How Psychologists Ask and Answer Questions Statistics Unit 2 – pg

What you need to know by the end of these notes: Distinguish the purposes of descriptive statistics and inferential statistics. Discuss the value of reliance on operational definitions and measurement in behavioral research.

Statistical Reasoning Statistical procedures analyze and interpret data and let us see what the unaided eye misses. Composition of ethnicity in urban locales

Describing Data Meaningful description of data is important in research. Misrepresentation can lead to incorrect conclusions.

Measures of Central Tendency Mean: The arithmetic average of scores in a distribution obtained by adding the scores and then dividing by their number. Median: The middle score in a rank-ordered distribution Mode: The most frequently occurring score in a distribution.

Measures of Variation Range: The difference between the highest and lowest scores in a distribution. Standard Deviation: average difference between each score and the mean Large SD = more spread out scores are from mean Small SD = more scores bunch together around the mean OBJECTIVE 3-14| Explain two measures of variation.

Calculating Standard Deviation Put scores in descending order (x) Find mean of scores (x) Subtract mean from every score ( x-x) Square the answer of #3 for each score (x-x)2 Calculate standard deviation…SD                                                                             SD = standard deviation SD = √∑ (x-x)2                ∑ = sum of           x = scores             n – 1                  x = mean              n = # of scores

Calculating Standard Deviation SCORES… 8, 7, 8, 5, 3, 6, 4, 8, 6, 5 SD = √∑ (x-x)2             n – 1 X X X X (X - X) (X - X) (X - X)2 (X - X)2 8 6 2 4 8 6 2 4 SD = √∑ (28)             10 – 1 8 6 2 4 7 6 1 1 6 6 SD = √ 28               9 6 6 5 6 -1 1 5 6 -1 1 SD = √ 3.11 4 6 -2 4 SD = 1.76 3 6 -3 9

Calculating Standard Deviation

Standard Deviation Often you will not be asked to actually calculate SD, but apply what you know of the concept For example…which of the following sets of data have the GREATEST SD? 1, 5, 7, 30 5, 10, 12, 18 30, 32, 34, 35 How do you figure this out???? Can estimate SD by looking at “spread” of #s Can find mean and compare each # to the mean

Standard Deviation Normal distribution = a distribution of scores that produces a bell-shaped symmetrical curve In this ‘normal curve” the mean, median and mode fall at exactly the same point The span of ONE SD on either side of the mean covers approximately 68.2% of the scores in a normal distribution OBJECTIVE 3-1 Average IQ = 100 Most (68.2%) people fall into 85-115 range IQ extremes are above 130 and below 70

Normal Curve  50 % 50 %  1 SD from the mean = 68.27 %

Measures of Central Tendency A Skewed Distribution Why is this distribution skewed? How would it change if you removed the families that made 90, 475 and 710?

Skewed Distributions ?? Negative vs. Positive Majority of scores above the mean…one or a few extremely LOW scores cause the mean to be less than the median score Majority of scores below mean…one or a few extremely HIGH scores cause mean to be greater than median score

Inferential Statistics involves estimating what is happening in a sample population for the purpose of making decisions about that population’s characteristics (based in probability theory) Basically, inferential statistics allow us to say…”if it worked for this population, we can estimate that it will work with the rest of the population” i.e. drug testing – if the meds worked for the sample, we estimate they will have the same effects on the rest of the population There is always a chance for error in whatever the findings may be, so the hypothesis and results must be tested for significance

Inferential Statistics Null Hypothesis – states that there is NO difference between two sets of data Purpose of null hypothesis… until the research SHOWS (by proving the original/alternative hypothesis) that there is a difference, the researcher must assume that any difference present is due to chance

Null Hypothesis Truth About Population NULL TRUE NULL FALSE REJECT NULL (accept original) Type I Error Correct decision Decision Researcher Makes ACCEPT NULL Correct decision Type II Error Type I Error: Reject the null (choosing the original hypothesis), yet the null is actually true Type II Error: Accept the null, yet the original hypothesis is actually correct

Null Hypothesis Original hypothesis - “A bomb threat was called into the front office, so we need to evacuate the school.” Null Hypothesis – “There is no bomb in the school, so we do not need to evacuate.” Truth About Population NULL TRUE NULL FALSE REJECT NULL Decision Researcher Makes ACCEPT NULL

Null Hypothesis Original hypothesis - “A bomb threat was called into the front office, so we need to evacuate the school.” Null Hypothesis – “There is no bomb in the school, so we do not need to evacuate.” Truth About Population NULL TRUE NULL FALSE REJECT NULL Type I Error Students evacuated, yet bomb squad does not find a bomb Erred on the side of caution Correct decision Students evacuated, bomb squad finds bomb & safely removes it…all are safe Decision Researcher Makes ACCEPT NULL Correct decision no evacuation, no bomb threat ignored, students stay in class & all are safe Type II Error Bomb threat is ignored, students stay in class, bomb goes off & students injured

Inferential Statistics