Descriptive Statistics
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Transcript of Descriptive Statistics
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StatisticsResearch Methods
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What’s in this PowerPoint?• Why learning statistics?• Two Perspectives of Statistics• Descriptive Statistics• Inferential Statistics
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Why is my evil
lecturer forcing me
to learn statistics?
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Why oh why? • What do you learn in this class?
Research
• What is research? To answer some interesting questions
• How do you answer the research questions? Collect data Explain & analyze the data
• Numbers = data
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Quantitative Research Process (Field, 2009)
Review of Literature
Review of Literature
??
?
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So you’ve done hypothesis…• Let’s identify the variables• For example:
Research Question• Is there a relationship between gender and
English competence? Hypothesis• There is a correlation between gender and
English competence Variables?
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What is variable?
Gender
English competence
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How’s the relationship?
gender English competence
Independent Variable
Dependent Variable
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Measuring Variables
Variables
categorical
Binary Only 2 categories
Nominal > 2 categories
Ordinal Categories w/ logical ORDER, difference doesn’t matter
continuous
Interval equal interval = equal difference
Ratio The difference makes sense, clear /natural 0
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So what level of measurements are our variables?Gender
• Categorical? Binary? Male vs. Female Nominal? Male vs.
Female vs. Gay vs. Lesbian
Ordinal? No!
• Continuous? Interval? No! Ratio? No!
English Competence
• Categorical? Binary? No.. Nominal? No.. Ordinal? Beginner vs.
Intermediate vs. Advanced (but…)
• Continuous? Interval? GPA 1.5-4 Ratio? 0-100
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But why do we need to know these?• Statistics is about explaining the
data in meaningful ways and as detailed as possible Meaningful • Clear (female is not male, GPA 3.00>1.50
but those with GPA 3.00 is not as twice smarter) descriptive statistics
Detailed• more accurate analyses, more accurate
explanation of the population inferential statistics
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Golden Rule• Aim for higher level of measurement
Binary
Nominal
Ordinal
IntervalRatio
preferred
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Data Prepara
tion
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Data – what is it?• In Quantitative research, data mostly
consist of numbers or words that are converted to numbers (such as in discourse analysis)
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How to prepare your data?• Use tools!
Calculator – um, really? MS Excel SPSS
• Why Excel? Ubiquitous Free Easy to use Can be converted to SPSS for more
detailed analyses
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Preparing the Data in MS Excel
• Open the file “Statistics-Complete.xls”
• Columns variables• Rows cases• Cell Address
Column A to ZZ Row 1, 2, 3 to ∞ Example: A2 column A, row
2
• First Row name of variable (for analysis)
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Perspectives of
Statistics
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Two perspectives• Descriptive Statistics
To describe or summarize the data Results of the data only
• Inferential Statistics To make inferences about the population
from the data (sample)
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Descriptive
Statistics
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How do you describe data?
Data Description
Itself (size)
Frequency (how many/often)
Percentage (how big)
Against each other
Central tendency (how they are
placed)
Mean
Median
Modus
Dispersion (how they are spread)
Low vs. High
RangeStandard Deviation
Against population
Normal distribution
Kurtosis
Skewness
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Let’s learn and practice• See the file “Statistics-complete.xls”• You will find the data for the variables “gender”
and “competence”• Variable in columns, cases in rows• Variable naming rules (for exporting to SPSS)
Short, explanatory Must be unique No spaces, blanks, or !,?, ‘, and * Must begin with a letter, followed by either a letter,
any digit, a full stop or symbols @, #, _ or $ Cannot end with a full stop or underscore Are not case sensitive
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Using Formula in MS Excel• Go to Tab “Formula”
Click the icon fx “Insert Function”
• Go to fx bar Click the icon fx, choose
from the dropdown menu
• Type “=“ at the formula bar, followed by the formula a pop-up text will guide
you on how the string of the formula should be)
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How do you describe data? By Itself• Frequency – how many? How often?
A.k.a. tallies, To count up the number of things or people in different categories
• Raw frequencies COUNT – the number of cases (e.g. how many
cases) COUNTIF – the number of cases based on
certain conditions (e.g. how many males/females)
SUM – the total of certain numbers (e.g. combining 2 variables)
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How do you describe data? By Itself• Group Sum/Percentage – how big?
Raw frequencies can be converted into percentages
Graphical display of data (a.k.a. pie charts) Other ways to display data (histogram,
line)
• How? Group the data – using COUNTIF Insert Chart – using Tab “Insert” |
“Column” or “Pie”
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How do you describe your data? Against each other• Central Tendency – how are they
placed among each other? The tendency of a set of numbers to
cluster around a particular value (Brown)
What are they?• Mean• Mode• Median
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How do you describe your data? Against each other
MeanA.k.a. averageSum of all values in a distribution divided by
the number of valuesAVERAGE
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How do you describe your data? Against each other
Mode• Frequently occurring values in a set of
numbers• MODE
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How do you describe your data? Against each other
Median• The middle value• The data needs to be sorted from smallest to
highest• MEDIAN
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How do you describe your data? Against each other• Dispersion
To what extent the individual values vary away from the central tendency
What are they?• Low-High• Range• Standard Deviation
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How do you describe your data? Against each other
Low-High• The lowest and the highest values• MIN, MAX
Range• The highest – the lowest + 1• Input the MIN and MAX and calculate
Standard Deviation• To what extent a set of scores varies in
relation to the mean• STDEV
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How do you describe your data? Against the population Normal Distribution – how representative
are they? A.k.a. Bell Curve How the values usually disperse in real
population
SDs -3 -2 -1 M 1 2 3
2.14% 13.59% 34.13% 34.13% 13.59% 2.14%
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How do you describe your data? Against the population
Kurtosis• How peaked or flat the curve• The more positive, the more peaked
Skewness• A few values are much larger or smaller than
the typical values found in the data set• Negative vs. positive
NP
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Checking Normality in MS Excel• Create a BIN (percentile
of your data)• Sort your data from the
lowest to the highest• Create the case number
(nth data) 81 is 20th data
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Using Normality Percentage1. Remember the percentage
of normality cumulative percentage• 2.14% lowest 2.14%• 13. 59% low 15.73%
(2.14 + 13.59)• 68.26% mid 83.99%
(2.14 + 13.59 + 68.26)• 13.59% high 97.58%• 2.14% highest 100%
2. Convert the data to meet the percentage of normality (e.g. the data in the file is 20, so 20 is 100%, 19.516 is 97.58%, and so on).
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Using Normality Percentage3. Identify the bin
numbers (cut points) E.g. 100% is 20th data
case in the file 81 97.58% is the approx.
19th data case 794. Decide how many times
the data occur within the bin numbers [FREQUENCY] 46-47 pts = 1 time, 46-52 pts= 2 times, and so on; the final one 81 should be 20 times
5. Decide the number of the data under 47 is 1 score, 47-52 is 2 scores, and so on.
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Using Mean (Average) & Standard Deviation1. Remember the
calculation for normality using average +/- standard deviation (-3 to 3)
2. Calculate the normality data for deciding bin numbers using the formula: M +/- (3*SD) M +/- (2*SD) M+ /- (1*SD)
• Follow Step. 4 & 5 in using normality percentage
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Generating the histogram1. Select the data in the ‘number of
data’2. Click in the Menu Bar – Insert |
Column | 2D-Column3. To make the histogram clearer,
click the whole histogram, right click ‘Select Data’• In ‘Horizontal (Category) Axis
Labels, click ‘Edit’• In ‘Axis Label Range’ bar,
select the bin numbers, then ‘OK’ and ‘OK’
4. To add the trendline, select the bar (yellow or green), click ‘Add Trendline’• In ‘Trendline Options’, select
‘polynomial’ and adjust the order (1/2/3/4) until it shows normality line
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Too complicated? Let’s try the smart way
• Activate Add-ins for Statistical Procedures
1
2
3
4
56
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Smart Way…• Once activated, you should have
something like this in your Menu:
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How to do descriptive Statistic?• Menu | Data Analysis | Descriptive
Statistics• Select the data range that you want
as an Input Range• Select the output range• Tick Summary Statistics• Voila!
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Inferential
Statistics