A
Alternative hypothesis
determination, 147
formation, 146–147
for single mean, 147–148
for single proportion, 148
for single variance, 148
Arithmetic mean, 29–30
B
Bar graph, 11–12
Binomial distribution function, 110
Box plot, 27–28
C
Categorical variable, 3–4
Center of gravity, 76
Central limit theorem, 105–106
Ceteris paribus, 165
Chebyshev theorem, 67–68
Chi-squared distribution function, 94–95
Coefficient of variation, 61–64
Composite statistical hypothesis, 142
Computational formula, 51–53
Confidence intervals, 122–125, 139–140, 156–161
Continuous dichotomous variable, 4
Continuous random variable, 82
Control variables, 165
Correlation coefficient, 59–60, 71
Covariance
population, 57–58
sample, 58–59
Critical value calculation, 155–156
Cumulative frequency distribution, 17
D
Degree of freedom, 72–74
Descriptive statistics
applications
coefficient of variation, 61–64
correlation coefficient, 59–60, 71
error, 75–77
Kurtosis, 80
properties of estimators, 74–75
relation between mean, median, and mode, 80
skewness, 78–79
standard error, 71–74
standardization, 69–70
sum of squares, 78
Z score, 64–68
measurement scales
categorical data, 3–4
dichotomous variables, 4
interval scale, 5
Likert scale, 4–5
nominal, 4
ordinal scale, 4
ratio scale, 5
numerical
measures of association, 57–60
measures of central tendency, 29–45
measures of dispersion, 45–57
qualitative variables
definition, 3
graphical methods, 10–14
tabular methods, 7–10
quantitative variables
definition, 3
graphical methods, 20–28
tabular methods, 14–20
types of tools, 5–7
Dichotomous variables, 4
Discrete dichotomous variable, 4
Discrete random variable, 82
Dot plot, 25
Dummy variables. See Dichotomous variables
E
Econometrics, 173
Error, 50, 75–77
Estimators, properties of, 74–75
Expected value. See Mean
F
F distribution function, 96–97
Frequency distribution, 17
qualitative variables, 7–10
quantitative variables, 14–17
G
Geometric mean, 34–37
Grouped data, 14
H
Harmonic mean, 37–38
Hinges, 20
Histogram, 20–22
Human capital, 166
I
Individual error, 75
Inductive statistics, 101
Interquartile range, 45–46
Interval estimation
definition, 121–122
one population mean, 125–137
Interval scale, 5
K
Kurtosis, 80
vs. normality, 93–94
L
Law of large numbers, 105
Likert scale, 4–5
M
MAE. See Mean absolute error
Margin of error, 122–125
Mean
of data summarized as frequencies, 41–42
for data with frequencies, 38–39
definition, 29
for grouped data, 42–43
of grouped data, 40–42
Mean absolute error (MAE), 76
Mean squared error (MSE), 78, 166
Mean squared regression (MSR), 166
Measurement scales
categorical data, 3–4
dichotomous variables, 4
interval scale, 5
Likert scale, 4–5
ordinal scale, 4
ratio scale, 5
Measures of association
correlation coefficient, 59–60, 71
population covariance, 57–58
sample covariance, 58–59
Measures of central tendency
arithmetic mean, 29–30
geometric mean, 34–37
harmonic mean, 37–38
mean, 29
mean for data with frequencies, 38–39
mean for grouped data, 42–43
mean of data summarized as frequencies, 41–42
mean of grouped data, 40–42
median, 43–44
mode, 44–45
quartiles, 43
sample mean, 30–34
trimmed mean, 34
weighted mean, 39–40
Measures of dispersion
algebraic relations for variance, 50–51
average of several variances, 53–54
computational formula, 51–53
error, 50
interquartile range, 45–46
population variance, 47
range, 45
sample variance, 47–48
standard deviation, 49–50
variance, 46–47
variance of data with frequency, 54–57
variance of grouped data, 57
Median, 43–44
Mode, 44–45
MSE. See Mean squared error
MSR. See Mean squared regression
N
Nominal data, 3–4
Normal distribution functions
area under with any mean and variance, 93
area under with mean zero and variance one, 85–86
description, 82–83
normality vs. Kurtosis, 93–94
normality vs. skewness, 93
probability values with excel, 86–88
properties, 83–84
standardizing values, 84–85
Null hypothesis
definition, 143–144
equality of two parameters, 144–145
of two means, 145
of two proportions, 146
of two variances, 146
Numerical descriptive statistics
measures of association, 57–60
measures of central tendency, 29–45
measures of dispersion, 45–57
O
Ogive, 22–23
Ordinal scale, 4
P
Panel data analysis, 178
Parameter, 5–6
Pearson coefficient of skewness, 80
Percentile, 17–18
Pie chart, 12–14
Point estimates, 74–75
Point estimation, 120–121
Pooled variance, 53
Population covariance, 57–58
Population variance, 47
Probability density function, 82
Probability distribution
for continuous random variable, 82
definition, 81
for discrete random variable, 82
p value, 154–155
Q
Qualitative variables
definition, 3
graphical methods
bar graph, 11–12
pie chart, 12–14
tabular methods
frequency distribution, 7–10
relative frequency, 10
Quantitative variables
graphical methods
box plot, 27–28
dot plot, 25
histogram, 20–22
Ogive, 22–23
scatter plot, 25–27
stem-and-leaf, 23–24
tabular methods
cumulative frequency distribution, 17
frequency distribution, 14–16
hinges, 20
percentile, 17–18
quartiles, 18–19
relative frequency distribution, 16
Quartiles, 18–19, 43
R
Random variable, 81
Range, 45
Ratio scale, 5
Regression analysis, 163–173
Relative frequency, 10
Relative frequency distribution, 16
S
Sample covariance, 58–59
Sample mean, 30–34
Sample size, 101–104, 137–138
Sample variance, 47–48
Sampling distribution
central limit theorem, 105–106
difference of two proportions, 113–114
law of large numbers, 105
mean vs. median efficiency, 116–118
one sample mean, 106–109
one sample proportion, 109–110
one sample variance, 114–115
two sample means, 110–113
two sample proporation, 113–114
two sample variance, 115–116
Scatter plot, 25–27
Simple hypothesis, 142–143
Skewness, 78–79
vs. normality, 93
Spatial econometrics, 178
Standard deviation, 49–50
Standard error, 66, 71–74
Standardization, 69–70
Statistical hypothesis, 142
Statistical inference, 101, 119, 150–152, 154–156
Stem-and-leaf, 23–24
Sum of squares, 78
T
t distribution function, 96
Test of hypothesis, 156–161
Test statistics, 148–150
Total sum of squares (TSS), 78
Trimmed mean, 34
TSS. See Total sum of squares
Type I error, 153
Type II error, 153
Type III error, 153
V
Variance
algebraic relations, 50–51
of data with frequency, 54–57
definition, 46–47
of grouped data, 57
pooled, 53
population, 47
sample, 47–48
W
Weighted mean, 39–40
Z
Z score, 64–68