Transcript Statistics
STATISTICS A way to organize data so that it has meaning! Descriptive - Allow us to make observations about the sample. Cannot make conclusions. Inferential – Allow us to generalize our findings from the sample to the population. Allow us to make conclusions. LEVELS OF DATA Nominal – used to name or categorize Ordinal – used to rank Interval – consistent units of measurement, equal spacing, no true zero point Ratio – same as interval, but with true zero point. DESCRIPTIVE STATISTICS Measures of Central Tendency Measures of Dispersion MEASURES OF CENTRAL TENDENCY Describe “typical” score in a distribution Mode, median, mean MODE Most frequently occurring number in data set *only measurement of central tendency that can be used with nominal level data If there are 2, call this a bimodal distribution MEDIAN Rank data ascending/descending order and find the “middle” number. Best indicator of central tendency when there is a skew b/c it is unaffected by extreme scores If n is odd, will be whole # If n is even, will be between two values MEAN Arithmetic average of a set Requires interval or ratio data Sum of all scores/n x1 + x2 + x3+…xn / n n = sample size Problem: Always pulled towards extreme scores or any skew of a distribution Look at standard deviation to help understand how far away most scores are from the average. WHY DO WE NEED TO CALCULATE THE MEAN, THE MEDIAN AND THE MODE? If they are all similar, you have very little distortion/skew! If both the median and mode are to one side of the mean, your data is skewed or distorted! GRAPHS ALLOW US TO QUICKLY SUMMARIZE DATA Bar graph Height of bars indicate % or frequency Titles and axis must be labeled to reflect the aim of the study! MEASURES OF DISPERSION Amount of spread/variability in data distribution How close is each individual score to the overall mean? RANGE Distance between top and bottom values of a set. Not for nominal numbers! Advantages: easy to calculate Disadvantages: distorted by extreme scores misleading Doesn’t tell us if the values are closely grouped around the mean or equally spaced across entire range STANDARD DEVIATION The average of how far the scores are from the mean Requires interval or ratio level data STANDARD DEVIATION = (S) 1. 2. 3. 4. 5. 6. Find mean of data set Subtract mean from each value = deviation (d) Square each (d) Find the sum of d2 Divide step 4 by (N-1) Take the square root of this number! STANDARD DEVIATION = (S) This tells you how far away (on average) the scores are from the mean in the sample. The larger the standard deviation, the more variability in your data. The less you can trust your mean score to be an accurate representation of a typical score! TI 80 MILLION MAGIC! Clear lists Enter your data Stat button 4: clear list 2nd function, 1 (for L1) Enter…screen will say “done” Stat button Cursor will be on 1: edit, hit enter Enter your data into L1, hit enter after each number Magical calculation! Stat button Arrow over to Calc Cursor will be on 1: 1-Var Stats, hit enter Screen will say “1-Var Stats” 2nd 1 (to tell it which list you want it to calculate from ) and hit enter MAGIC!!! Sx = standard deviation TI-SOMETHING MAGIC! On Clear your list Enter your data Stat button 1: 4 clear list 2nd 1 (L1) Enter (done) Stat button 1: Edit Enter data into L1 Magically calculate all of your descriptive stats!!! Stat button, arrow to calc 1: 1-Var Stats 2nd 1 (L1) Enter Will list LOTS of numbers (mean, median, mode & Sx =standard deviation)