Psychology Unit 1.6 - Research Methods - Statistics

How do psychologists ask & answer questions How do psychologists ask & answer questions? Last time we asked that we were discussing ‘Research Methods.’ This time we will look at the data. Stats is all about data.

Distinguish the difference between the purposes of descriptive & inferential statistics. Discuss the value of reliance on operational definitions & measurements in behavioral research. Statistical procedures analyze & interpret data & let us see what the unaided eye is missing.

Meaningful description of data is important in research. Misrepresentation can lead to incorrect interpretation.

Descriptive Statistics Use measures of central tendency: mean, median and mode Use measures of variation: range and standard deviation

Mean, Median, Mode, & Range Mean, median, and mode are three kinds of "averages." The MEAN is the “average” you're used to, where you add up all the numbers and then divide by the number of numbers. The MEDIAN is the “middle” value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. The MODE is the “most” often occurring value. If no number is repeated, then there is no mode for the list. The RANGE is the “difference” between the largest and smallest values.

The mean is the usual average, so: (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15 Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers. Joe DiMaggio was the AL MVP and had a batting avg of .357 in 1941. He also had an amazing 56 game hitting streak that is still a record.

The Mean is the Average. So any baseball player’s mean would equal the number of hits divided by the players at-bats. DiMaggio's 56 game hitting streak was amazing. However, Boston's Ted Williams hit .406 in the same season, no player has had as high an average since. DiMaggio won the American League Most Valuable Player, even though he had a lesser statistical year than Williams. Baseball averages are really just a mean. It is measured by dividing the # of hits over the # of at bats. And sometimes, real life can be “mean” as well!

The median is the middle value, so I'll have to rewrite the list in order: 13, 13, 13, 13, 14, 14, 16, 18, 21 There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number: So the median is = 14

13, 13, 13, 13, 14, 14, 16, 18, 21 The mode is the number that is repeated more often than any other, so the mode= 13 The largest value in the list is 21, and the smallest is 13, so the range is... 21 – 13 = 8. What is the mean? mean = 15 median? median = 14 mode? mode = 13 range? range = 8 In real life, suppose a company is considering expanding into an area and is studying the size of containers that competitors are offering. Would the company be more interested in the mean, the median, or the mode of their containers? Answer: the mode because they want to know what size tends to sell most often.

Is the mean the best indicator of family income???? A Skewed Distribution How are the results “skewed”??? Is the mean the best indicator of family income???? Probably not. That’s because of the outliers - $710,000 is one such example above. So range & standard deviation come into play to help be more of an accurate description of these statistics.

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 the mean. SMALL SD: More scores bunch together around the mean.

How do you calculate Standard Deviation? Good News - you will NEVER have to on a test. However, I want you to understand what it represents, so here you go! Which of the following sets of data have the GREATEST SD? 1, 5, 7, 30 5, 10, 12, 18 30, 32, 34, 35 How did you figure this out???? Can estimate SD by looking at the “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 exactly at 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. Average IQ = 100 Most people (68.2%) fall into 85-115 range IQ extremes are above 130 and below 70

<---50%---> <---50%---> Normal Curve You need to write this in your notes, copy it down, & memorize it. Period. There is no other way to do it. 1 SD from the mean = 68.27% 2 SD from the mean = 95.43% 3 SD from the mean = 99.73% 4 SD from the mean = 99.994%

YouTube: Schallhorn on Standard Deviation

Remember this? Wouldn’t this skew the curve? A Skewed Distribution Remember this? Wouldn’t this skew the curve? Is “mean” the best indicator of family income???? Probably not. That’s because of the outliers - $710,000 is one such example above. So range & standard deviation come into play to help be more of an accurate description of these statistics.

A Skewed Distribution: Negative vs. Positive Skewed to the Left Skewed to the Right - Majority of scores above the mean. One or few extremely LOW scores force the mean to be less than the median score. + Majority of scores below the mean. One or few extremely HIGH scores force the mean to be greater than median score.

A Skewed Distribution How are the results “skewed”???

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 stats allow us to say: “If it worked for this population, we can estimate it will work for the rest of the population.” ie - Drug Testing -- if the meds worked for the sample, we estimate they will have the same effect on the rest of the population. There is always a chance for error in whatever the findings may be, so the hypothesis & results must be tested for significance.

Inferential Statistics Statistical Significance - difference observed between 2 groups is probably NOT due to chance. The difference instead is likely due to a real difference between the samples. Data is “significant” when the likelihood of a difference being due to chance is less than 5 times out of 100. In other words... There is a 95% chance (or greater) likelihood that any difference seen is due to your independent variable shown numerically as p < .05 Important because if research is statistically significant it means that the results are probably not a fluke or due to chance.

Null Hypothesis = Opposite Hypothesis Inferential Statistics Null Hypothesis - States that there is NO difference between 2 sets of data. (basically the opposite of your hypothesis!) Null Hypothesis = Opposite Hypothesis Purpose... 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. In other words, not due to statistical significance.

Truth About Population Inferential Statistics Null Hypothesis - 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. **You don’t want to have errors! But, you could make them. Truth About Population NULL TRUE NULL FALSE** Decision Researcher Makes REJECT NULL (ACCEPT ORIGINAL) Type I Error Correct Decision ACCEPT NULL Correct Decision Type II Error ** If NULL FALSE - then the regular hypothesis is true!

Truth About Population Inferential Statistics Null Hypothesis Example - 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 ** If NULL FALSE - then the regular hypothesis is true! NULL TRUE NULL FALSE** Decision Researcher Makes REJECT NULL (ACCEPT ORIGINAL) Type I Error - students evacuated, yet bomb squad does not find a bomb. Erred on side of caution. Correct decision. Students evacuated, bomb squad finds bomb & safely removes it. All are safe! ACCEPT NULL Correct decision. No evacuation, no bomb. Threat ignored & students stay in class safe and sound. Type II Error - Bomb threat is ignored. Students stay in class, bomb goes off & students are injured.