Evaluating Data in Research

Joey finished at the 74 th percentile on his EOC Algebra test.  74 th percentile means  Above 74% of test takers  Actual #75, there is no 100 th percentile

 We look for……..

 A measure of central tendency is a single score that represents a whole set of scores.  Mean –  Average  most easily skewed by outliers (extreme numbers)  Median  Middle value (midpoint, or 50 th percentile)  (Place in sequential order and find middle number)  Mode  Most frequently occurring score

Statistical Reasoning  A Skewed Distribution Mode Median Mean One Family Income per family in thousands of dollars

HISTOGRAM HISTOGRAM : a bar graph depicting a frequency distribution, where the height of the bars indicates the frequency of a group of scores Calculate the Mean

MEAN Calculate the Median

MEAN MEDIAN Calculate the Mode

MEAN MEDIAN MODE

MEAN Measures of variability RANGE RANGE : difference between the highest and lowest scores (can be deceptive due to outliers) 111

MEAN measures of variability STANDARD DEVIATION STANDARD DEVIATION : how much any given score differs from the average, or mean score -1 sd +1 sd

MEAN STANDARD DEVIATION The more spread out the scores, the larger the STANDARD DEVIATION. -1 sd +1 sd

 How much does the data deviate from the mean?  Uses bell curve distribution  For ex: IQ – average =100  1sd +15 (85 – 115) = 68% of the pop.  2sd +30 (70 – 130 = 95% of the pop.

The equation for standard deviation is: (You won’t have to know this….) SD = Σ (score - mean) 2 number of scores

Bell Curve A graph of normal distribution  1 SD = 68% of scores  2 SD = 95% of scores  3 SD = 99.7% of scores

Weighing the odds…  2 High School punters  Kicker A:  mean distance: 39.8 yds  Standard deviation: + 14 yds.  Kicker B:  mean distance: 34.5 yds.  Standard deviation: + 4 yds.  Which player do you play? Player B – team will know where to run

 Z score  number that represents how many SD’s a particular score differs from the mean  The mean score for the class was 80, with a SD of 10.  Joey scored 60 on his test. What’s his z score?  Betsy scored a 95. what is her z score?

1. Representative samples are better than biased samples. 2. Less-variable observations are more reliable than those that are more variable. 3. More cases are better than fewer.

When is a study’s data significant?  When there is a significant difference between the results (data) for the control group and experimental group.  When the data is reliable (consistent)

 1. What is the mean of the following distribution of scores: 2, 3, 7, 6, 1, 4, 9, 5, 8, 2? A. 5 B. 4 C. 4.7 D. 3.7 E. 6 Answer: c

2. What is the median of the following distribution of scores: 1, 3, 7, 7, 2, 8, 4? a. 1 b. 2 c. 3 d. 4 Answer: d

3. What is the mode of the following distribution: 8, 2, 1, 1, 3, 7, 6, 2, 0, 2? a. 1 b. 2 c. 3 d. 7 Answer: b

4. Seven members of a Girl Scout troop report the following individual earnings from their sale of candy: $4, $1, $7, $6, $8, $2, and $7. In this distribution of individual earnings: a. The mean is equal to the mode and equal to the median b. The mean is less than the mode and equal to the median c. The mean is equal to the mode and greater than the median d. The mean is greater than the mode and greater than the median e. The mean is less than the mode and less than the median Mean=5, median=6, mode=7 Answer=e

Ethics in Research APA Ethical Guidelines –Informed Consent –No harm to patients –Confidentiality –Debriefing

Animal Testing Statistics to consider… Statistics to consider… 30,000,000 animals used for research each year constitutes 1% of animals killed each year to eat. 30,000,000 animals used for research each year constitutes 1% of animals killed each year to eat. 200,000 dogs and cats researched annually / animal shelters euthanize 50x that each year 200,000 dogs and cats researched annually / animal shelters euthanize 50x that each year Is it morally acceptable to place the well- being of humans above other animals regarding research?