statistics describe only some subset of a
population
-Principle of INCLUSIVENESS: for a given variable there must be a score or code for every observation made.
-Exclusiveness: Every observation can be assigned one and only one score/ answer.
• Calculate fractions, proportions, percentages, and rates, and convert between them
Implied denominator of a proportion is 100.
Chapter 2 Objectives: Organizing Data
• List and identify the basic levels of measurement and provide examples of eac
Nominal Sex (Male, Female) Subject Responds to Medication (Yes, No) Place of Birth (Chicago, New York, Chapel Hill,
etc.) Favorite Color (Red, Orange, Yellow, Green, Blue, etc.)
Ordinal (rank)Educational Class Level (Senior, Junior, Sophomore, etc.) Social Class Level (Upper class, middle class,
lower class) Order of Finishing (First, Second, Third, Fourth, etc.) Quality of Housing (Excellent, good, standard, poor..
Interval Fahrenheit Temperature (Ranging from -273 degrees to +infinity) IQ (Ranges from 0 to 200) Year (Ranges
forward and backward from an arbitrary point in time) Composite Scores or Indexes (Range may vary)
Ratio meaningful zero Kelvin Temperature (Ranges from absolute zero to +infinity) Weight and Height (Ranges from 0
to some maximum value) Distance (Ranges from 0 to some maximum value) Dollar Value (Ranges from –infinity to
+infinity)
Chapter 3 Objectives: Charts and Graphs
• Describe the purpose of graphing data and the basic rules for good graphing
Displaying data graphically enables you to see broad trends quickly and easily
-Detect errors in data collection, coding, or analysis, Detect outliers and other unusual cases that are not like the rest ,
Discern the general shape of the frequency distribution of data, Communicate with audiences that are not
statistically minded
• Describe and identify the basic methods of graphically displaying each class of variable
Pie chart: Nominal ordinal. Can simultaneously display both the raw counts in each category and the percent of all
cases in each category.
Bar chart: Nominal ordinal. Bivariate (two variables) relationships qualitative*quantitiative
Histogram: displaying distributions of Raw data Interval ratio
Freq Polygons and Line Graphs/Percen Freq Line Graphs: Interval ratio multiple overlapping dist of raw data & time
series. -The only situation in which you are NOT obligated to identify the data source below a graph is if you collected the data
yourself
Chapter 4 Objectives: Measuring Central Tendency
• Discuss the concepts of symmetry and skewness as the apply to distributions and averages
MODE: nominal/ ordinal
Mean: Interval/ratio
Median: Interval/ ratio when a graph is skewed
Chapter 5 Objectives: Measuring Dispersion
Sx = standard deviation for the interval/ratio variable
X
X = the individual observations (variable X)
IQV = K(100^2 - SUM(Percent^2)) / 100^2 (K - 1). With K = 2 and the two percents being 20 and 80, it can be seen that
the only correctly matching formula among the answer choices is IQV = 2(10000 - (2000 + 6400))/10000(1) = 0.32.
By itself, a measure of just central tendency is not enough to characterize a distribution.
Summing the deviation scores (unsquared) will *always* result in 0, sum of 3847,3, or any number other than 0
is wrong
Square of any number is positive. (Nominal ordinal)
• Describe and demonstrate the use of basic measures of dispersion for different data types
range is the difference between the maximum and minimum score which represents the total possible variation in the
sample distribution. which attempts to box in the dispersion from the outside inwards, (Interval ratio)
(max-min) score +value of rounding unit. Ex 50.5 add .5 if 50 you add 1
standard deviation describe the way scores are spread across the distribution in relation to center or mean.interval/ratio
Variance is the square of the standard deviation. Interval ratio
• Solve problems using the mean, standard, deviation,
normal distribution, and zscores ZX= standardized score for a value of X OR, the # of standard deviations raw
score (X-score) deviates from mean
X = an interval/ratio variable
X(bar) = the mean of X
z-score formula or basic knowledge of the normal distribution, we can quickly surmise that the z-score is equal to zero and,
lying at the exact same point as the mean and median of the distribution, bisects it into two parts with

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