Managerial Statistics
(9th edition – Gerald Keller)
All statistical terms
FROM A – Z (INCLUDING FORMULA’S AND PAGE NUMBERS)
RIJKSUNIVERSITEIT GRONINGEN
,Very useful pages:
- 914 flowchart statistical inference techniques
- Last two pages guide to statistical techniques
Term Definition Page
Assigning 177- 176
probability’s
Classical
Mathematically determine the probability
approach
How likely is the outcome (probability) to occur in the long-run
Relative
(estimates become better with a greater amount of
frequency
observations, based on a history of outcomes)
approach
The degree of belief that we hold in the subjective occurrence
Subjective
of an event (probability that a certain stock will increase in
approach
value)
Binomial When? 240
experiment The experiment consists of n repeated trials.
Each trial can result in just two possible outcomes. We call
one of these outcomes a success and the other, a failure. (example
The probability of success, denoted by p, is the same on 7.9, 242)
every trial. Failure = 1 – P
The trials are independent that is, the outcome on a trial
does not affect the outcome on other trials.
Bivariate Techniques applied to two (or more) sets of data and their 32
relationship cross-classification table (cross-tabulation table)
cross-
describes the relationship between two nominal variables
classification
table
Central limit Which states: given certain conditions, the arithmetic mean of a 306
theorem sufficiently large number of iterates of independent random
variables, each with a well-defined expected value and well-
defined variance, will be approximately normally distributed,
regardless of the underlying distribution
Chebbysheff’s General interpretation of the empirical rule: the proportion of 114
Theorem observations in any sample or population that lie within ‘k’
(example
1
standard deviation of the mean is at least 1 – for k > 1 4.10)
k²
Classes Frequency distribution by counting the number of observations 46
that fall into a category (0-15, >15-30, >31-45 etc.). Number of
(Table 3.2,
classes depend on the number of observations
p 49)
,Coefficient of Can be used when data are observational and the two 634
correlation variables are bivariate normally distrubuted.
(determine linear
(example
relationship
Formula: 16.6)
between
variables)
Test statistic:
(testing p = 0) Formula:
Degrees of
freedom
V=n–2
Coefficient of Measure the amount of variation in the dependent variable that 630
determination is explained by the variation in the independent variable
(example
Formula: R² - S²xy / S²xS²y 16.5)
Coefficient of The standard deviation of the observation divided by their 115
variation mean:
Formula population coefficient of variation:
Formula sample coefficient of variation:
collectively A set of events is jointly or collectively exhaustive if at least one -
exhaustive event of the events must occur.
Confidence A range of values so defined that there is a specified probability 335
interval that the value of a parameter lies within it
NOTE! When a value falls within the calculated confidence
interval (LCL and UCL) the H0 hypothesis is not rejected
Confidence Calculation of the confidence interval of the slope 628
interval estimator
Formula: B1 +- ta/2Sb1 (example
of β1
16.4)
Confidence The probability that the interval includes the actual value of μ 334
interval estimator resulting in a lower confidence limit (LCL) for ( - ) and an upper
of μ confidence limit (UCL) for ( + ). (Same approach as the rejection
region)
Confidence level
The probability 1 – α
(example
10.1)
Formula:
, NOTE! You cannot interpret the confidence estimate of μ as a 339
probability statement about μ. It is the probability statement
about the sample mean.
Confidence level Measure of reliability, the amount that an estimating procedure 6
will be correct (confidence 95% = the predicted procedure
based on the sample will be correct 95% of the time)
Continuous Value is uncountable (time spend to complete a task) 215
random variable
Covariance When? 127
Objective: Describe the relationship between two
variables
Data: Interval
Example
Formula:
4.17, 134)
Example
Coefficient of
Formula: 4.16, 128)
correlation
Least square line
coefficients Objective: method to product a straight line
Example
4.17, 134)
Formula’s:
Data The observed values of a variable (stock price of $45.23 etc.) 13
Deterministic Equations that allow you to determine the values of the 609
models dependent variable from the values of the independent
variables
Discrete random Can take on a countable number of values (flip a coin) 215
variable
(Requirement on page 216)
,Empirical rule 113
Error of Difference between the estimator and a parameter, expressed 348
estimation as B (bound on the error of estimation, formula on p. 348)
Calculate
sample size to
Formula:
estimate mean
Error variable The error accounts thus for all the variables, measurable and 610
immeasurable, that are not part of the model
Event Collection or set of one or more simple events in a sample space 176
Expected When? 587
frequency for a
Objective: analyze relationship between variables and
contingency
compare two or more populations
table
Data type: Nominal
(example
at same
Formula (same as chi-squared) : page)
Rejection region v = (row – 1)(column – 1)
F-Distribution Is the sampling distribution of the ration of two sample variances -
Finite population Correction related to the size of the population relative to the 307
correction factor sample (20x larger population and the correction can be
ignored).
, First-Order Linear Used to analyze the relationship between two variables 610
Model (coefficients are population parameter and often unknown!)
(simple linear
regression
Formula: y = β0 + β1x + e
model)
Symbol definition at page 610
Frequency Represents the categories and the number of counts. Relative 18
distribution frequency distribution: relation to the total (i.e. percentage)
Bar/pie chart Bar chart: display frequencies, pie chart: display relative
frequencies (simple presentation of numbers and categories)
Histograms Graphical representation of data to obtain information. Used 44-57
when data are interval, base is the interval, height is the
frequency.
Positively skewed: mean is larger than the median
Negatively skewed: mean is smaller than the median
Drawback: lose potentially useful information by classifying
observations
Hypothesis Reject null hypothesis: enough evidence to infer that the
alternative hypothesis is true
Do not reject null hypothesis: there is not enough evidence to
infer that the alternative hypothesis is true
Null hypothesis 368
H0: Described as the status quo, if there is not enough evidence
the null hypothesis will not be rejected (you’re innocent until it’s
proven you’re guilty). If there is enough evidence, the null
hypothesis will be rejected in favor of the alternative hypothesis.
Alternative
hypothesis
(9th edition – Gerald Keller)
All statistical terms
FROM A – Z (INCLUDING FORMULA’S AND PAGE NUMBERS)
RIJKSUNIVERSITEIT GRONINGEN
,Very useful pages:
- 914 flowchart statistical inference techniques
- Last two pages guide to statistical techniques
Term Definition Page
Assigning 177- 176
probability’s
Classical
Mathematically determine the probability
approach
How likely is the outcome (probability) to occur in the long-run
Relative
(estimates become better with a greater amount of
frequency
observations, based on a history of outcomes)
approach
The degree of belief that we hold in the subjective occurrence
Subjective
of an event (probability that a certain stock will increase in
approach
value)
Binomial When? 240
experiment The experiment consists of n repeated trials.
Each trial can result in just two possible outcomes. We call
one of these outcomes a success and the other, a failure. (example
The probability of success, denoted by p, is the same on 7.9, 242)
every trial. Failure = 1 – P
The trials are independent that is, the outcome on a trial
does not affect the outcome on other trials.
Bivariate Techniques applied to two (or more) sets of data and their 32
relationship cross-classification table (cross-tabulation table)
cross-
describes the relationship between two nominal variables
classification
table
Central limit Which states: given certain conditions, the arithmetic mean of a 306
theorem sufficiently large number of iterates of independent random
variables, each with a well-defined expected value and well-
defined variance, will be approximately normally distributed,
regardless of the underlying distribution
Chebbysheff’s General interpretation of the empirical rule: the proportion of 114
Theorem observations in any sample or population that lie within ‘k’
(example
1
standard deviation of the mean is at least 1 – for k > 1 4.10)
k²
Classes Frequency distribution by counting the number of observations 46
that fall into a category (0-15, >15-30, >31-45 etc.). Number of
(Table 3.2,
classes depend on the number of observations
p 49)
,Coefficient of Can be used when data are observational and the two 634
correlation variables are bivariate normally distrubuted.
(determine linear
(example
relationship
Formula: 16.6)
between
variables)
Test statistic:
(testing p = 0) Formula:
Degrees of
freedom
V=n–2
Coefficient of Measure the amount of variation in the dependent variable that 630
determination is explained by the variation in the independent variable
(example
Formula: R² - S²xy / S²xS²y 16.5)
Coefficient of The standard deviation of the observation divided by their 115
variation mean:
Formula population coefficient of variation:
Formula sample coefficient of variation:
collectively A set of events is jointly or collectively exhaustive if at least one -
exhaustive event of the events must occur.
Confidence A range of values so defined that there is a specified probability 335
interval that the value of a parameter lies within it
NOTE! When a value falls within the calculated confidence
interval (LCL and UCL) the H0 hypothesis is not rejected
Confidence Calculation of the confidence interval of the slope 628
interval estimator
Formula: B1 +- ta/2Sb1 (example
of β1
16.4)
Confidence The probability that the interval includes the actual value of μ 334
interval estimator resulting in a lower confidence limit (LCL) for ( - ) and an upper
of μ confidence limit (UCL) for ( + ). (Same approach as the rejection
region)
Confidence level
The probability 1 – α
(example
10.1)
Formula:
, NOTE! You cannot interpret the confidence estimate of μ as a 339
probability statement about μ. It is the probability statement
about the sample mean.
Confidence level Measure of reliability, the amount that an estimating procedure 6
will be correct (confidence 95% = the predicted procedure
based on the sample will be correct 95% of the time)
Continuous Value is uncountable (time spend to complete a task) 215
random variable
Covariance When? 127
Objective: Describe the relationship between two
variables
Data: Interval
Example
Formula:
4.17, 134)
Example
Coefficient of
Formula: 4.16, 128)
correlation
Least square line
coefficients Objective: method to product a straight line
Example
4.17, 134)
Formula’s:
Data The observed values of a variable (stock price of $45.23 etc.) 13
Deterministic Equations that allow you to determine the values of the 609
models dependent variable from the values of the independent
variables
Discrete random Can take on a countable number of values (flip a coin) 215
variable
(Requirement on page 216)
,Empirical rule 113
Error of Difference between the estimator and a parameter, expressed 348
estimation as B (bound on the error of estimation, formula on p. 348)
Calculate
sample size to
Formula:
estimate mean
Error variable The error accounts thus for all the variables, measurable and 610
immeasurable, that are not part of the model
Event Collection or set of one or more simple events in a sample space 176
Expected When? 587
frequency for a
Objective: analyze relationship between variables and
contingency
compare two or more populations
table
Data type: Nominal
(example
at same
Formula (same as chi-squared) : page)
Rejection region v = (row – 1)(column – 1)
F-Distribution Is the sampling distribution of the ration of two sample variances -
Finite population Correction related to the size of the population relative to the 307
correction factor sample (20x larger population and the correction can be
ignored).
, First-Order Linear Used to analyze the relationship between two variables 610
Model (coefficients are population parameter and often unknown!)
(simple linear
regression
Formula: y = β0 + β1x + e
model)
Symbol definition at page 610
Frequency Represents the categories and the number of counts. Relative 18
distribution frequency distribution: relation to the total (i.e. percentage)
Bar/pie chart Bar chart: display frequencies, pie chart: display relative
frequencies (simple presentation of numbers and categories)
Histograms Graphical representation of data to obtain information. Used 44-57
when data are interval, base is the interval, height is the
frequency.
Positively skewed: mean is larger than the median
Negatively skewed: mean is smaller than the median
Drawback: lose potentially useful information by classifying
observations
Hypothesis Reject null hypothesis: enough evidence to infer that the
alternative hypothesis is true
Do not reject null hypothesis: there is not enough evidence to
infer that the alternative hypothesis is true
Null hypothesis 368
H0: Described as the status quo, if there is not enough evidence
the null hypothesis will not be rejected (you’re innocent until it’s
proven you’re guilty). If there is enough evidence, the null
hypothesis will be rejected in favor of the alternative hypothesis.
Alternative
hypothesis
