Inferential Statistics Formula Sheet

Name:______Block:______

Chi Squared (x2)

Set up a table of your data by mode
Compute expected cell frequencies for each cell in the table ecf = row total x column total

grand total (# total answers)

Compute Chi Square

x2 = Σ (Oi – Ei)2 Σ – means to add up all E – Expected Cell Frequency

Ei O – original number in chart

Compute your degrees of freedom

df = (#categories – 1)(#groups – 1)

5. Compare x2calc to x2crit using critical values table

6. If X2calc > X2crit you can reject your null hypothesis, and your data is VALID because you can generalize to the larger population!

Mann-Whitney U

Set up a table to rank all the values in the data set from least to greatest. This is Table 1.
If there is a “tie” create an adjusted rank

To do this, you must add the original ranks, and find the average

After ranking, separate data points into experimental and control groups – keeping the original adjusted ranks
Add up the ranks assigned to the smaller of the experimental or control group (R1) and the ranks of the larger group (R2)
Calculate U = n1n2 + n1 (n1 + 1) – R1 n = the total number of participants in the group

2 R= added ranks

5. Repeat for R2

6. Use the lower of the 2 values, and then use the critical value table – if U calc is = or < U crit, there IS a significant difference between the control and experimental groups and you would REJECT Ho

Wilcoxin Test (W)

Discard the results of any participant who scored the same in both trials
Compute the difference between the two scores of each participant
Rank the differences, giving the smallest a rank of 1
Adjust the ranks for ties
Give the ranks a sign (positive or negative)
Add up all the ranks for the participants who did best in condition A; then add up all the ranks for those who best in B
The smaller of these two figures is known as T
Look up the T score on the table. If your value is equal to or lower than the value in the 0.05 column, your result is significant at p < 0.05. If it is equal to or lower than that in the 0.01 column, it is significant at p < 0.01 (i.e. even less likely to have occurred due to chance)

Name:______Block:______

Chi Squared Class Activity

Directions: Use the Chi Squared Test to analyze the validity of the following set of data

The study: A researcher wanted to test the affects cell phone usage had on college student’s ability to notice their surroundings. They set up a test in which a clown was asked to ride a uni-cycle through a crowd of students. One group of students had cell phones while the other did not.

Hypothesis: Students walking around a college campus will be less likely to see a clown on a uni-cycle than those no on cell phones

Null Hypothesis: There will no difference in the occurrence of students noticing the clown, or the difference will be due to chance

Saw Clown / Did not see Clow / Row Total
Group 1: Phone / 2
Ecf: / 5
Ecf:
Group 2: No phone / 6
Ecf: / 1
Ecf:
Column total

1. What type of data do you use Chi Squared for? ______

2. Find the Row Total, Column Total, and ECF for each group

3. Compute Chi Squared calculations in area below:

4. Use your critical value chart to determine if you can reject your null hypothesis (circle). YES NO

The study: A researcher wanted to determine if a person’s memory could be altered based on post-event information. To test the thought, the researcher had 3 groups of students watch a video of a robbery. To describe the robbery, the researcher used different words. Students were then asked if they remember what color the car was. It was blue.

Hypothesis: Students will remember different colors for the car based on the post-event information supplied by the researcher

Null Hypothesis: There will no difference in the students memory, or any difference will be due to chance

Blue / Red / Yellow / Row Total
Group 1: “Slow Car” / 2
Ecf: / 1
Ecf: / 4
Group 2: “Fast Car” / 1
Ecf: / 4
Ecf: / 3
Group 3: “Car” / 4
Ecf: / 1
Ecf: / 1
Ecf:
Column total

1. What type of data do you use Chi Squared for? ______

2. Find the Row Total, Column Total, and ECF for each group

3. Compute Chi Squared calculations in area below:

4. Use your critical value chart to determine if you can reject your null hypothesis (circle). YES NO

Name:______Block:______

Chi Squared Homework

Directions: Use the Chi Squared Test to analyze the validity of the following set of data

Hypothesis: Students walking around a college campus will be less likely to see a clown on a uni-cycle than those no on cell phones

Null Hypothesis: There will no difference in the occurrence of students noticing the clown, or the difference will be due to chance

Saw Clown / Did not see Clown / Row Total
Group 1: Phone / 1
Ecf: / 3
Ecf:
Group 2: No phone / 5
Ecf: / 2
Ecf:
Column total

1. What type of data do you use Chi Squared for? ______

2. Find the Row Total, Column Total, and ECF for each group

3. Compute Chi Squared calculations in area below:

4. Use your critical value chart to determine if you can reject your null hypothesis (circle). YES NO

Hypothesis: Students will remember different colors for the car based on the post-event information supplied by the researcher

Null Hypothesis: There will no difference in the students memory, or any difference will be due to chance

Blue / Red / Yellow / Row Total
Group 1: “Slow Car” / 2
Ecf: / 4
Ecf: / 6
Group 2: “Fast Car” / 0
Ecf: / 7
Ecf: / 3
Group 3: “Car” / 7
Ecf: / 1
Ecf: / 2
Ecf:
Column total

1. What type of data do you use Chi Squared for? ______

2. Find the Row Total, Column Total, and ECF for each group

3. Compute Chi Squared calculations in area below:

4. Use your critical value chart to determine if you can reject your null hypothesis (circle). YES NO

Name:______Block:______

Mann Whitney U Class Work Activity

Directions: Use the Mann Whitney U test to analyze the validity of the following set of data

The Study: A student is conducting an experiment to see if listening to rock music while studying can help to increase the score you will receive on a test. In order to do this experiment, the student had two groups of students. One group studied with rock music, the other studied in silence.

Hypothesis: Participants will perform better on a history test when they study in silence

Null Hypothesis: Participants scores will be no different if they study in silence or listening to music, or any difference will be due to chance.

Score of students listening to rock music / Score of students studying in silence
90 / 100
70 / 75
40 / 50
65 / 75
85 / 80
80 / 75
65 / 90
70 / 75
80 / 80
85 / 100

1. What type of data do you use Mann Whitney U for? ______

2. Order the data from least to greatest

3. Adjust the rank for ties

4. Organize 2 separate charts

5. Add up the ranks for each chart

6. Compute the Mann Whitney U test

7. Use your critical value chart to determine if you can reject your null hypothesis (circle). YES NO

Scores from least to greatest / Rank / Adjusted Rank
Control group Score / Adjusted Rank
Added Ranks:

Mann Whitney U Calculations:

The Study: A student is conducting an experiment to determine if Gatorade really does not a person run faster. They set up two groups, one group drank Gatorade while the other did not. The researcher recorded the times

Hypothesis: Participants will run faster if they drink Gatorade

Null Hypothesis: Participants times will not differ whether they drink Gatorade or not, or any difference will be due to chance

Time of participants who drank Gatorade (in min) / Time of participants who did not drink Gatorade
4 / 7
5 / 7.5
4 / 6
5.5 / 5
3 / 4
6 / 8
5 / 7
5.5 / 9
6 / 5
8 / 3

1. What type of data do you use Mann Whitney U for? ______

2. Order the data from least to greatest

3. Adjust the rank for ties

4. Organize 2 separate charts

5. Add up the ranks for each chart

6. Compute the Mann Whitney U test

7. Use your critical value chart to determine if you can reject your null hypothesis (circle). YES NO

Scores from least to greatest / Rank / Adjusted Rank
Control group Score / Adjusted Rank
Added Ranks:

Mann Whitney U Calculations:

Name:______Block:______

Mann Whitney U Homework

Directions: Use the Mann Whitney U test to analyze the validity of the following set of data

Hypothesis: Participants will perform better on a history test when they study in silence

Null Hypothesis: Participants scores will be no different if they study in silence or listening to music, or any difference will be due to chance.

Score of students listening to rock music / Score of students studying in silence
80 / 70
60 / 75
50 / 100
70 / 80
90 / 85
80 / 90
65 / 95
75 / 80
85 / 100
85 / 100

1. What type of data do you use Mann Whitney U for? ______

2. Order the data from least to greatest

3. Adjust the rank for ties

4. Organize 2 separate charts

5. Add up the ranks for each chart

6. Compute the Mann Whitney U test

7. Use your critical value chart to determine if you can reject your null hypothesis (circle). YES NO

Scores from least to greatest / Rank / Adjusted Rank
Control group Score / Adjusted Rank
Added Ranks:

Mann Whitney U Calculations:

Hypothesis: Participants will run faster if they drink Gatorade

Null Hypothesis: Participants times will not differ whether they drink Gatorade or not, or any difference will be due to chance

Time of participants who drank Gatorade (in min) / Time of participants who did not drink Gatorade
5 / 10
6 / 7.5
4 / 8
4.5 / 6
7 / 4
3 / 5
6 / 9
5.5 / 9.5
4 / 8
8 / 3

1. What type of data do you use Mann Whitney U for? ______

2. Order the data from least to greatest

3. Adjust the rank for ties

4. Organize 2 separate charts

5. Add up the ranks for each chart

6. Compute the Mann Whitney U test

7. Use your critical value chart to determine if you can reject your null hypothesis (circle). YES NO

Scores from least to greatest / Rank / Adjusted Rank
Control group Score / Adjusted Rank
Added Ranks:

Mann Whitney U Calculations:

Name:______Block:______

Wilcoxin Test Class Work

Directions: Use the Wilcoxin test to analyze the validity of the following set of data

The Study: A researcher wants to test how well people know their true height. They asked participants how tall they thought they were and then measured them and recorded their actual height.

Hypothesis: There will be a difference between participants’ perceived height and actual height

Null Hypothesis: There is no difference between a participants’ perceived height and actual height

Reported Height / 68 / 74 / 82.25 / 66.5 / 69 / 68 / 71 / 70 / 70 / 67 / 68 / 70
Measured Height / 66.8 / 73.9 / 74.3 / 66.1 / 67.2 / 67.9 / 69.4 / 69.9 / 68.6 / 67.9 / 67.6 / 68.8
Difference (d)
Ranks of Differences
Adjusted Ranks
Signed Ranks

1. What type of data do you use Wilcoxin for? ______