Different Types of Data • Qualitative • Quantitative – Nominal scale – used to count number of cases (e.g. girls = 1, boys = 2) – Ordinal scale – ranked – 1st, 2nd, 3rd etc. – Interval scale – equal intervals between consecutive values on number scale, but no zero point (e.g. Fahrenheit vs. Celsius, IQ scale) – Ratio scale – ratio between numbers, has zero point (e.g. person running 10 miles is running twice as far as someone running 5 miles) Agenda • ** Please turn in your notes. • Warm Up: Please do the sheet on your desk • 1. Go over completed parts of packet • 2. Correlation Coefficients • 3. Finish Research Methods Packet • 4. Start Statistics • 5. Standard Deviation Practice (if time) • HW: Read and take notes on pages 46-55 • Study for Vocabulary Quiz next class. Interpreting Data… • Measures of Central Tendency… – Mean • average – Median • Middle number • If even number of numbers, take the average of the two middle numbers – Mode • Occurs the most often • Bimodal: two modes • Multimodal: three or more modes Graphical representations… • Data shown in curves – Can be normal or skewed • Generally result is normal curve (bell shaped curve, normal distribution) – Mean, median, mode fall at highest point on curve. • Skewed distributions – Asymmetrical, most scores grouped at one end. • Negatively skewed • Positively skewed Normal Distribution Negatively Skewed Distribution Positively Skewed Distribution Measures of variation • Variance tells us more… – How much scores differ from one another and from the mean • Measures include – Range – Variance – Standard deviation Range • Spread of scores in a distribution. – Largest score minus smallest score – For example: Distribution 1: 32 35 36 36 37 38 40 42 42 43 43 45 Distribution 2: 32 32 33 33 33 34 34 34 34 34 35 45 Both have a range of 13, but there is a difference in amount of variability. So… Variance • How spread out a distribution is. • It is computed as the average squared deviation of each number from its mean. For example, for the numbers 1, 2, and 3, the mean is 2 and the variance is: σ2 = In other words… Variance… • Step One -Find the mean of the scores. • Step Two -Subtract the mean from every score. • Step three -Square the results of step two. • Step Four -Sum the results of step three. 5 isfour variance • Step Five -Divide the results of Step step by N-1. • Step Six -Take the square of step five. Step 6 is standard root deviation Standard Deviation • Square root of the variance • Most commonly used measure of spread Standard Deviation Lower case sigma means 'standard deviation'. Capital sigma means 'the sum of'. x bar means 'the mean' 68, 95, 99.7 rule • 99.7% of scores fall within 3 standard deviations of the mean (above and below) • 95% of scores fall within 2 standard deviations of the mean • 68% fall within 1 standard deviation How To Organize Data • Frequency distribution – Histogram – Frequency polygon Histogram Frequency Polygon Scatterplots • Illustrate the strength and direction of correlations graphically • Paired X and Y scores for each subject are plotted as single points on a graph • Slope of a line that best fits the pattern of points suggests the degree and direction of the relationship between the two variables Different Scatterplots • • • • • Fig. 1: r =1 Fig. 2: r = -1 Fig. 3: r = 0 Fig. 4: r = ~0.65 See the handout about computing correlation coefficients. Inferential Statistics • Evaluates possibility that a correlation is a real relationship, not just chance • Statistical significance (p) is measure of the likelihood of the difference between groups • Real difference is more likely with: – large differences between the means of frequency distribution – small standard deviations – large sample The p value and significance • Lower the p value, the less likely results were due to chance • For a difference to be significant, p usually needs to be less than 0.05