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

• The average distance of scores from the mean

x X-Mean

9 9-6=3

2 2-6=-4

6 6-6=0

7 7-6=1

Sum=24Mean=24/4=6

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 9

2 2-6=-4 16

6 6-6=0 0

7 7-6=1 1

Sum=24Mean=24/4

=6

Sum(X-mean)2= 26

Standard Deviation continued• Step 4: Calculate the variance

• Step 5: Calculate standard deviation

Variance= N-1= number of scores or participants – 1

Variance= 26/ (4-1)= 26/3

Standard deviation=

Standard deviation=

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?

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

92= degrees of freedom (df)

N-2 (n1+n2-2)= 40+54-2=94-2=92

What statistical test is this?

Independent samples t-test because we are comparing two groups

What does 92 stand for and how do we calculate it?

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 = .01What statistical test is this?

Correlation because we are measuring the direction and strength between two variables

What does 33 stand for and how do we calculate it?33= degrees of freedom (df)

n-2 = 35-2=33 (subtract two because there are 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 statistical test is this?

One way ANOVA because we are comparing 3 groups of students

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 is 1.23? The F ratio

If we set an alpha level of .05 would this result be statistically significant? No, .06 is greater

than .05