Descriptive Statistics & Data Displays (MUST BE DONE WITHIN 12 HOURS)

For this assignment you will need to download and open a data file that is posted in the Course Content folder and titled “descriptive dataset.sav”.

Perform analyses in SPSS on three (3) variables (one nominal, one ordinal, and one interval-level variable) to obtain appropriate descriptive statistics (e.g., measures of central tendency, dispersion, and distribution) related to the sample. Be sure to choose appropriate descriptive statistics that correspond with the level of measurement (nominal/ordinal/interval) for each of the three variables selected. For example, only the mode, frequency, or percentage of total cases can be reported for a nominal variable.

Create data displays (e.g., histogram graphs, bar graphs, line graphs, pie charts) of related variables — that is, variables that would make sense to compare based on what it is they are measuring

Export or paste your output into a Word document. Describe the results. Identify whether data are normally distributed. (e.g., you may choose to also write about the data distribution’s skew and kurtosis.) Write up the results of these analyses as they would appear in a research report. Use the APA manual or the OWL at Purdue Writing with Statistics webpage for formatting guidance. Be sure to discuss your analyses.

Write a short paragraph that highlights your understanding of why exploratory data is a critical part of any statistical analysis. The rationale must include definitions of key concepts and course citations to demonstrate your understanding.

Additional information on how to create data displays is available in Pallant Chapter 7, found in the Course Readings folder. You must show a high level of understanding of the importance of using descriptive statistics to receive full credit on this assignment. You must also format the data displays within the body of your assignment. Be sure your SPSS-created data displays are exported and formatted properly to your Word document.

Module overview :

Chapter two will discuss computing and understanding averages, applying scales, and levels of measurement related to central tendency. Chapter three discussed the variability and tools used to compute dispersion.

Module Outcomes/Objectives:

Formulate innovative business solutions that incorporate the use of statistical software. Integrate knowledge of statistical theory and quantitative data analysis as shown in scholarly and practitioner applied business research. Construct an independent evaluation of underlying assumptions and requirements of statistical designs and techniques.

NOTE* I attached below the Salkind Chapters 2,3,4,7, also attached my classmate’s assignment as an example but make sure please all writing must be original

“descriptive dataset.sav”. Attached Files: Survey_SPSS and Chapters 2,3,4

Chapter 2    
Means to an End:
Computing and

Understanding Averages

What You Will Learn in Chapter 2

 Understanding measures of central tendency

 Computing the mean for a set of scores

 Computing the median for a set of scores

 Computing the mode for a set of scores

 Understanding and applying scales or levels
of measurement

 Selecting a measure of central tendency

Measures of Central Tendency

 The AVERAGE is one value that best
represents a set of scores

 Another name for AVERAGES is measures of
central tendency

 Examples include the mean, median, and
mode

Computing the Mean

 is the mean value of the group of scores.

 Σ (sigma) tells you to add together whatever
follows it.

 X is each individual score in the group.

 The n is the sample size.

Steps to Computing the Mean

1. List the entire set of values in one or more
columns. These are all the Xs.

2. Compute the sum or total of all of the values.

3. Divide the total or sum by the number of
values.

Things to Remember

. . .

 The mean is sometimes represented by the letter M.

 n = sample size N = population size

 Sample mean is the measure of central tendency
that best represents the population mean.

 It is also called the arithmetic mean.

 Mean is like the fulcrum on a seesaw.

 Mean is VERY sensitive to extreme scores that can
skew or distort findings.

Weighted Mean

 Step 1: List all values for which the mean is being

calculated. (List them only once.)

 Step 2: List the frequency with which each value
occurs.

 Step 3: Multiply the value by the frequency, as
shown in the third column.

 Step 4: Sum all of the values in the Value
Frequency column.

 Step 5: Divide by the total frequency.

Median

 The median is defined as the midpoint in a
set of scores.

 It’s the point at which one half, or 50%, of the
scores fall above, and one half, or 50%, fall
below.

Steps to Finding the Median

1) List the values, in order, either from highest
to lowest or lowest to highest.

2) Find the middlemost score. That’s the
median.

BUT . . .

 What if there are two middle scores?

 The median is simply the mean of the two
middle values.

A Little About Percentiles . . .

 Percentile ranks are used to define the

percentage of cases equal to and below a
certain point on a distribution.

 75th percentile means that the score
received is at or above 75% of all other
scores in the distribution.

 Median is always at the 50th percentile.

Critical Thinking

 Why use the median instead of the mean?

Things to Remember
 The mean is the middle point in a set of

values, whereas the median is the middle
point in a set of cases.

 Because the median cares about the
number of cases, extreme scores (i.e.,
outliers) do not impact it.

Computing the Mode

 Mode = most frequently occurring value

 This is the least precise measure of central
tendency.

 When two values occur the same number of
times, there is bimodal distribution.

Steps to Finding Mode

 List all values in the distribution, but list each
value only once.

 Tally the number of times each value occurs.

 The value occurring the most is the mode.

Example of Finding Mode

Party Affiliation Number or Frequency
Democrats 90
Republicans 70
Independents 140

Multimodal

 Bimodal = Distribution with two modes

 Trimodal = Distribution with three modes

 Trimodal distributions are unlikely when
dealing with a large set of data points, but
they are possible.

Scales of Measurement

 Level of measurement dictates what specific

measure of central tendency you will use.

 Measurement is the assignment of values to
outcomes following a set of rules.

 Each of the four levels has a particular set of
characteristics.

Four Flavors of Scales of Measurement

 Nominal
 Ordinal
 Interval
 Ratio

Nominal Level of Measurement

 Defined by the characteristics of an outcome

that fit into one and only one class or
category

 These are mutually exclusive.
 Examples include gender and political

affiliation.

Ordinal Level of Measurement

 The characteristic of things being measured

here is that they are ordered.
 Example: Ranking candidates for a job

Interval Level of Measurement

 Based on some underlying continuum, such

that we can talk about how much more a
higher performance is than a lesser one

 The intervals, spaces, or points along the
scale are equal to one another.

Ratio Level of Measurement

 An assessment tool at the ratio level of

measurement is characterized by the
presence of an absolute zero on the scale.

 Examples: Zero molecular movement and
zero light

When to Use What . . .

 Use mode when the data are qualitative,

categorical, or nominal (e.g., eye color or
political party) and values can only fit into
one category (i.e., mutually exclusive).

 Use median when you have extreme scores.

 Use mean when the data do not include
extreme scores (i.e., outliers) and are not
qualitative, categorical, or nominal.

Using the Computer: Descriptive Statistics

The SPSS Output

Chapter 2     �Means to an End:�Computing and Understanding Averages�

What You Will Learn in Chapter 2
Measures of Central Tendency
Computing the Mean
Steps to Computing the Mean
Things to Remember . . .
Weighted Mean
Median
Steps to Finding the Median
BUT . . .
A Little About Percentiles . . .
Critical Thinking
Things to Remember
Computing the Mode
Steps to Finding Mode
Example of Finding Mode
Multimodal
Scales of Measurement
Four Flavors of Scales of Measurement
Nominal Level of Measurement
Ordinal Level of Measurement
Interval Level of Measurement
Ratio Level of Measurement
When to Use What . . .
Using the Computer: Descriptive Statistics
The SPSS Output

Chapter 3    
Viva La Différence:

Understanding Variability

What You Will Learn in Chapter 3

 Understanding the value of variability as a

descriptive tool

 Computing the range

 Computing the standard deviation

 Computing the variance

 Understanding what the standard deviation and
variance have in common and how they are
different

Why Understanding Variability
Is Important

 Variability reflects how scores differ from one
another.

 Also called spread or dispersion

Measures of Variability

 Three measures of variability are commonly
used to reflect the degree of variability,
including range, standard deviation, and
variance.

 Typically report the average and the
variability together to describe a distribution

Computing the Range

 Range is the most general estimate of

variability

 There are two types of range, although the
most commonly used is the exclusive range.

Exclusive Range

 General formula for range

 Also known as the exclusive range

 Range = h − l

 Where h is the highest score, and l is the
lowest score

Inclusive Range

 Inclusive Range = h − l + 1

 This type of range is less commonly seen.

 Where h is the highest score, and l is the
lowest score
Salkind, Statistics for People Who (Think They) Hate Statistics Excel 2016 6th Edition, SAGE Inc. © 2017

Computing Standard Deviation

 Most frequently used measure of variability

 SD = s = represents the average amount of
variability in a set of scores

Important Symbols

 s = standard deviation

 Σ = sigma, which tells you to find the sum of what
follows it

 X = each individual score

 = X-bar = mean of all of the scores in the
sample

 n = sample size

Why n – 1?

 Standard deviation is an estimate of the

POPULATION standard deviation.

 To make it an unbiased estimate, you must
subtract 1 from n.

 This artificially inflates the SD (it makes it
bigger) because it makes the denominator
smaller.

Things to Remember . . .

 Standard deviation is computed as the average

distance from the mean.

 The larger the standard deviation, the more
spread out the values are.

 Like the mean, the standard deviation is sensitive
to extreme scores.

 If s = 0, then there is no variability among scores,
and the scores are essentially identical in value.

Computing Variance

 Variance = standard deviation squared

 If you take the standard deviation and never
complete the last step (taking the square
root), you have the variation.

Standard Deviation or Variance

 While the formulas are quite similar, the two
are also quite different.

 Standard deviation is stated in original units.

 Variance is stated in units that are squared.

Using the Computer to Compute

Understanding and Interpreting

Real-World Stats

 Stapelberg and colleagues looked at variability

in heart rate as it related to coronary heart
disease.

 They found decreased heart rate variability in
both depressive disorders and coronary heart
disease.

 Researchers think that both diseases disrupt
control feedback loops that help the heart
function efficiently.

Chapter 3     �Viva La Différence: Understanding Variability

What You Will Learn in Chapter 3

Why Understanding Variability Is Important

Measures of Variability
Computing the Range
Exclusive Range
Inclusive Range
Computing Standard Deviation
Important Symbols
Why n – 1?
Things to Remember . . .
Computing Variance
Standard Deviation or Variance
Using the Computer to Compute
Understanding and Interpreting
Real-World Stats

Chapter 4    
A Picture Really Is Worth

a Thousand Words

What You Will Learn in Chapter 4

 Understanding why a picture is really
worth a thousand words

 Creating a histogram and a polygon
 Understanding the different shapes of

different distributions
 Using SPSS to create incredibly cool charts
 Creating different types of charts and

understanding their application and uses

Why Illustrate Data?

 A visual representation is an effective way to
examine the characteristics of a data set.

Ten Ways to a Great Figure

1. Minimize the junk.
2. Plan before you start creating.
3. Say what you mean; mean what you say.
4. Label everything.
5. Communicate ONE idea.
6. Keep things balanced.
7. Maintain the scale in the graph.
8. Simple is best, and less is more.
9. Limit the number of words.
10. The chart alone should convey what you want

to say.

Creating a

Frequency Distribution

 Method of tallying and representing the
number of times a certain score occurs

 Usually group scores into interval
classes/ranges

The Classiest of Intervals

 A class interval is a range of numbers.

 This is the first step in the creation of a
frequency distribution.

Creating Class Intervals

 Step 1: Determine the size of each interval. Select

a class interval that has a range of 2, 5, 10, or 20
data points.

 Step 2: Select a class interval so that 10–20 of the
class intervals cover the entire range of data.

 Step 3: Begin listing the class interval with a
multiple of that interval.

 Step 4: The largest interval goes at the top of the
frequency distribution.

Frequency Distribution
 Step 1. Determine the range.
 Step 2. Decide on the number of class

intervals.
 Step 3. Decide on the size of the class

interval.
 Step 4. Decide the starting point for the first

class.
 Step 5. Create the class intervals.
 Step 6. Put the data into the class intervals.

Frequency Distribution Example

Creating a Histogram

 Step 1: Using a piece of graph paper, place
values at equal distance along the x-axis.
Now identify the midpoint of the class
intervals.

 Step 2: Draw a bar or column around each
midpoint that represents the entire class
interval, and make its height represent the
frequency of that class interval.

Histograms

 Class Intervals
Along the x-Axis

Hand-Drawn Histogram

Tally-Ho Method

 A continuous line
that represents the
frequencies of
scores within a class
interval

Frequency Polygon

Cumulative Frequency Distribution

Other Cool Charts

 Column
Chart

Line Chart

Cool Ways to Chart Data

 Pie Chart

Using the Computer to Illustrate Data

 Creating Histogram Graphs

Using the Computer to Illustrate Data
 Creating Bar Graphs

Using the Computer to Illustrate Data
 Creating Line Graphs

Using the Computer to Illustrate Data
 Creating Pie Graphs

Chapter 4     �A Picture Really Is Worth a Thousand Words�

What You Will Learn in Chapter 4
Why Illustrate Data?
Ten Ways to a Great Figure
Creating a Frequency Distribution
The Classiest of Intervals
Creating Class Intervals
Frequency Distribution
Frequency Distribution Example
Creating a Histogram
Histograms
Hand-Drawn Histogram
Tally-Ho Method
Frequency Polygon
Cumulative Frequency Distribution
Other Cool Charts
Line Chart
Cool Ways to Chart Data
Using the Computer to Illustrate Data
Using the Computer to Illustrate Data
Using the Computer to Illustrate Data
Using the Computer to Illustrate Data

Chapter 7   
Hypotheticals and You:
Testing Your Questions

What You Will Learn in Chapter 7

 Understanding the difference between a

sample and a population

 Understanding the importance of the null
and research hypotheses

 Using criteria to judge a good hypothesis

What Is a Hypothesis?

 An “educated guess”

 Its role is to reflect the general problem
statement or question that is driving the
research.

 Translates the problem or research question
into a form that can be tested

Samples and Populations

 Population: The large group to which you

would like to generalize your findings

 Sample: The smaller, representative group of
the population that is used to do the
research

 Sampling error: A measure of how well a
sample represents the population

Hypotheses

 Two major types
 Research hypotheses
 Null hypotheses

 Null hypotheses refer to populations and are
written in Greek symbols

 Research hypotheses refer to samples and
are written in Roman symbols

The Null Hypothesis

 Statements that contain two or more things

that are equal (unrelated) to one another

H0 : µ1 = µ2

 The starting point—it is accepted as true
without knowing more information

 Benchmark to compare actual outcomes

The Research Hypothesis

 Statement that there is a relationship

between two variables

 Statements of inequality

 There are two types of research hypotheses

 Directional

 Nondirectional

Nondirectional Research Hypotheses

 Reflect a difference, but the direction is not
specified

 Use a two-tailed test

Nondirectional Research Hypothesis
Example

 H1 : X1 ≠ X2

Directional Research Hypotheses

 Reflect a difference, and the direction is
specified

 Use the one-tailed test

Differences Between Null and
Research Hypotheses

What Makes a Good Hypothesis?

In sum, good hypotheses should
 be stated in declarative form,

 posit a relationship between variables,

 reflect a theory or a body of literature on
which they are based,

 be brief and to the point, and

 be testable.

Chapter 7   �Hypotheticals and You: Testing Your Questions�

What You Will Learn in Chapter 7
What Is a Hypothesis?
Samples and Populations
Hypotheses
The Null Hypothesis
The Research Hypothesis
Nondirectional Research Hypotheses

Nondirectional Research Hypothesis Example

Directional Research Hypotheses

Differences Between Null and Research Hypotheses

What Makes a Good Hypothesis?

DESCRIPTIVE A

ALYSIS

DESCRIPTIVE A

LYSIS

Examining Measurements of Central Tendencies

This discussion board is based on the measurement of central tendencies whereas the nominal, ordinal, interval and ratio allow researcher to analyze data. Each of these measurements provide researchers with the ability to measure sets of data that do not represent numerical values. Salkind (201

) defined a level measurement with an outcome that fit into one and only class or category as nominal. The level of measurement assigns value to a specific item than assign a value to the item based on the appeal to an individual. The nominal measurement that I chose was labor force status. The descriptive characteristics that were chosen for the completion of the data set were represented some form of employment. Salkind (2017) explained the ordinal measurement as the characteristic of the assigning order or ranking data. The ordinal measurement that I chose was a ranking of how individuals view their political affiliations. The characteristics were assigned a value which for the mean, median and mode to be determined. The sum of a data set divide by the number data points represents the mean (Salkind, 2017). The mean for a data set may be skewed based on extreme number contained in the set of number. By focusing on the median, Salkind (2017) defined as a true midpoint of the data set that does not take in consideration extreme number. The median produces a more conclusive number that is related to the true data without influences. When analyzing data, situations may occur where the data is repetitive. This repetition of the number in a data is known as the mode (Salkind, 2017). A data set may have multiple modes and may have greater determining factor mean and how the data is interpreted.

Nominal Data

The nominal data set for ‘Labor for status’ comprised of

descriptive terms that represents some phase of employment. The data were assigned numbers 0 to 9 based on the stage of employed (e.g. “working fulltime” =1). The data set consisted of

575

respondents of which only one data was missing. The data shows that nearly

0% of respondents reported that were “working fulltime”. The corresponding value associated with “working fulltime” was 1. The data show that most respondents are employed in some fashion calculating a mean of

2.57

, median of 1 and a mode of 1. The median of 1 seems to be an anomaly in the data based on the data set range of nine. The standard deviation of

and variance of

5.044

. Based on the information analyzed, 68% of the respondents are represented between .33 and 4.81. The variance shows the consistency of the data based on the distance from .33 to 4.81.

	Statistic s
Labor force status
		N				Valid	574
			Missing				1
		Mean	2.57
	Std. Error of Mean	.094
	Median	1.00
	Mode
		Std. Deviation	2.246
	Variance	5.044
		Skewness	1.088
	Std. Error of Skewness		.102
		Kurtosis	-.392
	Std. Error of Kurtosis	.204
		Range		7
		Minimum
		Maximum			8

Valid

57.1

12.2

1.4

3.3

11.1

2.8

10.3

1.7

574

100.0

Missing

Total

100.0

Labor force status
	Frequency		Percent		Valid Percent	Cumulative Percent
Working full time	3 28	57.0		57.1
Working part-time	70		12.2	69.3
Temporarily not working			1.4	70.7
Unemployed, laid off	19		3.3	74.0
Retired	64		11.1	85.2
School	16		2.8	88.0
Keeping house	59		10.3	98.3
Other	10		1.7				100.0
			Total	99.8
NA	.2
				575

Ordinal Data

The ordinal data set for ‘Think of self as liberal or conservative’ comprised of 10 descriptive terms that represents some political affiliation. The data were assigned numbers, or range of 0 to 9 based on what extent they represented the political affiliation (e.g. “extremely liberals” =1). The data set consisted of 575 respondents of which 28 data was missing. The data shows that nearly 72% of respondents reported that were “

Moderate

”. The corresponding value associated with “Moderate” was 4. This data set shows that individuals political affiliation lies down the middle as displayed with a mean of

3.7

, median of 4 and a mode of 4. The standard deviation of

1.411

and variance of

1.990

. The standard deviation shows that 68% of the individuals are willing to accept other individuals’ point of view by identifying as slightly affiliated with the political mindset.

Statistics

Valid

Missing

Mean

Std. Error of Mean

Median

Mode

Std. Deviation

Variance

Skewness

Std. Error of Skewness

Kurtosis

Std. Error of Kurtosis

Range

Minimum

Maximum

Think of self as liberal or conservative
	547
	28
3. 77
.060
4.00
4
1.411
1.990
.037
.104
-.672
.209
6

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

3.8

13.4

14.1

1.4

100.0

Total

547

100.0

Missing

Total

575

100.0

Think of self as liberal or conservative
Extremely liberal	21	3.7		3.8
Liberal	109	19.0	19.9	23.8
Slightly liberal		77		13.4	14.1	37.8
Moderate	189	32.9	34.6	72.4
Slightly conservative	86.5
Conservative	66	1 1.5	12.1	98.5
Extremely conservative	1.5
95.1
DK	4.9

Interval Data

The scale data set for ‘Respondent ID’ comprised of individual that receive a number as they respondent to the survey. The data were assigned numbers, or range of 1 to 575 based on when they competed and submitted the information. The data set consisted of 575 respondents of which 1 data was missing. The data provide few measurements of central tendencies due the fact that there is no repetition and the data are straightforward.

Range

Minimum

Maximum

Mean

Std. Deviation

Skewness

Kurtosis

Statistic

Std. Error

575

574

575

.102

575

Descriptive Statistics
						Statistic	Std. Error
Respondent id number	288.00	166.132	.000	-1.200	.203
Valid N (listwise)

References

Salkind, N. J. (2017). Statistics for people who (think they) hate statistics (Sixth edition.).

Thousand Oaks, CA: SAGE Publications, Inc.

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