Unformatted text preview: Experimental Design & Describing Data
Lecture 2 Overview Experimental Design Summarizing Data Graphing & Frequency Distributions Measures of Central Tendency Measures of Variability (spread) Experimental Design Experimental Design involves how we get our data and the kinds of interpretation we can make about our data. Three Designs Experimental Observational (correlational) Quasiexperimental A study that manipulates one or more specific variable(s), and examines the outcome of the manipulation. A study that examines how "things" are related, but nothing is manipulated. An experiment done in a natural setting. Types of Variables Independent Variable (IV) Dependent Variable (DV) Extraneous Variables The variable you manipulate in an experiment, or use to make a prediction in an observational study Outcome you are measuring Variables other than the IV that may affect the DV What are the IV and DV?
A researcher asks 120 students to come into her lab and take the Big Five Inventory, which measures personality traits such as conscientiousness and extraversion. She also asks them for their GPA. She wants to know whether students who are high in conscientiousness get better grades than students who are low in conscientiousness. Levels of the IV Sometimes called "treatments" One value of the IV Example: A drug treatment Group 1 gets 0 mg of the drug Group 2 gets 10 mg of the drug Group 3 gets 20 mg of the drug Three levels of the IV What are the levels of the IV?
A researcher asks 120 students to come into her lab and take the Big Five Inventory, which measures personality traits such as conscientiousness and extraversion. She also asks them for their GPA. She wants to know whether students who are high in conscientiousness get better grades than students who are low in conscientiousness. Putting it together Example 1: IV = Preparation level for the SAT Levels of the IV = 2 DV = Score on the SAT Took a prep class Did not take a prep class Experimental, Observational, or Quasi observational design? Example 2 IV = Type of Stove Levels = 2 DV = Tastiness of cookies Gas Electric Identify the IV, DV, & Levels Cortisol is often used as a marker of stress. Peggy wants to study how watching films affects cortisol. In an experiment, she has one group watch a nature show, one group watch a violent film, and one watch a humorous film. Then she measures their cortisol level. Identify the IV, DV, & Levels Fred studies eyewitness testimony. In an experiment, participants watch a video of a crime. Fred then shows them a set of mugshots, one of which is the criminal. In one group, some of the other pictures look similar to the criminal. In the other group, the other pictures look very different from the criminal. Fred measures how many people correctly identify the criminal. Identify the IV, DV, & Levels Jean predicts that younger persons feel more entitled than older persons. She gives a group of teenagers, college students, middleaged adults, and elderly persons a survey that measures how entitled they feel. Age Describing Data Frequency Distributions Graphing Measures of Central Tendency Frequency Distributions Raw Scores Frequency Scores obtained from the experiment or data collection How often each score occurs Beck Depression Inventory
21 item scale, each item on a 02 scale 0 09 The person is not depressed 10 18 Mild to moderate depression 19 29 Moderate to severe depression 30 63 Severe depression 5 12 7 8 8 20 29 20 21 10 12 4 13 8 34 2 8 11 62 10 11 33 10 8 6 5 7 6 24 6 Simple Frequency Distribution
Scores arranged from highest to lowest and recording how often each score is observed Score 2 4 5 6 7 8 Freq 1 1 2 3 2 5 Score 10 11 12 13 20 21 Freq 3 2 2 1 2 1 Score 24 29 33 34 62 Freq 1 1 1 1 1 Grouped Frequency Distribution
Compilation of scored into equal sized ranges (class intervals) plus frequencies within each interval
BDI Scores (class interval) Below 5 59 1014 1519 2024 2529 3034 Above 34 2 12 8 0 4 1 1 2 Graphing Frequency Distributions
BDI Score Frequencies
6 5 Frequency 4 3 2 1 0 2 4 5 6 7 8 10 11 12 13 20 21 24 29 33 34 62 Score Graphing Frequency Distributions 15 9 7 9 6 Create a simple frequency distribution of the following:
17 3 19 8 4 4 8 7 6 16 13 4 5 7 11 13 8 19 9 7 Create a simple frequency distribution
3 4 5 6 7 8 9 11 13 15 16 17 19 1 3 1 2 4 3 3 1 2 1 1 1 2 Measures of Central Tendency Mean Median Mode "the average" the value after adding up all the values in the distribution and dividing by the total number of values. "the middle" the number that cuts distribution in half "the most" the number that occurs most frequency in the distribution Mean (average) Add up all of the values and divide by the total number of values To get the mean: 1. Add up all values 2. Divide by the total number of scores Median (middle) The middle number cuts the scores in half (50th percentile) To get the Median: 1. Order the scores from lowest to highest or highest to lowest. 2. Use the formula. This tells you the position 3. Find the sore that lies at this position. Mode (most) The number that is repeated in the distribution the most times To get the Mode: 1. Create a simple frequency distribution of the raw scores. 2. See which value (or values) is highest Properties of the Mean The sum of the deviations around the mean is always zero
1 2 3 4 5 3 3 3 3 3 2 1 0 1 2 =0 The sum of the squared deviations around the mean is always minimized
1 2 3 4 5 3 3 3 3 3 2 1 0 1 2 22 = 4 12 = 1 02 = 0 12 = 1 22 = 4 Xbar = 3 Xbar = 3 =0 = 10 Properties of Median & Mode Medain Mode Less sensitive to changes in outliers and skew than the mean (use with ratio, ordinal, or interval data) Completely resistant to outliers and skew (use with ratio, ordinal, interval, or nominal) Which would you use? IQ scores Types of dogs performing in a dog show Income, where most people in the sample make between $10,000 and $50,000, and 1 person makes over $500,000 annually Happiness scores, on a 15 interval scale Finding the Mean, Median, & Mode in Normal & Skewed Distributions Mean Medi an Mode Mean Mode Median Mode Mean Median Find the Mean, Median, & Mode
15 9 7 9 6 17 3 19 8 4 4 8 7 6 16 13 4 5 7 11 13 8 19 9 7 Find the Mean, Median, & Mode
25 9.36 8 7 N Mean Median Mode Variability (spread) The "farapartness" of the scores in a distribution Are they tightly bunched together? Or scattered all over? Range & Interquartile Range Range Highest score minus the lowest score Interquartile Range (IQR) Range of scores that captures the middle 50% of the data Percentile Score Point at which a 75th percentile minus the 25th percentile specified percentage of the distribution falls below this score Range
Subtract the lowest (minimum) value from the highest (maximum) value Interquartile Range Interquartile Range
Q1 = (N+1)*.25 Q3 = (N+1)*.75
Interquartile range =
To calculate the Interquartile range: 1. Order the scores from lowest to highest or highest to lowest (like you did to find the median). 2. Use the formulas to find Q1 and Q3. These tell you the position of each. 3. Find the score that lies at these positions. 4. Subtract the Q1 score from the Q3 score. Q3 score Q1 score 15 9 7 9 6 Find the Min, Max, Range, Interquartile Range
17 3 19 8 4 4 8 7 6 16 13 4 5 7 11 13 8 19 9 7 Find the Min, Max, Range, Interquartile Range
Min Max Range Q1 value Q3 value IQ range 3 19 16 6 (6.5 between 6 and 7th position) 13 (19.5 between 19 & 20th position) 7 Variance A statistical term referring to the average of the squared distances between the observed scores and the mean of the observed scores. Population Sample Calculating Variance Standard Deviation The square root of the variance Most common metric for measuring spread Population Sample Calculating Standard Deviation 15 9 7 9 6 Calculate the Variance and the Standard Deviation (both ways)
17 3 19 8 4 4 8 7 6 16 13 4 5 7 11 13 8 19 9 7 Results Mean = 9.36 2 = 21.83, s2 = 22.74 = 4.67, s = 4.77 Next Time Graphing Data ZScores Effect Sizes Other Descriptive Statistics ...
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 Spring '10
 Ryne
 Standard Deviation, Interquartile range, simple frequency distribution

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