4 Ordinal Ordinal= Categories and Rank Order It orders along a continuum First, Second, ThirdRanks in the militaryLikert ScalesBut the difference BETWEEN levels is NOT EQUAL
5 IntervalInterval- Categories, rank order, and equal intervals between numbersFahrenheit Scale- the difference between 20 and 30 degrees is the same as the difference between 70 and 80 degreesHowever 80 degrees is not twice as hot as 40 degrees because there is no ABSOLUTE ZERO for this we need a…..
6 RatioRatio Scales- Categories, rank order, equal intervals and Have an absolute Zero or a true zero point which represents an absence of the thing being measuredLength, Volume, Time0 seconds, 30 seconds, 60 seconds
7 Why does the scale matter In order to make accurate comparisonsIn order to do mathematical manipulationsSo you must know about the scale to determine if the statistical analysis means anythingWhich scales allow you to determine an average score?
8 Averages- Measures of Central Tendency Mode- the most common scoreWith what type of scale can you find the mode?When might it be more useful?Median- the score at the mid point. 50% of the scores are above and 50% are belowWith what type of scale can you find the median?When might it be most useful?Mean- AverageWith which scales can you find the mean?When might it be most useful
9 THE MEANThe mean is most commonly used in statistical analysis as it can be manipulated algebraically. However it can be influenced byExtreme scoresNon linear distributionsThe NORMAL CURVE- most scores are likely to fall near the mean
11 Presenting Data Frequency distribution Grouped frequency Histogram Bar graphFrequency polygon
12 A few other terms to know Population: included ALL member of groupSample: subset of the target populationRange- the distance from the lowest to highest score. Can be used to compare variability between two groups. Group 1: , Group 2: 25-69Average deviation- a number that represents how scores arrange themselves around the mean (or deviate from the mean). Could we take the scores, subtract the mean and average them?
13 Variance- A way to solve the ZERO problem Variance- A way to solve the ZERO problem. We subtract the mean from the score and square it so we have all positive numbers. Then we take the average (with N-1 for population vs sample). Better, but the result is squared and squares are difficult to work with.Standard Deviation- Take the square root of the variance. Ah…now we have a number that represents the deviation from the mean.
14 What the SD tells usThis figure tells us about the scores. Example- the MMPI-If a score falls within 1 SD then the client is in Normal Range and this can not be interpreted due to issues of CHANCE
15 Degrees of FreedomRemember the N-1? Why did we subtract 1 from the number in the sample? Well, basically it is due to the degrees of freedom you have to change numbers. See if we have 3 scores with a mean of 5 (5, 10, 15) and are allowed to change them as long as we still get a mean of 5, we can change 2 of them and this will tell us what the third score will have to be. This is true even if you have 25 scores. The last one is determined- thus we subtract one score so that when we have new scores, this last one does not count in the statistical analysis. What if we had two separate groups, how many degrees of freedom would we have? Three groups?
16 One vs Two Tailed TestsTails are the ends of the curve. This is the area that is extreme and if relationships fall this far away from the mean, it is unlikely to have occurred by chance alone.One tailed tests only predict one direction. This test is more powerfulTwo tailed tests predict possible occurrences in both directions
17 Parametric vs Non Parametric tests Parametric tests mean the data falls along the normal curveNon Parametric tests: Data does not fall along the normal curve and different forms of calculations will be necessary to make any meaningful interpretations about the dataWE WILL FOCUS ON PARAMETRIC TESTS
18 Review WOW…you’ve learned a lot in one day!! NOIR Measures of Central TendencyWays to present DataVarianceStandard DeviationsNormal (bell) curveSkewed CurvesOne vs Two Tailed TestsParametric vs Non Parametric TstsSkewed graphsThese are the fundamentals you need to understand statistics