STATS DAY First a few review questions

Which of the following correlation coefficients would a statistician know, at first glance, is a mistake? A. 0.0 B +1.1 C +1.0 D -.7 E -.2

Which of the following is measure of central tendency? A Mean B Correlation C Random Sample D Frequency Distribution E Histogram

Most psychologists accept a difference between groups as “real,” or significant, under which of the following conditions? A p<.5 B p<.3 C p<.1 D p<.05 E p=0

Descriptive Statistics Descriptive statistics are used to organize and summarize data. They provide an overview of numerical data

Descriptive Statistics Key descriptive statistics include: measures of central tendency Measures of variability The coefficient of correlation

Central Tendency Mean The Mean or average is probably the most commonly used method of describing central tendency. To compute the mean all you do is add up all the values and divide by the number of values. 15, 20, 21, 20, 36, 15, 25, 15

15, 20, 21, 20, 36, 15, 25, 15 The sum of these 8 values is 167, so the mean is 167/8 = 20.875.

Median is the score found at the exact middle of the set of values For example, if there are 500 scores in the list, score #250 would be the median. 15,15,15,20,20,21,25,36

15,15,15,20,20,21,25,36 There are 8 scores and score #4 and #5 represent the halfway point. Since both of these scores are 20, the median is 20. If the two middle scores had different values, you would have to take the average of the two middle scores.

mode The most frequently occurring value is the mode. 15,15,15,20,20,21,25,36 So the Mode is…………………

the value 15 occurs three times and is the mode bimodal distribution there are two values that occur most frequently 3, 6, 7, 7, 8, 8, 9, 0 The model should be 7 and 8

15,15,15,20,20,21,25,36 For this set we just used what would the mean, median, and mode be? -20.875, 20, and 15 If the distribution was truly normal (bell shaped curve) then these would all be equal.

Range Range is simply the highest value minus the lowest value . 15,15,15,20,20,21,25,36 The range in this example is: 36-15=21

Bar Graphs A bar graph uses vertical bars to represent the data. The height of the bars usually represent the frequencies for the categories that sit on the X axis. Note that, by tradition, the X axis is the horizontal axis and the Y axis is the vertical axis. Bar graphs are typically used for categorical variables.

Histograms A histogram is a graphic that shows the frequencies and shape that characterize a quantitative variable.

Variability Refers to how much the scores in a data set vary from each other and from the mean

Standard Deviation Is an index of the amount of variability in a set of data.

Speed (mph) Set A Perfection Blvd 35 34 33 37 38 40 36 33 34 30 35 34 33 37 38 40 36 33 34 30 Mean = 35 SD = 2.87 Set B Wild Street 21 37 50 28 42 37 39 25 23 48 Mean = 35 SD = 10.39

Standard Deviation To transform a raw score into z-score units, just use the following formula:                      Raw score - Mean Z-score =     ---------------                     Standard Deviation

What if it’s not bell shaped? Normal Skewed Skewed Right Left The mean, median, and mode are affected by what is called skewness (i.e., lack of symmetry) in the data.

Look at the above figure and note that when a variable is normally distributed, the mean, median, and mode are the same number. If you go to the end of the curve, to where it is pulled out the most, you will see that the order goes mean, median, and mode as you “walk up the curve” for negatively and positively skewed curves.

Skewed up rules! You can use the following two rules to provide some information about skewness even when you cannot see a line graph of the data (i.e., all you need is the mean and the median): 1.      Rule One. If the mean is less than the median, the data are skewed to the left. 2.      Rule Two. If the mean is greater than the median, the data are skewed to the right.

Statistical significance (p) is a mathematical tool used to determine whether the outcome of an experiment is the result of a relationship between specific factors or due to chance.

Statistical Significance The statistical analysis of the data will produce a number that is statistically significant if the p value falls below 5% aka p<.05. In other words, if the likelihood of an event is statistically significant, the researcher can be 95% confident that the result did not happen by chance

Statistical Significance The lower the p value the less likely the results were due to chance.

Statistical Significance If the p value was 1 in 100 it would look like p<.01