Research Statistics Objective: Students will acquire knowledge related to research Statistics in order to identify how they are used to develop research conclusions. Drill: Reading Quiz today! I hope you have your Cornell Notes up to date as the quiz will cover notes you have taken to date from readings due from the beginning of the unit to today.

The challenger Explosion

Review from last class What is a correlation? What does it do? What is an experiment? How is it different from a correlation?

Descriptive Statistics Used to describe or summarize sets of data from all Inferential Statistics Used to make generalizations about the populations from which the samples were drawn.

Correlation Coefficient Correlation Coefficient: Statistic ranging from –1.00 to +1.00; the sign indicates the direction and strength of the relationship Closer the statistic is to –1.00 or to +1.00, the stronger the relationship Correlation of 0.00 demonstrates no relationship between the variables Positive Correlation: Increases in one variable are matched by increases in the other variable Negative Correlation: Increases in one variable are matched by decreases in the other variable Correlation does not demonstrate causation: Just because two variables are related does NOT mean that one variable causes the other to occur Example: +.82 correlation between general intelligence scores and SAT scores in a national sample. What does this mean? Table of Contents Exit

Correlation Scatterplot: Often used to plot correlations

Fig. 1.7 The correlation coefficient tells how strongly two measures are related. These graphs show a range of relationships between two measures, A and B. If a correlation is negative, increases in one measure are associated with decreases in the other. (As B gets larger, A gets smaller.) In a positive correlation, increases in one measure are associated with increases in the other. (As B gets larger, A gets larger.) The center-left graph (“medium negative relationship”) might result from comparing anxiety level (B) with test scores (A): Higher anxiety is associated with lower scores. The center graph (“no relationship”) would result from plotting a person’s shoe size (B) and his or her IQ (A). The center-right graph (“medium positive relationship”) could be a plot of grades in high school (B) and grades in college (A) for a group of students: Higher grades in high school are associated with higher grades in college.

Illusory Correlation Illusory Correlation the perception of a relationship where none exists Illusory Correlation

Correlation Coefficient Researchers have discovered that individuals with lower income levels report having fewer hours of total sleep. Therefore, Income and sleep levels are positively correlated Income and sleep levels are negatively correlated Income and sleep levels are inversely correlated Income and sleep levels are not correlated Lower income levels cause individuals to have fewer hours of sleep

Correlation Coefficient Which of the following correlation coefficients represents the strongest relationship between two variables? +.30 +.75 +1.3 -.85 -1.2

Measures of Central Tendency Chapter 1: Introduction to Psychology Measures of Central Tendency Mean - the arithmetic average Median - the center score Mode - the score that occurs the most

Histograms and Polygons help you to visually see the mode, median and mean. X axis= independent variable Y axis= dependent variable What can we learn from the chart below? What do you think scores were like for students in the graph below? Histogram Bimodal Test Scores Polygon

Measures of Variability Chapter 1: Introduction to Psychology Measures of Variability Range - the difference between the highest and lowest score Variance- The degree to which a set of values varies from the mean of the set of values. Standard deviation - reflects the average distance between every score and the mean

Standard Deviation How to calculate standard deviation 1. Collect your data. Example- a set of test scores (55,64,78, 82 and 95) 2. Determine the mean 3. Subtract the mean from each number; Square each number Add squares together; divide by number of items Take the square root to find standard deviation http://www.howcast.com/videos/259994-how-to-calculate-standard-deviation/

Standard Deviation Which has the larger spread of data? Which has the most “bunching” around the mean? How would this help us understand data?

A Question Who is the more consistent golfer? An individual who has scores that have a lower standard deviation? A golfer who has scores that have a higher standard of deviation?

Standard Deviation For the AP Psych test, you won’t necessarily be calculating standard deviation, but do need to know it’s importance as it relates to analyzing data. For example, with the numbers below, which of the following has the greatest Standard Deviation? 1, 5, 7, 30 5, 10, 12, 18 30, 32, 34, 35 You can estimate this by looking at the spread. Standard Deviation has to do with the degree of variance from the mean.

Normal Distribution: The Bell CURVE

Normal Distribution: Mean is in the middle. Same number of scores above and below the mean. Mean, median and mode fall in the same point for a normal distribution or bell curve.

Standard deviation and IQ: A Normal Distribution/bell curve You do need to know these percentages: 55 70 85 100 115 130 145 2.14% 13.59% 34.13% 0.13% 95.44% 68.26% Wechsler IQ score Number of score 50% fall below the mean 50% fall above the mean 1 SD from the mean= 68.26% 2 SD from the mean = 95.45% 3 SD from the mean = 99.73% 4 SD from the mean = 99.994% 50% fall above the mean in a normal distribution and 50% fall below the mean

Z Score: Measure of how many standard deviations you are away from the mean. T-score: A standard score that sets the mean to fifty and standard deviation to ten. Used on a number of tests including the MMPI

Questions about the SAT Test: What is the median and mode? What percent of the scores are between 300 and 600? What percent of the scores are between 400-600? What percent of the scores are between 500-700 What percent of the scores are between 300 and 700? What percent of the scores are less then 500? If a student scored 700, what would be their z-score?

Sample Question Percy has an IQ that is two standard deviations above the mean. How high is his IQ?

Question Lily scored 145 on an IQ test with a mean of 100 and a standard deviation of 15. What is her Z-score? -3 -1.5 +.67 1.5 +3

Question In a normal distribution, what percentage of the scores in the distribution falls within one standard deviation on either side of the mean? 34% 40% 50% 68% 95%

SKEWED DISTRIBUTION

Statistical Reasoning A Skewed Distribution Why is this distribution skewed? Mode, Median and Mean are not in the same place. Shape of data is not symmetrical. 15 20 25 30 35 40 45 50 90 475 710 70 Mode Median Mean One Family Income per family in thousands of dollars

You may have a negative distribution if a student bombed his test while the majority of the class did well. It effects the mean and the distribution of scores. You may have a positive distribution if you have a student who scored much higher than the rest of the class which effects the mean.

Type of Distribution Emma scores a perfect 100 on a test that everyone else fails. If we were to graph the distribution, it would be: Symmetrical Normal Positively skewed Negatively skewed A straight line

Question Which statistical measure of central tendency is most affected by extreme scores? Mean Median Mode Skew Correlation

Inferential Statistics Allows us to say what worked for the sample population will work for the entire population. They allow us to generalize the results. Example: If meds worked for the sample, we estimate that they will have the same effects on the rest of the population. There is always a chance for error, so the hypothesis and results have to be tested for significance. Statistically Significant: Differences that are unlikely due to chance.

What happens if statistics reveal that your hypothesis is wrong? Null Hypothesis: General statement that there is no relationship between two items. Hypothesis: CHS students are noisy. Null Hypothesis: CHS students are quiet. Conclude your hypothesis (alternate to the null hypothesis) is true If research reveals that data is statistically significant Reject Null Hypothesis