Descriptive Statistics

Mean Average of the numbers (sum of the numbers divided by how many numbers there are) 10+6+2 = 18 There are 3 numbers so divide 10 by 3 18/3 The mean would be 6

Marginal Means if there are two factors, the marginal mean is the mean for each level of a factor ignoring the other factor Hungry Not Hungry Marginal means for type of service requested Volunteer 3.44 4.72 4.08 Donate 3.51 2.75 3.13 Marginal means for hunger 3.48 2.74

Standard Deviation x X-Mean 9 9-6=3 2 2-6=-4 6 6-6=0 7 7-6=1 Sum=24 The average distance of scores from the mean Step 1 and 2: Calculate the mean of the data, and then subtract the mean from each of the scores

Standard Deviation continued Step 3: Square each of the deviations and then take the sum of the squared deviations (sum of squares) x X-Mean (X-mean)2 9 9-6=3 2 2-6=-4 16 6 6-6=0 7 7-6=1 1 Sum=24 Mean=24/4=6 Sum(X-mean)2= 26

Standard Deviation continued Step 4: Calculate the variance Step 5: Calculate standard deviation Variance= 𝑆𝑢𝑚(𝑋−𝑀𝑒𝑎𝑛)2/𝑛−1 N-1= number of scores or participants – 1 Variance= 26/ (4-1)= 26/3 Standard deviation= 𝑆𝑢𝑚(𝑋−𝑀𝑒𝑎𝑛)2/𝑛−1 Standard deviation= 26/3

Choosing a statistical test What is your goal? Comparing group means? How many groups do you have? Are the groups independent or dependent? Looking for a relationship between variables?

Independent Samples t-test Number of groups one One sample t-test Two Independent Samples t-test Paired Samples t-test Two or more ANOVA

A one sample t-test can be used when computing the difference between a sample mean to an population mean An independent samples t-test can be used when computing the difference between to sample means (girls versus boys in the sample, control versus experiment), A paired samples t-test can be used when comparing the same participants (pre to post) A correlation is used when computing the strength of a relationship between two variables, if they are related the variables behave similarly   An ANOVA can be used to compare the means of two or more factors

Hypothesis: Regular coffee drinkers (n=40) have higher heart rate compared to non-coffee drinkers (n=54) t(92)=-6.94, p=.04 What does 92 stand for and how do we calculate it? What statistical test is this? 92= degrees of freedom (df) N-2 (n1+n2-2)= 40+54-2=94-2=92 Independent samples t-test because we are comparing two groups What is -6.94? The t-test statistic If we set an alpha level of .05 would this result be statistically significant? Yes, .04 is less than .05

Hypothesis: There is a negative relationship between the number of drinks a person has and the number of people who think you’re as cool as you do (n=35) r(33) = -.85, p = .01 What does 33 stand for and how do we calculate it? What statistical test is this? 33= degrees of freedom (df) n-2 = 35-2=33 (subtract two because there are two variables) Correlation because we are measuring the direction and strength between two variables What is -.85? The correlation coefficient, tells us strength and direction of the correlation If we set an alpha level of .05 would this result be statistically significant? Yes, .01 is less than .05

Hypothesis: Students who study (n=5)will do better on on the exam compared to students who go out (n=5) or students who binge watch netflix the night before (n=5) F(2, 12) = 1.23, p = .06 What do the 2 and 12 stand for and how do we calculate them? 2 and 12= degrees of freedom (df) K-1 = Number of levels of the independent variable -1 = 3-1=2 N-K= Total number of students- number of levels= 15-3=12 What statistical test is this? One way ANOVA because we are comparing 3 groups of students If we set an alpha level of .05 would this result be statistically significant? What is 1.23? The F ratio No, .06 is greater than .05