Chapter 10

http://members.aol.com/johnp71/javastat.html

Goal

Not only to be able to analyze your own data but to understand the literature that you read.

Data Analysis

StatisticsParameter

Reporting your Results

With words….With numbers….With Charts/Graphs…

Data

CategoricalQuantitative

Quantitative

In this chapter:CorrelationFrequency

distributionsMeasures of Central Tendency

MeanVariability

Standard deviation

Distributions

Skewed Distributions Positive – scores trailing to the

right with a majority at the lower end

Negative – scores trailing to the left

Curve “Skewness”

Distributions

Normal Large majority of scores in the

middle Symmetrical Bell-shaped Mean, median, and mode are

identical

Types of Curves...

The Normal Curve:

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

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

Variability

Range Low to High Quick and dirty estimate of

variabilityStandard Deviation

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.

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)

Normal Curve: By Standard Deviation

% of Scores in 1 SD

2 Standard deviations?

What can you tell me about these groups?

Group A30 subjectsMean = 25SD = 5Median = 23Mode = 24

Group B30 subjectsMean = 25SD = 10Median = 18Mode= 13

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 = ??

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.

Standard Scores

A method in which to compare scores Z scores – expressed as deviation

scores Example:

Test 1= 80Test 2 = 75

Example

Test 1: mean = 85, SD = 5Test 2: mean = 65, SD = 10

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.

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

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.

Example

Probability of selecting a person that is between the mean and

–2SD?

Z-Scores

For any z score we know the probability

Appendix B

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.

Determining Relationships Between Scores

Correlation

Relationships

We can’t assign blame or cause & effect, rather how one variable influences another.

Correlation

Helpful to use scatterplots

Plotting the relationship between two variables

Age = 11 Broad Jump = 5.0 feet

Age

Feet

5

11

5.0

Plot some more (Age & Broad Jump)

Age

Feet

Do you see a relationship??

Outliers

Differ by large amounts from the other scores

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”

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)

Correlation

Correlation Strength

Very Strong .90 - 1.0

Strong .80 - .89

Moderate .50 - .79

Weak < .50

Types of relationships

Test Your Skill

Guess the Correlation

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

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)

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?

Summarizing Data

Frequency TableBar Graphs/Pie ChartsCrossbreak Table

A graphic way to report a relationship between two or more categorical variables.

Assignment

Under assignments on my web page there is an excel spreadsheet published entitled “assignment 1”.

Download the spreadsheet by clicking here assignments

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

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

Assignment

5. Make a bar graph for the mean Total, Trig, LDL, HDL values.