Correlational Research Detects relationships between variables Does NOT

Correlational Research • Detects relationships between variables. • Does NOT say that one variable causes another. There is a positive correlation between ice cream and shark attacks. Does that mean that ice cream causes shark attacks?

Measured using a correlation coefficient. • A statistical measure of the extent to which two factors relate to one another

How to Read a Correlation Coefficient

Which of the following has the strongest relationship? 1) 2) 3) 4) 5) 6) . 5 -. 98 -. 75. 005

Create a Scatterplot with the data: Number of doors a car has 2 3 4 5 6 7 8 Average Driving Speed 73 75 60 55 50 48 45 What kind of correlation exists? Relatively Strong Negative

Scatterplots Perfect positive correlation (+1. 00) Scatterplot is a graph comprised of points that are generated by values of two variables. The slope of the points depicts the direction, while the amount of scatter depicts the strength of the relationship.

Correlational Research • Correlation is the relationship between two variables. • Positive correlation – both values increase • Negative correlation – One variable increases, while the other decreases. • Correlational Coefficient – strength of the relationship 0= no relationship +1 or – 1 = perfect relationship Examples: SAT scores and success in college; Red wine and heart attacks; Prejudice and age; length of marriage and hair loss, etc.

Scatterplots Perfect negative correlation (-1. 00) No relationship (0. 00) The Scatterplot on the left shows a negative correlation, while the on the right shows no relationship between the two variables.

Scatterplot The Scatterplot below shows the relationship between height and temperament in people. There is a moderate positive correlation of +0. 63.

Illusory Correlation The perception of a relationship where no relationship actually exists. Parents conceive children after adoption. Do not conceive Adopt Confirming evidence Disconfirming evidence Do not adopt Disconfirming evidence Confirming evidence Michael Newman Jr. / Photo Edit Conceive

Confounding Variables • Length of a marriage has a positive correlation with hair loss in men. • Does marriage cause hair loss? • Do balding men make better husbands? • Does another factor underline this correlation?

Correlation and Causation or

Which of the following would prove his prediction? 1) 2) 3) 4) 5) 6) . 5 -. 05. 80 -. 68. 51. 005

Think of a confounding variable + Correlation btw. Men with nice cars and wealth. Conclusion: having a nice car makes you wealthy + Correlation btw. wearing bifocals and cancer. Conclusion: wearing bifocals may lead to cancer - Correlation btw. hours spent at the tutoring center and scores on college exams. • Conclusion: Studying is bad for exam scores • • •

Illusory Correlation The perception of a relationship where no relationship actually exists. Parents conceive children after adoption. Do not conceive Adopt Confirming evidence Disconfirming evidence Do not adopt Disconfirming evidence Confirming evidence Michael Newman Jr. / Photo Edit Conceive

Coach Z thinks there is a relationship between the average height of his girls varsity basketball team and the number of wins they have each season. • What kind of correlation does he believe exists? • What are two things coach Z could do to investigate this relationship?

Correlation between avg. height of a girls basketball team and wins 21 Wins 18 15 12 9 6 3 65 67 69 71 Avg. Height 73

• • • Which of the following is this probably a scatterplot for? A) GPA and days at School B) Height and Weight C) Self Esteem and Depressive Moods D) Weight and Reading Level

STATS • The average person has one ovary and one testicle!

Measures of Central Tendency • Single score that represents a whole set of scores • Mode • Mean • Median

Mode • Simplest • Most frequently occurring score in a data set • 40, 67, 72, 76, 83, 83, 88, 93, 98 • What is the Mode? 83

When the Mode does not tell the whole story Midterm Scores: 55, 81, 85, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100 How does the mode misrepresent our data?

Mean • Most reported measure of central tendency • The average of a data set – Total sum of all of the scores/divided by the number of scores Mean is most accurate when there is least variation (range).

Good/Bad Tips for the night 10, 5, 10, 20, 5 Mean = 10 Income 100, 000, 60, 000, 75, 000, 80, 000, 8, 000. Mean = 1, 663, 000

Skewness One or a few extremely low scores pull the mean below the median. One or a few extremely high scores pull the mean below the median.

A Skewed Distribution Are the results positively or negatively skewed?

Median The midpoint or 50 th percentile Arrange all data from highest to lowest Find Center- Average if given an even number of data sets Incomes: 84, 000, 100, 000, 60, 000, 75, 000, 80, 000, 8, 000.

Seven members of a boys' club reported the following individual earnings from their sale of cookies: $2, $9, $8, $10, $4, $9, and $7. In this distribution of individual earnings? A) B) C) D) E) the median is greater than the mean and greater than the mode. the median is less than the mean and less than the mode. the median is greater than the mean and less than the mode. the median is less than the mean and greater than the mode. the median is equal to the mean and equal to the mode.

Measures of Variation Range and Standard Deviation

Measures of Variation Range- the gap between the lowest and highest scores

The standard deviation is kind of the "mean of the mean, " and often can help you find the story behind the data. Tells you how likely the scores will look like the mean.

M: 7. 1 SD: . 5 M: 5. 1 SD: 1. 2 M: 4. 2 SD: . 8 M: 4 SD: 1. 6 ? M: 3. 6 SD: 1. 98 M: 3. 5 SD: 1. 6 M: 2. 5 SD: . 5 M: 2. 1 SD: 2. 0

Standard Deviation Which of the following data sets would have the highest and lowest standard deviation? 1. 2. 3. 4. 15, 16, 12, 14, 15, 17. 25, 1. 5, . 5 7, 20, 4, 20, 0, 5 1, 500, 42, 0, 0, 150

Agenda • Hand in Psych. Sim (please put in folder) • Statistical Significance – What is it? why is it important? • The Normal Curve and Standard Deviation – Where do we see it? How do we use it? • Stats Practice – Partner practice for quiz. • HW: – Psych. Sim: Desc. Stats – Psych. Port 3 • Quiz tomorrow Module 3

Statistical Significance • A result that is not likely to occur randomly, (by chance) but rather is likely to be attributable to a specific cause is statistically significant. • Can be strong or weak – Strong= the results are probably not due to chance (sampling error) – Weak= the results might be due to chance. • The level at which one can accept whether an event is statistically significant is known as the significance level or p-value.

Standard Deviation- whether scores are packed together or dispersed • When the scores are tightly clustered the standard deviation is small. • When the scores are spread apart there is a relatively large standard deviation.

Variance • Another way to look at the variability of the data • To get the variance: square the standard deviation. So if the standard deviation is 5 the variance is ? .

Standard Deviation To understand this concept, it can help to learn about what statisticians call normal distribution of data. • mean = median = mode • symmetry around the center • 50% of values less than the mean and 50% greater than the mean • Many things closely follow a Normal Distribution: – – – – Heights of people SAT test scores Infant weights size of things produced by machines IQ scores blood pressure Shoe size

But let me show you graphically what a standard deviation represents. . .

One standard deviation (the red area on the above graph) accounts for around 68 percent of the people in this group. Two standard deviations away from the mean (the red and green areas) roughly 95 percent of the people. Three standard deviations (the red, green and blue areas) account for about 99 percent of the people.

Percentiles

But let me show you graphically what a standard deviation represents. . .

Question 1 IQ scores have a mean of 100 and a standard deviation of 15, what percentage of people would score above 85? A) 84% B) 27% C) 75% D) 94% E) 99%

Practice Question 2: In a normal distribution of intelligence test scores with a mean of 100 and a standard deviation of 15 what percentage of people would score above 115? A) B) C) D) E) 95 68 16 84 98

In a normal distribution of intelligence test scores with a mean of 100 and a standard deviation of 15 what percentage would be closest to people that would score below 85? A) B) C) D) E) 95 68 16 84 97

Q 3: In a normal distribution of height in men with a mean of 70 inches and a standard deviation of 2 inches. If Devin is in the 98 percentile, which of the following is closest to his height? A) B) C) D) E) 6’ 0” 6’ 6” 5’ 8” 6’ 2” 5’ 10”

64 66 68 70 72 74 76

Practice Question 3 Amy’s SAT score is in the 99 th percentile. (Remember SAT scores have a mean of 1100 and a standard deviation of 160. Of the following, which score is closest to this? A) 950 B) 1100 C) 1580 D) 1400 E) 1260

. 2% 620 780 940 1100 1260 1420 1580

Computing • Compute the mean for the data set. • Compute the deviation by subtracting the mean from each value. • Square each individual deviation. • Add up the squared deviations. • Divide by one less than the sample size. • Take the square root.

HOW TO? • The standard deviation is a measure of how spread out your data are. Computation of the standard deviation is a bit tedious. The steps are: • Compute the mean for the data set. • Compute the deviation by subtracting the mean from each value. • Square each individual deviation. • Add up the squared deviations. • Divide by one less than the sample size. • Take the square root.

Question 1 In a normal distribution of scores with a mean of 82 and a standard deviation of 7, what percentage of people would score above 75? A) 84% B) 27% C) 75% D) 98% E) 99%

. 2% 55 70 85 100 115 130 145

But let me show you graphically what a standard deviation represents. . .

. 2% 64 66 68 70 72 74 76

. 2% 620 780 940 1100 1260 1420 1580

Practice Questions Amy’s SAT score is in the 99 th percentile. (Remember SAT scores have a mean of 1100 and a standard deviation of 160. Of the following, which score is closest to this? A) 950 B) 1100 C) 1580 D) 1400 E) 1260