chapter 10 javastat.html
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TRANSCRIPT
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Chapter 10
http://members.aol.com/johnp71/javastat.html
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Goal
Not only to be able to analyze your own data but to understand the literature that you read.
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Data Analysis
StatisticsParameter
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Reporting your Results
With words….With numbers….With Charts/Graphs…
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Data
CategoricalQuantitative
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Quantitative
In this chapter:CorrelationFrequency
distributionsMeasures of Central Tendency
MeanVariability
Standard deviation
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Distributions
Skewed Distributions Positive – scores trailing to the
right with a majority at the lower end
Negative – scores trailing to the left
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Curve “Skewness”
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Distributions
Normal Large majority of scores in the
middle Symmetrical Bell-shaped Mean, median, and mode are
identical
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Measures of Central Tendency
Mode Median
Point at which 50% of scores fall above and below
Not necessarily one of the actual scores in the distribution
Most appropriate if you have skewed data
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Measures of Central Tendency
Mean Uses all scores in a distribution Influenced by extreme scores Mean = sum of scores divided by
the number of scores
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Variability
Range Low to High Quick and dirty estimate of
variabilityStandard Deviation
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Standard Deviation
1. Calculate the mean2. Subtract the mean from each
score3. Square each of the scores4. Add up all the squares5. Divide by the total number of
scores = variance6. Take the square root of the
variance.
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Standard Deviation
The more spread out the scores the larger the standard deviation.
If the distribution is normal then the mean + two standard deviations will encompass about 95% of the scores. (+ three SD = 99% of scores)
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Normal Curve: By Standard Deviation
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% of Scores in 1 SD
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2 Standard deviations?
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What can you tell me about these groups?
Group A30 subjectsMean = 25SD = 5Median = 23Mode = 24
Group B30 subjectsMean = 25SD = 10Median = 18Mode= 13
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Calculate the Standard Deviation and Average
Use your text (p. 207-208)
Check your scores with this link.
Scores:12, 10, 6, 15,
17, 20, 16, 11, 10, 16, 22, 17, 15, 8
Mean = ??SD = ??
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Excel
Now go to the following web page and click on “class data”: assignments
Calculate mean, median, mode, SD for the ACT and Writing column data.
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Standard Scores
A method in which to compare scores Z scores – expressed as deviation
scores Example:
Test 1= 80Test 2 = 75
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Example
Test 1: mean = 85, SD = 5Test 2: mean = 65, SD = 10
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Probability
We can think of the percentages associated with a normal curve as probabilities.
Stated in a decimal form.If something occurs 80% of the
time it has a probability of .80.
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Example
We said that 34% of the scores (in a normal distribution) lie between the mean and 1SD.
Since 50% of the scores fall above the mean then about 16% of the scores lie above 1SD
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Example
The probability of randomly selecting an individual who has a score at least 1SD above the mean?
P=.16Chances are 16 out of 100.
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Example
Probability of selecting a person that is between the mean and
–2SD?
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Z-Scores
For any z score we know the probability
Appendix B
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Z-Scores
Can also be calculated for non-normal distributions.
However, cannot get probabilities values if non-normal.
If have chosen a sample randomly many distributions do approximate a normal curve.
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Determining Relationships Between Scores
Correlation
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Relationships
We can’t assign blame or cause & effect, rather how one variable influences another.
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Correlation
Helpful to use scatterplots
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Plotting the relationship between two variables
Age = 11 Broad Jump = 5.0 feet
Age
Feet
5
11
5.0
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Plot some more (Age & Broad Jump)
Age
Feet
Do you see a relationship??
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Outliers
Differ by large amounts from the other scores
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Correlation….
Is a mathematical technique for quantifying the amount of relationship between two variables
Karl Pearson developed a formula known as “Pearson product-moment correlation”
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Correlation
Show direction (of relationship)Show strength (of relationship)Range of values is 0 - 1.0
(strength)0 = no relationship1 = perfect relationshipValues may be + or - (direction)
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Correlation
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Correlation Strength
Very Strong .90 - 1.0
Strong .80 - .89
Moderate .50 - .79
Weak < .50
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Types of relationships
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Test Your Skill
Guess the Correlation
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Quick Assignment
For the same excel spreadsheet that we opened earlier calculate a correlation coefficient for the ACT vs. Tricep.
Make a scatterplot of tricep vs. ACT.
Scatterplot and correlation for ACT vs. Writing
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Coefficient of Determination
Determines the amount of variability in a measure that is influenced by another measure
I.e. how much does the broad jump vary due to varied ages?
Calculated as r2 (Corr. Squared)
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Example:
Say that strength and 40yard sprint time have an r = .60
How much does a variation in strength contribute to the variation in sprint speed?
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Summarizing Data
Frequency TableBar Graphs/Pie ChartsCrossbreak Table
A graphic way to report a relationship between two or more categorical variables.
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Assignment
Under assignments on my web page there is an excel spreadsheet published entitled “assignment 1”.
Download the spreadsheet by clicking here assignments
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Assignment
1. Calculate the mean, mode, and median for body density, ACT Score, and Reading Score on sheet 1
2. Calculate the mean and SD for TC, Trig, HDL, and LDL on sheet 2
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Assignment
3. Calculate a correlation coefficient for body density and age, ACT and Reading Scores, TC and LDL, and Trig and HDL
4. Make a scatterplot for HDL and Trig as well as LDL and Total
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Assignment
5. Make a bar graph for the mean Total, Trig, LDL, HDL values.