Data Analysis Plan Purpose to tell a story To construct a coherent narrative that explains findings argues against other interpretations and supports conclusions Three basic steps 1 Getting to know the data to examine the data set the raw numbers and play around with 2 Summarizing the data use descriptive statistics mean median modes variability to 3 Confirm what the data reveal most commonly using the null hypothesis significance the raw numbers summarize the data testing NHST Getting to know the data Look at raw numbers and check for errors and outliers Errors are impossible numbers outside possible range Outliers are in the possible range but are exceptional Could be an error or a true score from an unusual participant really did not expect these scores data set example from class Decision rules for errors and outliers 1 You fix errors if you can 2 You eliminate outliers if appropriate Follow the rules of the journal or organization where the results will be presented reported 3 Either way you must specify the amount of data eliminated and your reason or rule for elimination Look at a picture of raw numbers Stem and Leaf plots Histogram frequency distribution Examine underlying distribution of raw scored looking for unusual distribution Normal Distribution Symmetrical centered frequency Rarely ever get it likely to get other than normal Skew distribution if extremely skewed you may want to transform the scores using logarithms or changing the scale you use Positive skew tail trails off to the positive side Negative skew tail trails off to the negative side Bimodal distribution has two humps modes high points can be problematic for further analysis refer to experts for appropriate data analysis Summarize the Data Purpose is to describe the data 1 To indicate what is a typical score central tendency 2 To assess the degree to which the scores in the data set differ from one another dispersion variability Measures of Central Tendency 1 Mode most frequently occurring score Example 2 3 4 5 5 5 5 5 5 6 7 8 9 Mode 5 obviously Example 1 2 3 4 5 6 7 8 9 Median 5 2 Median the middle score 50 of your scores fall below and 50 fall above it 3 Mean arithmetic average or mean sum of scores divided by number of scores sum of all numbers N Mean median mode normal distribution In a skewed distribution the mean may not be the best measure of central tendency as it is skewed and doesn t show the typical score In this case the median would be a better measure of central tendency to go by Measures of Variability Dispersion how numbers differ Range Variance officially highest score lowest score the sum of the squared deviations of the scores around the mean divided by Example 1 2 3 4 5 5 5 5 6 7 7 8 Range 1 8 or 7 either N or N 1 variance of a set of numbers or the population variance the sum of the squares divided by N sum of squares N an estimate of the variance of a population based on a sample the sum of squares divided by n 1 Use when making inferences Sum of squares N 1 Standard Deviation the square root of the variance An index of strength of the relationship between the IV and the DV that is independent of Effect size or effect magnitude the sample size How large an effect does the IV have on the DV Useful for a researcher because some variables have a very large effect and some have a very small effect small is hard to see and large is very easy to see Example suppose you suffer from chronic back pain you see an advertisement that says enjoy immediate relief with acupuncture you look at their study and their actual data two groups one was a placebo the other was real acupuncture scored their pain relief on a scale after the acupuncture you notice there was not a very strong effect between the placebo group and the acupuncture group with a rating of 3 and 4 But then you look at another study and the effects are rated 1 to 9 with the relief being at a high 9 for the acupuncture group For D a value of 20 indicates a small magnitude effect 50 is a medium effect 80 is a large magnitude of effect D is a ratio of the difference between the means at two levels of an IV divided by the standard deviation of the population the difference between means divided by a measure of variability As variability increases SD increases D decreases lower effect size Example Suppose you have two levels of an IV and the means for these are 8 and 5 The difference between the two is three Medium effect If there is moderate variability in the dv say population SD 6 then d 3 6 5 Power the probability of correctly rejecting a false null hypothesis Because the SD is used as the denominator for this measure it is independent of sample size Thus you can compare effect sizes across research studies using various sample sizes Meta analysis