Sign Out Sheet Statistics

Tim Kariger, Paolo Ramirez, Taylor Young

Description of Topic

• Determine if sign outs are associated with:– Gender– Class Subject– Class Block– 1/3 of Block

Procedure

• Gather complete sign out sheets from Mr. Rohrmiller

• Mrs. McNelis & Mr. Rohrmiller determine gender, and remove name

• Recorded Gender, Subject, Time Out, Block and 1/3 of Block

Gender proportions

• Of the 1481 subjects,61.44% were female38.56% were male

Block frequency

• 3rd is most frequent, but only by 4

50

100

150

200

250

300

350

400

450

Block

0 1 2 3 4 5 6

Collection 7 Histogram

Block 1: 280 (18.9%)Block 2: 349 (23.57%)Block 3: 428 (28.9%)Block 4: 424 (28.63%)

Gender Frequency/BlockEnglishFemale: unimodal, right skewedMale: bimodal, roughly symmetric

Social StudiesFemale: Unimodal, roughly symmetricMale Unimodal, left skewed

gen

der

0

20

40

60

F

20

40

60

M

Block

0 1 2 3 4 5 6

Collection 1 Histogram

Gen

der

0102030405060

F

102030405060

M

Block

0 1 2 3 4 5 6

Collection 2 Histogram

Conclusion about pop.

• More females than males used the bathroom

• Students use the bathroom more frequently in the later half of the day (3rd & 4th)

Study hall Chi squared test (block vs 3rd)

State:-Categorical data-SRS-All expected counts greater then 5

Check:-3rd of block and block number are categories-sign out pages were randomly selected-All counts greater than 5

Conditions met, chi squared distribution,Chi squared test for independence.

99.41...4.15

)4.159(

1.14

)1.1422(

exp

exp)( 2222 obs

DF=6

Test of Collection 5 Test for Independence

First attribute (categorical): Block

Second attribute (categorical): Third_of_Block

First attribute: Block Number of categories: 4Second attribute: Third_of_Block Number of categories: 3 Alternative hypothesis: There is an association betw een Block and Third_of_Block

The test statistic, chi-square, is 41.99. There are 6 degrees of freedom (the number of row s minus one times the number of columns minus one).

If it w ere true that Block w ere independent of Third_of_Block (the null hypothesis), and the sampling process w ere performed repeatedly, the probability of getting a value for chi-square this great or greater w ould be < 0.0001.

RowSummary

Column Summary

BlockBlockBlock

2 3 4

Block

1

1

2

3

Third_of_Block

22 (14.1) 9 (15.4) 60 (54.1) 13 (20.4)

8 (12.8) 8 (13.9) 52 (48.9) 26 (18.4)

4 (7.1) 20 (7.7) 18 (27.0) 10 (10.2)

34 37 130 49

104

94

52

250

P(x>41.99)= .0001

Study hall Chi squared test (block vs 3rd) cont.

• Ho: There is no association between 3rd of block and block given that it’s study hall.

• Ha: There is an association between 3rd of block and block given that it’s study hall

• We reject the Ho because the p-value of .0001 is less than =.05

• We have sufficient evidence that there is an association between 3rd of block, and block when in study hall

Independence test (block and subject)

Test of Collection 7 Test for Independence

First attribute (categorical): Subject

Second attribute (categorical): Block

First attribute: Subject Number of categories: 6Second attribute: Block Number of categories: 4 Alternative hypothesis: There is an association betw een Subject and Block

The test statistic, chi-square, is 381.2. There are 15 degrees of freedom (the number of row s minus one times the number of columns minus one).

If it w ere true that Subject w ere independent of Block (the null hypothesis), and the sampling process w ere performed repeatedly, the probability of getting a value for chi-square this great or greater w ould be < 0.0001.

The numbers in parentheses in the table are expected counts.

RowSummary

Column Summary

SubjectSubjectSubjectSubjectSubject

foreign language math science Social Studies study hall

Subject

English

1

2

3

4

Block

21 (46.9) 25 (47.3) 50 (45.2) 98 (46.1) 52 (47.3) 34 (47.3)

107 (58.4) 5 (58.9) 52 (56.3) 73 (57.5) 75 (58.9) 37 (58.9)

43 (71.7) 91 (72.2) 51 (69.1) 64 (70.5) 49 (72.2) 130 (72.2)

77 (71.0) 129 (71.6) 86 (68.4) 9 (69.9) 74 (71.6) 49 (71.6)

248 250 239 244 250 250

280

349

428

424

1481DF=15

2.381...3.47

)3.4725(

9.46

)9.4622(

exp

exp)( 2222 obs

P(x>381.2)= .0001

State:-categorical data-SRS-all expected counts are greater than 5

Check:-Block number and subject are categories-Data randomly collected-All expected cell counts are more than 5

Condition met, chi distribution,Chi squared test for independence

Conclusion of block and subject test

•Ho: there is no association between subject and block•Ha: there is an association between subject and block•We reject the Ho because the p-value of .0001 is less than alpha=.05•We have sufficient evidence that there in an association between block and subject

Gender and subject chi squared testTest of Collection 7 Test for Independence

First attribute (categorical): Subject

Second attribute (categorical): Gender

First attribute: Subject Number of categories: 6Second attribute: Gender Number of categories: 2 Alternative hypothesis: There is an association betw een Subject and Gender

The test statistic, chi-square, is 50. There are 5 degrees of freedom (the number of row s minus one times the number of columns minus one).

If it w ere true that Subject w ere independent of Gender (the null hypothesis), and the sampling process w ere performed repeatedly, the probability of getting a value for chi-square this great or greater w ould be < 0.0001.

The numbers in parentheses in the table are expected counts.

RowSummary

Column Summary

SubjectSubjectSubjectSubjectSubject

foreign language math science Social Studies study hall

Subject

English

F

MGender

129 (152.4) 188 (153.6) 126 (146.9) 144 (149.9) 144 (153.6) 179 (153.6)

119 (95.6) 62 (96.4) 113 (92.1) 100 (94.1) 106 (96.4) 71 (96.4)

248 250 239 244 250 250

910

571

1481

50...6.153

)6.153188(

4.152

)4.152129(

exp

exp)( 2222 obs

State:-Categorical data-SRS-All expected counts greater than 5

Check:-Gender and subjectare categories-Data collected randomly-All counts greater than 5

Conditions met, chi squared modelChi squared test for independence

P(x>50)= .0001Ho: there is no association between gender and subjectHa: there is an association between gender and subject

DF=5

Gender and subject chi squared test

• We reject the Ho because the p-value of .0001 is less than alpha=.05

• We have sufficient evidence that there is an association between gender and what subject you sign out.

Ho: there is no association between gender and sign out subjectHa: there is an association between gender and sign out subject

Conclusion

• Block of the day helps determine what subject • When in study hall, which 3rd of the block you

sign out in has to do with what block of the day you’re in

• Which gender you are affects what subject you sign out in.

Bias and errors

• Gender was based off name and handwriting– Gender could have been wrongly called– Several names could be either male or female

• Monotonous data could have been input wrongly

• Teachers have different lunches, sign-outs during lunch could not be counted

• Teachers have different plan periods during which they have no students to sign-out

Bias and errors (cont.)

• Not all sign-outs were to the bathroom, and we can’t guarantee that all students actually went to the destination they signed

• We assume that student accurately signed out at the time specified.

• Cannot guarantee that every teacher turns their sheets in

Special Thank You…

Santa Claus

OsamaJesus &

ME signing out at

THIS time , going to HEREcoming back NOW