Data Analysis Test 1 UARK Pullen

Statistics

The science of collecting, organizing, analyzing, interpreting and presenting data

Descriptive Statistics

The collection, organization, presentation and summary of data

ex) mean, median, mode

Inferential Statistics

Generalizing from a sample to a population and making decisions

ex) 200 students = sample

entire student body = population

Data Set

Collection of data values as a whole (what goes into excel)

Observation

Each data value (goes into data sets)

ex) genders

Subject (or individual)

An item for study

ex) an employee in your company

Variable

A characteristic about the subject

ex) an employee's income or gender

Data Type: Categorical/Nominal/Qualitative

Values are described by words rather than numbers

ex) gender, ethnicity

Data Type: Numerical/Quantitative

Measuring a value

Type of Numerical/Quantitative = Discrete

Countable number of values (integers or whole numbers)

Type of Numerical/Quantitative = Continuous

Variable that can have any value in an interval value

Ratio Data

Strongest type of data, has a definite zero and starting point (quantitative)

--> can add, subtract, multiple, divide, mean + STD

ex) GPA, money

Interval Data

Second strongest type of data, a ranking with number associated/anything without a definite zero

--> can mean, STD but cannot add, subtract, multiple, divide

ex) 1-5 rating, temperature

Ordinal Data

Third type of data, a ranking system without numbers associated with data

--> can do frequency counts or %

ex) year in school, excellent fair poor

Nominal Data

Weakest type of data, straight words with no meaning behind the answers (qualitative)

--> can do frequency counts or %

ex) favorite food, gender, ethnicity

Type of Data Set = time series data

each observation in the sample represents a different equally spaced point in time

Type of Data Set = Cross sectional data

each observation represents a different individual unit (person) at the same point in time

Univariate

one variable

(histograms, descriptive statistics)

Bivariate

two variables

(scatter plots, 2 sample hypothesis, simple regression)

Multivariate

more than two variables

(anova, multiple regression)

Control group

the group that does not receive the experimental treatment

Experiment group

exposed to manipulation of independent variable

4 steps to construct a histogram

1) Find the min and max value

2) Define the # of bins/classes

3) Define the bin/class width

4) Define the upper limit

How to find the min and max value

In excel: =min(data)

=max(data)

How to define the # of bins/classes

its based on the # of observations (n)

How to define the bin/class width

(max - min) / # of bins

How to define the upper limit

It must be larger than the maximum value!

ex) max value = 676.42 width = 80

Make upper limit 680 then decrease by increments of 80

How to find relative frequency

frequency # / total #

how to find cumulative frequency

add each sum of preceding frequencies / total

skewed left

mean < median < mode

negative #

skewed right

mode < median < mean

positive #

symmetric

mean = median = mode

skewness is close to zero

Modal class

class with the highest frequency

Unimodal

one mode

Bimodal

two modes

Multimodal

more than two modes

Mean

average

excel: =average(data)

Median

Middle number

excel: =median(data)

Mode

The value that occurs most frequently in a given data set

excel: =mode(data)

Sample

statistic

portion of people

x-bar

Population

parameter

whole number

mu

Frequencies

number based off classes/bins

Skew excel function

=skew(data)

--> < 0 = negative skewed

--> > 0 = positive skewed

--> = 0 = normal distribution

Kurtosis

measures the peak/height of the curve of the distribution

Leptokurtic

positive kurtosis

sharper rising peak; > 0

Platykurtic

negative kurtosis

slower rising peak; < 0

Mesokurtic

normal distribution

= 0

Kurtosis excel function

=kurt(data)

Range equation

max - min

Population variance equation

Population standard deviation equation

the square root of the population variance

Sample variance equation

sample standard deviation equation

the square root of the sample variance

Population variance excel equation

=var.P(data)

Sample variance excel equation

=var(data)

Population standard deviation excel equation

=stdev.P(data)

Sample standard deviation excel equation

=stdev(data)

Trimmed mean

the mean of the data values left after "trimming" a specified percentage of the smallest and largest data values from the data set

--> 10% take off the lowest and highest values

--> 20% take off the lowest 2 and highest 2 values

KEEP WHOLE NUMBERS NOT % (like dont change 2% to .02 bc its wrong)

growth rate equation

=(present / initial) ^1/(n-1) - 1

Sharpe Ratio equation

(mean return - risk-free rate) / standard deviation return

(mean Xi - Rf) / std dev Si

--> you want the higher number

Sharpe Ratio

When looking at returns, look Xi values

When looking at risks, look at Si values

--> you want the higher number

Empirical Rule

Total area = 1 or 100%

Only use when normal distribution!!!