5 Functions

In the last section, you were asked to convert the “smoker” column to logical values. The solution is fairly simple:

birthweight$smoker == "yes"

##  [1] FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE FALSE  TRUE
## [13]  TRUE  TRUE FALSE  TRUE FALSE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE FALSE
## [25] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE FALSE
## [37]  TRUE FALSE FALSE  TRUE  TRUE FALSE

birthweight$smoker <- (birthweight$smoker == "yes")

birthweight

Table 5.1: The birthweight data frame.

ID	birth.date	location	length	birthweight	head.circumference	weeks.gestation	smoker	maternal.age	maternal.cigarettes	maternal.height	maternal.prepregnant.weight	paternal.age	paternal.education	paternal.cigarettes	paternal.height	low.birthweight	geriatric.pregnancy
1107	1/25/1967	General	52	3.23	36	38	FALSE	31	0	164	57	NA	NA	NA	NA	FALSE	FALSE
697	2/6/1967	Silver Hill	48	3.03	35	39	FALSE	27	0	162	62	27	14	0	178	FALSE	FALSE
1683	2/14/1967	Silver Hill	53	3.35	33	41	FALSE	27	0	164	62	37	14	0	170	FALSE	FALSE
27	3/9/1967	Silver Hill	53	3.55	37	41	TRUE	37	25	161	66	46	NA	0	175	FALSE	TRUE
1522	3/13/1967	Memorial	50	2.74	33	39	TRUE	21	17	156	53	24	12	7	179	FALSE	FALSE
569	3/23/1967	Memorial	50	2.51	35	39	TRUE	22	7	159	52	23	14	25	NA	TRUE	FALSE
365	4/23/1967	Memorial	52	3.53	37	40	TRUE	26	25	170	62	30	10	25	181	FALSE	FALSE
808	5/5/1967	Silver Hill	48	2.92	33	34	FALSE	26	0	167	64	25	12	25	175	FALSE	FALSE
1369	6/4/1967	Silver Hill	49	3.18	34	38	TRUE	31	25	162	57	32	16	50	194	FALSE	FALSE
1023	6/7/1967	Memorial	52	3.00	35	38	TRUE	30	12	165	64	38	14	50	180	FALSE	FALSE
822	6/14/1967	Memorial	50	3.42	35	38	FALSE	20	0	157	48	22	14	0	179	FALSE	FALSE
1272	6/20/1967	Memorial	53	2.75	32	40	TRUE	37	50	168	61	31	16	0	173	FALSE	TRUE
1262	6/25/1967	Silver Hill	53	3.19	34	41	TRUE	27	35	163	51	31	16	25	185	FALSE	FALSE
575	7/12/1967	Memorial	50	2.78	30	37	TRUE	19	7	165	60	20	14	0	183	FALSE	FALSE
1016	7/13/1967	Silver Hill	53	4.32	36	40	FALSE	19	0	171	62	19	12	0	183	FALSE	FALSE
792	9/7/1967	Memorial	53	3.64	38	40	TRUE	20	2	170	59	24	12	12	185	FALSE	FALSE
820	10/7/1967	General	52	3.77	34	40	FALSE	24	0	157	50	31	16	0	173	FALSE	FALSE
752	10/19/1967	General	49	3.32	36	40	TRUE	27	12	152	48	37	12	25	170	FALSE	FALSE
619	11/1/1967	Memorial	52	3.41	33	39	TRUE	23	25	181	69	23	16	2	181	FALSE	FALSE
1764	12/7/1967	Silver Hill	58	4.57	39	41	TRUE	32	12	173	70	38	14	25	180	FALSE	FALSE
1081	12/14/1967	Silver Hill	54	3.63	38	38	FALSE	18	0	172	50	20	12	7	172	FALSE	FALSE
516	1/8/1968	Silver Hill	47	2.66	33	35	TRUE	20	35	170	57	23	12	50	186	TRUE	FALSE
272	1/10/1968	Memorial	52	3.86	36	39	TRUE	30	25	170	78	40	16	50	178	FALSE	FALSE
321	1/21/1968	Silver Hill	48	3.11	33	37	FALSE	28	0	158	54	39	10	0	171	FALSE	FALSE
1636	2/2/1968	Silver Hill	51	3.93	38	38	FALSE	29	0	165	61	NA	NA	NA	NA	FALSE	FALSE
1360	2/16/1968	General	56	4.55	34	44	FALSE	20	0	162	57	23	10	35	179	FALSE	FALSE
1388	2/22/1968	Memorial	51	3.14	33	41	TRUE	22	7	160	53	24	16	12	176	FALSE	FALSE
1363	4/2/1968	General	48	2.37	30	37	TRUE	20	7	163	47	20	10	35	185	TRUE	FALSE
1058	4/24/1968	Silver Hill	53	3.15	34	40	FALSE	29	0	167	60	30	16	NA	182	FALSE	FALSE
755	4/25/1968	Memorial	53	3.20	33	41	FALSE	21	0	155	55	25	14	25	183	FALSE	FALSE
462	6/19/1968	Silver Hill	58	4.10	39	41	FALSE	35	0	172	58	31	16	25	185	FALSE	TRUE
300	7/18/1968	Silver Hill	46	2.05	32	35	TRUE	41	7	166	57	37	14	25	173	TRUE	TRUE
1088	7/24/1968	General	51	3.27	36	40	FALSE	24	0	168	53	29	16	0	181	FALSE	FALSE
57	8/12/1968	Memorial	51	3.32	38	39	TRUE	23	17	157	48	NA	NA	NA	NA	FALSE	FALSE
553	8/17/1968	Silver Hill	54	3.94	37	42	FALSE	24	0	175	66	30	12	0	184	FALSE	FALSE
1191	9/7/1968	General	53	3.65	33	42	FALSE	21	0	165	61	21	10	25	185	FALSE	FALSE
431	9/16/1968	Silver Hill	48	1.92	30	33	TRUE	20	7	161	50	20	10	35	180	TRUE	FALSE
1313	9/27/1968	Silver Hill	43	2.65	32	33	FALSE	24	0	149	45	26	16	0	169	TRUE	FALSE
1600	10/9/1968	General	53	2.90	34	39	FALSE	19	0	165	57	NA	NA	NA	NA	FALSE	FALSE
532	10/25/1968	General	53	3.59	34	40	TRUE	31	12	163	49	41	12	50	191	FALSE	FALSE
223	12/11/1968	General	50	3.87	33	45	TRUE	28	25	163	54	30	16	0	183	FALSE	FALSE
1187	12/19/1968	Silver Hill	53	4.07	38	44	FALSE	20	0	174	68	26	14	25	189	FALSE	FALSE

Converting the dates (currently stored as characters) to a more usable format is not as simple, and will require a function.

R is filled with functions. We have already used a few: read.csv(), class(), dim(), mean(), colnames(), as.logical(), and as.numeric(). To find the documentation on a function, use the ? character. This opens a page containing details on the function in the help pane.

5.1 Basic functions

?table
table(birthweight$geriatric.pregnancy, birthweight$low.birthweight)

##        
##         FALSE TRUE
##   FALSE    33    5
##   TRUE      3    1

Functions are invoked by name, with any arguments provided inside of parentheses. For example, the chisq.test() function, which runs a Chi-squared test, requires either a matrix or two vectors as arguments, and provides a number of options that may be set by the user.

?chisq.test
chisq.test(birthweight$geriatric.pregnancy, birthweight$low.birthweight)

## Warning in chisq.test(birthweight$geriatric.pregnancy,
## birthweight$low.birthweight): Chi-squared approximation may be incorrect

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  birthweight$geriatric.pregnancy and birthweight$low.birthweight
## X-squared = 2.7398e-31, df = 1, p-value = 1

If no parameters are provided to the options, the default values are used. In some cases, this works well.

mean(birthweight$birthweight[birthweight$geriatric.pregnancy])

## [1] 3.1125

# the ! character is used for negation
mean(birthweight$birthweight[!birthweight$geriatric.pregnancy])

## [1] 3.333947

Other times, it is necessary to adjust the options in order for a function to behave as you expect.

mean(birthweight$paternal.age)

## [1] NA

mean(birthweight$paternal.age, na.rm = TRUE)

## [1] 28.76316

sd(birthweight$paternal.age, na.rm = TRUE)

## [1] 7.061254

5.2 Combining functions

The “birth.date” column is currently stored as a character vector. But what if we wanted to look at the birth weights of babies born in December? Let’s split the day, month, and year into separate columns.

R has a function called strsplit():

?strsplit
strsplit(birthweight$birth.date, split = "/")

## [[1]]
## [1] "1"    "25"   "1967"
## 
## [[2]]
## [1] "2"    "6"    "1967"
## 
## [[3]]
## [1] "2"    "14"   "1967"
## 
## [[4]]
## [1] "3"    "9"    "1967"
## 
## [[5]]
## [1] "3"    "13"   "1967"
## 
## [[6]]
## [1] "3"    "23"   "1967"
## 
## [[7]]
## [1] "4"    "23"   "1967"
## 
## [[8]]
## [1] "5"    "5"    "1967"
## 
## [[9]]
## [1] "6"    "4"    "1967"
## 
## [[10]]
## [1] "6"    "7"    "1967"
## 
## [[11]]
## [1] "6"    "14"   "1967"
## 
## [[12]]
## [1] "6"    "20"   "1967"
## 
## [[13]]
## [1] "6"    "25"   "1967"
## 
## [[14]]
## [1] "7"    "12"   "1967"
## 
## [[15]]
## [1] "7"    "13"   "1967"
## 
## [[16]]
## [1] "9"    "7"    "1967"
## 
## [[17]]
## [1] "10"   "7"    "1967"
## 
## [[18]]
## [1] "10"   "19"   "1967"
## 
## [[19]]
## [1] "11"   "1"    "1967"
## 
## [[20]]
## [1] "12"   "7"    "1967"
## 
## [[21]]
## [1] "12"   "14"   "1967"
## 
## [[22]]
## [1] "1"    "8"    "1968"
## 
## [[23]]
## [1] "1"    "10"   "1968"
## 
## [[24]]
## [1] "1"    "21"   "1968"
## 
## [[25]]
## [1] "2"    "2"    "1968"
## 
## [[26]]
## [1] "2"    "16"   "1968"
## 
## [[27]]
## [1] "2"    "22"   "1968"
## 
## [[28]]
## [1] "4"    "2"    "1968"
## 
## [[29]]
## [1] "4"    "24"   "1968"
## 
## [[30]]
## [1] "4"    "25"   "1968"
## 
## [[31]]
## [1] "6"    "19"   "1968"
## 
## [[32]]
## [1] "7"    "18"   "1968"
## 
## [[33]]
## [1] "7"    "24"   "1968"
## 
## [[34]]
## [1] "8"    "12"   "1968"
## 
## [[35]]
## [1] "8"    "17"   "1968"
## 
## [[36]]
## [1] "9"    "7"    "1968"
## 
## [[37]]
## [1] "9"    "16"   "1968"
## 
## [[38]]
## [1] "9"    "27"   "1968"
## 
## [[39]]
## [1] "10"   "9"    "1968"
## 
## [[40]]
## [1] "10"   "25"   "1968"
## 
## [[41]]
## [1] "12"   "11"   "1968"
## 
## [[42]]
## [1] "12"   "19"   "1968"

This is a good start. However, the output of strsplit() is a list containing 42 vectors of length 3, while the columns of birthweight are vectors of length 42.

A note on lists:

Lists are ordered collections of objects, which can be of any type. Unlike vectors, lists may contain elements of different types. To subset a list, use the $ or [[ operator.

The unlist() function will “flatten” a list into a vector.

unlist(strsplit(birthweight$birth.date, split = "/"))

##   [1] "1"    "25"   "1967" "2"    "6"    "1967" "2"    "14"   "1967" "3"   
##  [11] "9"    "1967" "3"    "13"   "1967" "3"    "23"   "1967" "4"    "23"  
##  [21] "1967" "5"    "5"    "1967" "6"    "4"    "1967" "6"    "7"    "1967"
##  [31] "6"    "14"   "1967" "6"    "20"   "1967" "6"    "25"   "1967" "7"   
##  [41] "12"   "1967" "7"    "13"   "1967" "9"    "7"    "1967" "10"   "7"   
##  [51] "1967" "10"   "19"   "1967" "11"   "1"    "1967" "12"   "7"    "1967"
##  [61] "12"   "14"   "1967" "1"    "8"    "1968" "1"    "10"   "1968" "1"   
##  [71] "21"   "1968" "2"    "2"    "1968" "2"    "16"   "1968" "2"    "22"  
##  [81] "1968" "4"    "2"    "1968" "4"    "24"   "1968" "4"    "25"   "1968"
##  [91] "6"    "19"   "1968" "7"    "18"   "1968" "7"    "24"   "1968" "8"   
## [101] "12"   "1968" "8"    "17"   "1968" "9"    "7"    "1968" "9"    "16"  
## [111] "1968" "9"    "27"   "1968" "10"   "9"    "1968" "10"   "25"   "1968"
## [121] "12"   "11"   "1968" "12"   "19"   "1968"

When functions are “nested,” the operation in the innermost set of parentheses is performed first. In the example above, the unlist() function is applied to the output of strsplit(), changing a list to a vector. Since the goal was to split one column into three columns, this combination of functions is not effective.

We are going to need to apply some function to each item in the list that allows us to retrieve the first element of the vector.

5.3 The apply() family of functions

One of the most useful groups of functions in R is the apply() family of functions. This group of functions execute a provided function on every element of a data structure.

apply takes a matrix, applies a function either by row or by column, and returns a vector.

# by row
apply(birthweight[,c("maternal.cigarettes", "paternal.cigarettes")], 1, sum)

##  [1] NA  0  0 25 24 32 50 25 75 62  0 50 60  7  0 14  0 37 27 37  7 85 75  0 NA
## [26] 35 19 42 NA 25 25 32  0 NA  0 25 42  0 NA 62 25 25

# by column
apply(birthweight[,c("maternal.cigarettes", "paternal.cigarettes")], 2, sum)

## maternal.cigarettes paternal.cigarettes 
##                 396                  NA

mapply takes a function and applies it to the elements of one or more vectors.

mapply(sum, birthweight$maternal.cigarettes, birthweight$paternal.cigarettes)

##  [1] NA  0  0 25 24 32 50 25 75 62  0 50 60  7  0 14  0 37 27 37  7 85 75  0 NA
## [26] 35 19 42 NA 25 25 32  0 NA  0 25 42  0 NA 62 25 25

tapply takes two vectors, applies a function to the subsets of the first based on the categories in the second vector, and returns a table.

tapply(birthweight$birthweight, birthweight$smoker, mean)

##    FALSE     TRUE 
## 3.509500 3.134091

lapply takes a list, applies a function to each element, and returns a list.

sapply takes a list, applies a function to each element, and returns a list that has been simplified as much as possible.

lapply(strsplit(birthweight$birth.date, split = "/"), '[[', 1)

## [[1]]
## [1] "1"
## 
## [[2]]
## [1] "2"
## 
## [[3]]
## [1] "2"
## 
## [[4]]
## [1] "3"
## 
## [[5]]
## [1] "3"
## 
## [[6]]
## [1] "3"
## 
## [[7]]
## [1] "4"
## 
## [[8]]
## [1] "5"
## 
## [[9]]
## [1] "6"
## 
## [[10]]
## [1] "6"
## 
## [[11]]
## [1] "6"
## 
## [[12]]
## [1] "6"
## 
## [[13]]
## [1] "6"
## 
## [[14]]
## [1] "7"
## 
## [[15]]
## [1] "7"
## 
## [[16]]
## [1] "9"
## 
## [[17]]
## [1] "10"
## 
## [[18]]
## [1] "10"
## 
## [[19]]
## [1] "11"
## 
## [[20]]
## [1] "12"
## 
## [[21]]
## [1] "12"
## 
## [[22]]
## [1] "1"
## 
## [[23]]
## [1] "1"
## 
## [[24]]
## [1] "1"
## 
## [[25]]
## [1] "2"
## 
## [[26]]
## [1] "2"
## 
## [[27]]
## [1] "2"
## 
## [[28]]
## [1] "4"
## 
## [[29]]
## [1] "4"
## 
## [[30]]
## [1] "4"
## 
## [[31]]
## [1] "6"
## 
## [[32]]
## [1] "7"
## 
## [[33]]
## [1] "7"
## 
## [[34]]
## [1] "8"
## 
## [[35]]
## [1] "8"
## 
## [[36]]
## [1] "9"
## 
## [[37]]
## [1] "9"
## 
## [[38]]
## [1] "9"
## 
## [[39]]
## [1] "10"
## 
## [[40]]
## [1] "10"
## 
## [[41]]
## [1] "12"
## 
## [[42]]
## [1] "12"

sapply(strsplit(birthweight$birth.date, split = "/"), '[[', 1)

##  [1] "1"  "2"  "2"  "3"  "3"  "3"  "4"  "5"  "6"  "6"  "6"  "6"  "6"  "7"  "7" 
## [16] "9"  "10" "10" "11" "12" "12" "1"  "1"  "1"  "2"  "2"  "2"  "4"  "4"  "4" 
## [31] "6"  "7"  "7"  "8"  "8"  "9"  "9"  "9"  "10" "10" "12" "12"

The result of this nested pair of functions is a vector of months encoded as numbers stored as characters.

5.4 Custom functions

What if we want to do this for all three fields, but we don’t want to write the code three times?

Take a few minutes to dissect the following function, working from the inside out. What does each piece do?

# custom function takes a vector of dates and returns a data frame with columns day, month, and year
split_MMDDYYYY <- function(date_vector){
  date_list = lapply(seq(1:3), function(i){
    as.integer(sapply(strsplit(date_vector, split = "/"), '[[', i))
  })
  names(date_list) = c("month", "day", "year")
  as.data.frame(do.call("cbind", date_list))
}

split_MMDDYYYY(birthweight$birth.date)

Table 5.2: Results of split_MMDDYYYY(birthweight$birth.date).

month	day	year
1	25	1967
2	6	1967
2	14	1967
3	9	1967
3	13	1967
3	23	1967
4	23	1967
5	5	1967
6	4	1967
6	7	1967
6	14	1967
6	20	1967
6	25	1967
7	12	1967
7	13	1967
9	7	1967
10	7	1967
10	19	1967
11	1	1967
12	7	1967
12	14	1967
1	8	1968
1	10	1968
1	21	1968
2	2	1968
2	16	1968
2	22	1968
4	2	1968
4	24	1968
4	25	1968
6	19	1968
7	18	1968
7	24	1968
8	12	1968
8	17	1968
9	7	1968
9	16	1968
9	27	1968
10	9	1968
10	25	1968
12	11	1968
12	19	1968

birthweight <- cbind(birthweight, split_MMDDYYYY(birthweight$birth.date))

The cbind() function combines objects by column. Now that we have the birth month in its own column, we can get the mean of birth weight by month.

tapply(birthweight$birthweight, birthweight$month, mean)

##        1        2        3        4        5        6        7        8 
## 3.215000 3.600000 2.933333 3.062500 2.920000 3.273333 3.105000 3.630000 
##        9       10       11       12 
## 2.965000 3.395000 3.410000 4.035000

5.5 Exercise 3: summarizing the data

Pick one or more of the following questions to answer, or come up with one of your own. Work together. Once you’ve answered a question in one way, can you come up with alternate code that generates the same answer?

• Are preterm babies more likely to have low birth weight?
• What is the ratio of maternal cigarettes to paternal cigarettes for births at each of the hospitals?
• Do taller mothers have taller partners? Do they have longer babies?

5.6 Merging data frames

For this example experiment, we also have placental miRNA expression data. These values are not from real samples, but have been manipulated to roughly reproduce the effect observed by Maccani et al. 2010.

download.file("https://raw.githubusercontent.com/ucdavis-bioinformatics-training/2022_February_Introduction_to_R_for_Bioinformatics/main/miRNA.csv", "miRNA.csv")
mir <- read.csv("miRNA.csv", row.names = 1)

mir

Table 5.3: The mir data frame.

	sample.27	sample.1522	sample.569	sample.365	sample.1369	sample.1023	sample.1272	sample.1262	sample.575	sample.792	sample.752	sample.619	sample.1764	sample.516	sample.272	sample.1388	sample.1363	sample.300	sample.57	sample.431	sample.532	sample.223	sample.1107	sample.697	sample.1683	sample.808	sample.822	sample.1016	sample.820	sample.1081	sample.321	sample.1636	sample.1360	sample.1058	sample.755	sample.462	sample.1088	sample.553	sample.1191	sample.1313	sample.1600	sample.1187
miR-16	46	56	47	54	56	59	49	55	62	63	46	52	46	61	49	46	61	60	46	70	60	60	57	68	49	59	54	69	58	55	68	63	70	77	56	65	42	63	66	64	50	57
miR-21	52	43	40	35	59	47	42	45	55	45	42	43	40	51	43	44	47	48	39	51	44	46	49	47	48	56	52	41	55	52	46	39	57	55	46	58	54	54	48	47	44	46
miR-146a	98	97	87	96	84	96	88	97	96	104	103	92	98	97	91	105	77	89	105	84	94	87	116	98	98	101	86	98	102	93	125	104	111	124	101	101	107	106	102	104	111	86
miR-182	53	45	63	41	46	50	49	50	62	51	64	58	57	59	55	60	60	65	40	48	49	52	48	57	55	74	49	51	53	52	60	43	46	56	50	60	63	60	50	42	67	43

In this object, the rows are the gene identifiers, and the columns are the samples.

mir <- as.data.frame(t(mir))
mir$ID <- gsub("sample.", "", rownames(mir))
experiment <- merge(birthweight, mir)

What did these lines of code do? Explore each of them, looking up the function help using ? as necessary.

experiment

Table 5.4: The experiment data frame.

ID	birth.date	location	length	birthweight	head.circumference	weeks.gestation	smoker	maternal.age	maternal.cigarettes	maternal.height	maternal.prepregnant.weight	paternal.age	paternal.education	paternal.cigarettes	paternal.height	low.birthweight	geriatric.pregnancy	month	day	year	miR-16	miR-21	miR-146a	miR-182
27	3/9/1967	Silver Hill	53	3.55	37	41	TRUE	37	25	161	66	46	NA	0	175	FALSE	TRUE	3	9	1967	46	52	98	53
57	8/12/1968	Memorial	51	3.32	38	39	TRUE	23	17	157	48	NA	NA	NA	NA	FALSE	FALSE	8	12	1968	46	39	105	40
223	12/11/1968	General	50	3.87	33	45	TRUE	28	25	163	54	30	16	0	183	FALSE	FALSE	12	11	1968	60	46	87	52
272	1/10/1968	Memorial	52	3.86	36	39	TRUE	30	25	170	78	40	16	50	178	FALSE	FALSE	1	10	1968	49	43	91	55
300	7/18/1968	Silver Hill	46	2.05	32	35	TRUE	41	7	166	57	37	14	25	173	TRUE	TRUE	7	18	1968	60	48	89	65
321	1/21/1968	Silver Hill	48	3.11	33	37	FALSE	28	0	158	54	39	10	0	171	FALSE	FALSE	1	21	1968	68	46	125	60
365	4/23/1967	Memorial	52	3.53	37	40	TRUE	26	25	170	62	30	10	25	181	FALSE	FALSE	4	23	1967	54	35	96	41
431	9/16/1968	Silver Hill	48	1.92	30	33	TRUE	20	7	161	50	20	10	35	180	TRUE	FALSE	9	16	1968	70	51	84	48
462	6/19/1968	Silver Hill	58	4.10	39	41	FALSE	35	0	172	58	31	16	25	185	FALSE	TRUE	6	19	1968	65	58	101	60
516	1/8/1968	Silver Hill	47	2.66	33	35	TRUE	20	35	170	57	23	12	50	186	TRUE	FALSE	1	8	1968	61	51	97	59
532	10/25/1968	General	53	3.59	34	40	TRUE	31	12	163	49	41	12	50	191	FALSE	FALSE	10	25	1968	60	44	94	49
553	8/17/1968	Silver Hill	54	3.94	37	42	FALSE	24	0	175	66	30	12	0	184	FALSE	FALSE	8	17	1968	63	54	106	60
569	3/23/1967	Memorial	50	2.51	35	39	TRUE	22	7	159	52	23	14	25	NA	TRUE	FALSE	3	23	1967	47	40	87	63
575	7/12/1967	Memorial	50	2.78	30	37	TRUE	19	7	165	60	20	14	0	183	FALSE	FALSE	7	12	1967	62	55	96	62
619	11/1/1967	Memorial	52	3.41	33	39	TRUE	23	25	181	69	23	16	2	181	FALSE	FALSE	11	1	1967	52	43	92	58
697	2/6/1967	Silver Hill	48	3.03	35	39	FALSE	27	0	162	62	27	14	0	178	FALSE	FALSE	2	6	1967	68	47	98	57
752	10/19/1967	General	49	3.32	36	40	TRUE	27	12	152	48	37	12	25	170	FALSE	FALSE	10	19	1967	46	42	103	64
755	4/25/1968	Memorial	53	3.20	33	41	FALSE	21	0	155	55	25	14	25	183	FALSE	FALSE	4	25	1968	56	46	101	50
792	9/7/1967	Memorial	53	3.64	38	40	TRUE	20	2	170	59	24	12	12	185	FALSE	FALSE	9	7	1967	63	45	104	51
808	5/5/1967	Silver Hill	48	2.92	33	34	FALSE	26	0	167	64	25	12	25	175	FALSE	FALSE	5	5	1967	59	56	101	74
820	10/7/1967	General	52	3.77	34	40	FALSE	24	0	157	50	31	16	0	173	FALSE	FALSE	10	7	1967	58	55	102	53
822	6/14/1967	Memorial	50	3.42	35	38	FALSE	20	0	157	48	22	14	0	179	FALSE	FALSE	6	14	1967	54	52	86	49
1016	7/13/1967	Silver Hill	53	4.32	36	40	FALSE	19	0	171	62	19	12	0	183	FALSE	FALSE	7	13	1967	69	41	98	51
1023	6/7/1967	Memorial	52	3.00	35	38	TRUE	30	12	165	64	38	14	50	180	FALSE	FALSE	6	7	1967	59	47	96	50
1058	4/24/1968	Silver Hill	53	3.15	34	40	FALSE	29	0	167	60	30	16	NA	182	FALSE	FALSE	4	24	1968	77	55	124	56
1081	12/14/1967	Silver Hill	54	3.63	38	38	FALSE	18	0	172	50	20	12	7	172	FALSE	FALSE	12	14	1967	55	52	93	52
1088	7/24/1968	General	51	3.27	36	40	FALSE	24	0	168	53	29	16	0	181	FALSE	FALSE	7	24	1968	42	54	107	63
1107	1/25/1967	General	52	3.23	36	38	FALSE	31	0	164	57	NA	NA	NA	NA	FALSE	FALSE	1	25	1967	57	49	116	48
1187	12/19/1968	Silver Hill	53	4.07	38	44	FALSE	20	0	174	68	26	14	25	189	FALSE	FALSE	12	19	1968	57	46	86	43
1191	9/7/1968	General	53	3.65	33	42	FALSE	21	0	165	61	21	10	25	185	FALSE	FALSE	9	7	1968	66	48	102	50
1262	6/25/1967	Silver Hill	53	3.19	34	41	TRUE	27	35	163	51	31	16	25	185	FALSE	FALSE	6	25	1967	55	45	97	50
1272	6/20/1967	Memorial	53	2.75	32	40	TRUE	37	50	168	61	31	16	0	173	FALSE	TRUE	6	20	1967	49	42	88	49
1313	9/27/1968	Silver Hill	43	2.65	32	33	FALSE	24	0	149	45	26	16	0	169	TRUE	FALSE	9	27	1968	64	47	104	42
1360	2/16/1968	General	56	4.55	34	44	FALSE	20	0	162	57	23	10	35	179	FALSE	FALSE	2	16	1968	70	57	111	46
1363	4/2/1968	General	48	2.37	30	37	TRUE	20	7	163	47	20	10	35	185	TRUE	FALSE	4	2	1968	61	47	77	60
1369	6/4/1967	Silver Hill	49	3.18	34	38	TRUE	31	25	162	57	32	16	50	194	FALSE	FALSE	6	4	1967	56	59	84	46
1388	2/22/1968	Memorial	51	3.14	33	41	TRUE	22	7	160	53	24	16	12	176	FALSE	FALSE	2	22	1968	46	44	105	60
1522	3/13/1967	Memorial	50	2.74	33	39	TRUE	21	17	156	53	24	12	7	179	FALSE	FALSE	3	13	1967	56	43	97	45
1600	10/9/1968	General	53	2.90	34	39	FALSE	19	0	165	57	NA	NA	NA	NA	FALSE	FALSE	10	9	1968	50	44	111	67
1636	2/2/1968	Silver Hill	51	3.93	38	38	FALSE	29	0	165	61	NA	NA	NA	NA	FALSE	FALSE	2	2	1968	63	39	104	43
1683	2/14/1967	Silver Hill	53	3.35	33	41	FALSE	27	0	164	62	37	14	0	170	FALSE	FALSE	2	14	1967	49	48	98	55
1764	12/7/1967	Silver Hill	58	4.57	39	41	TRUE	32	12	173	70	38	14	25	180	FALSE	FALSE	12	7	1967	46	40	98	57