Lesson 3 - Quantitative Analysis (Statistics)

Question 1

Population

Answer 1

the total number of some entity. The total number of planners preparing for the 2011 AICP exam would be a population.

Question 2

Sample

Answer 2

a subset of the population. For example, 25 candidates out of the total number of planners preparing for the 2011 AICP exam.

Question 3

Descriptive Statistics

Answer 3

describe the characteristics of a population.

Question 4

Inferential Statistics

Answer 4

determine characteristics of a population based on observations made on a sample from that population. We infer things about the population based on what is observed in the sample.

Question 5

Central tendency

Answer 5

the typical or representative value of a dataset. There are several ways to report central tendency, including mean, median, and mode.

appropriate measure of central tendency depends on data type and situation

Question 6

Mean

Answer 6

he average of a distribution. The mean of [2, 3, 4, 5] is 3.5.

Question 7

Weighted mean

Answer 7

when there is greater importance placed on specific entries or when the frequency distribution results in a representative value being assigned for each class.

Question 8

Median

Answer 8

the middle number of a ranked distribution. The median of [2, 3, 4, 6, 7] is 4.

Question 9

Mode

Answer 9

the most frequent number in a distribution. The modes of [1, 2, 3, 3, 5, 6, 7, 7] are 3 and 7. There can be more than one mode for a data set.

Question 10

Nominal data

Answer 10

is classified into mutually exclusive groups that lack intrinsic order. Race, social security number, and sex are examples of nominal data. Mode is the only measure of central tendency that can be used for nominal data.

Question 11

Ordinal data

Answer 11

has values that are ranked so that inferences can be made regarding the magnitude. However, ordinal data has no fixed interval between values. Educational attainment or a letter grade on a test are examples of ordinal data. Mode and median are the only measures of central tendency that can be used for ordinal data.

Question 12

Interval data

Answer 12

is data that has an ordered relationship with a magnitude. For temperature, 30 degrees is not twice as cold as 60 degrees. Mean is the best measure of interval data. Where the data is skewed median can be used.

Question 13

Ratio data

Answer 13

has an ordered relationship and equal intervals. Distance is an example of ratio data because 3.2 miles is twice as long as 1.6 miles. Any form of central tendency can be used for this type of data.

Question 14

Qualitative Variables

Answer 14

can be nominal or ordinal

Question 15

Quantitative Variables

Answer 15

can be interval or ratio.

Question 16

Continuous Variables

Answer 16

can have an infinite number of values, such as 1.1111.

Question 17

Dichotomous Variables

Answer 17

can only have two possible values, such as unemployed or employed which are symbolized as 0 and 1.

Question 18

Hypothesis Test

Answer 18

allows for a determination of possible outcomes and the interrelationship between variables.

Question 19

Null Hypothesis

Answer 19

shown as H0 is a statement that there are no differences. For example, a Null Hypothesis could be that Traffic Calming has no impact on traffic speed.

Question 20

Alternate Hypothesis

Answer 20

designated as H1, proposes the relationship - Traffic Calming reduces traffic speed.

Question 21

Normal distribution (data)

Answer 21

is one that is symmetrical around the mean. This is a bell curve.

Question 22

Distribution skewed to the right

Answer 22

has a few high numbers (outliers) that pull the mean to the right. For example, if there are three $20 million homes in your community, it is likely to skew the mean home value to the right.

Question 23

Distribution skewed to the left

Answer 23

has a few low numbers (outliers) that pull the mean to the left. When taking the AICP exam, for instance, a few people may give up and walk out resulting in a few very low scores, which would skew the mean score to the left.

Question 24

Range (dispersion)

Answer 24

the simplest measure of dispersion. The range is the difference between the highest and lowest scores in a distribution. The age range of the respondents in a neighborhood survey goes from 18-year-old to 62-year-old. This results in a range of 44.

Question 25

Variance (dispersion)

Answer 25

the average squared difference of scores from the mean score of a distribution.Variance is a descriptor of a probability distribution, how far the numbers lie from the mean.

Question 26

Standard Deviation (dispersion)

Answer 26

is the square root of the variance. For instance, if we want to know the difference in wages among three employees at a planning department, we need to calculate the mean, variance, and standard deviation. If the employees earn $10, $20, and $35 per hour, the mean is $21.67. This means that employee 1 makes ($10 - $21.67) = $11.67 less than the mean; employee 2 makes ($20 - $21.67) = $1.67 less than the mean; and employee 3 makes ($35 - $21.67) = $13.33 more than the mean.

To compute the variance, we first square each difference and sum it. (11.67)2+ (1.67)2 + (13.33)2 = 136.19 + 2.79 + 177.69 = 316.67. We then divide 316.67 by the number of samples minus 1, which gives us 316.67/(3-1) = $158.33.

The standard deviation is simply the square root of the variance. In this case, the square root of 158.33 is $12.58.

Question 27

Coefficient of Variation (dispersion)

Answer 27

measures the relative dispersion from the mean and is measured by taking the standard deviation and dividing by the mean.

Question 28

Standard Error (dispersion)

Answer 28

is the standard deviation of a sampling distribution. Standard errors indicate the degree of sampling fluctuation. The larger the sample size the smaller the standard error.

Question 29

Confidence Interval (dispersion)

Answer 29

gives an estimated range of values which is likely to include an unknown population parameter. The width of the confidence interval gives us an idea of how uncertain we are about the unknown parameter. A wide interval may indicate that we need more data before we can make a definitive statement. You frequently see confidence intervals provided on the polls. For example, 42% of California residents support one presidential candidate, 36% support another candidate, and 22% undecided, +/- 3%. This 3% is the confidence interval.

Question 30

Chi Square (testing)

Answer 30

a non-parametric test statistic that provides a measure of the amount of difference between two frequency distributions. Chi Square is commonly used for probability distributions in inferential statistics. This Chi Square distribution is used to test the goodness of fit of an observed distribution to a theoretical one.

Question 31

z-score (testing)

Answer 31

a measure of the distance, in standard deviation units, from the mean. This allows one to determine the likelihood, or probability that something would happen.

Question 32

t-test (testing)

Answer 32

allows the comparisons of the means of two groups to determine how likely the difference between the two means occurred by chance. In order to conduct a t-test, one needs to know the number of subjects in each group, the difference between the means of each group, and the standard deviation for each group.

Question 33

ANOVA (testing)

Answer 33

an analysis of variance. It studies the relationship between two variables, the first variable must be nominal and the second is interval.

Question 34

Correlation (testing)

Answer 34

tests the strength of the relationship between variables. The Correlation Coefficient indicates the type and strength of the relationship between variables, ranging from -1 to 1. The closer to 1 the stronger the relationship between the variables. For example, you would expect a strong correlation coefficient between score on the AICP exam and hours of study. Squaring the correlation coefficient results in an r2

Question 35

Regression (testing)

Answer 35

a test of the effect of independent variables on a dependent variable. A regression analysis explores the relationship between variables. For example, AICP Exam Score depends on number of hours studied, years of experience, and educational attainment. The result could show that for every 50 hours studied the score increases by 10%.

Question 36

Sampling Error (testing)

Answer 36

occurs when one has taken a sample from a larger population. The sample is not representative of the population as a whole, creating a sampling error.

Question 37

Nonsampling error

Answer 37

is one that cannot be explained by the representativeness of the sample. A nonsampling error can occur as a result of respondents misunderstanding a question or misreporting their answer and can also including missing values.