Data - Technical University of Denmark

eNote 13

eNote 13

Data

1

2

eNote 13 INDHOLD

Indhold 13 Data 13.1 Introduction, Randomized Blocks Design 13.2 General factor structure . . . . . . . . . . 13.3 Hierarchial . . . . . . . . . . . . . . . . . . 13.4 Split-plot . . . . . . . . . . . . . . . . . . . 13.5 Analysis of covariance . . . . . . . . . . . 13.6 Random coefficient analysis . . . . . . . . 13.7 Repeated measures . . . . . . . . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

1 3 6 15 17 22 27 31

13.1 Introduction, Randomized Blocks Design NIR prediction of HPLC measurements, complete data Key words: Randomized Blocks, Paired design Description In a pharmaceutical company the use of NIR (Near Infrared Reflectance) spectroscopy was investigated as an alternative to the more cumbersome (and expensive) HPLC method to determine the content of active substance in tablets. Number of observations: 10 Variable Description hplc nir

The HPLC measurement The NIR predicted value

eNote 13

13.1 INTRODUCTION, RANDOMIZED BLOCKS DESIGN

3

Source Brockhoff and Thierry-Carstensen (2003). Test set validation using simple statistical methods. Internal Report Analysis Depending on the purpose: 1)Linear regression. 2) Randomized block design analysis: ANOVA with random tablet effect and fixed method (NIR/HPLC) effect or equivalently a paired t-test. Get the data

eNote 13


4

NIR prediction of HPLC measurements, missing data Key words: Randomized Blocks, Paired design, missing values Description In a pharmaceutical company the use of NIR (Near Infrared Reflectance) spectroscopy was investigated as an alternative to the more cumbersome (and expensive) HPLC method to determine the content of active substance in tablets. Number of observations: 20 tablets Missing values: 5 on each variable. Variable

Description

hplc nir

The HPLC measurement The NIR predicted value

Source Brockhoff and Thierry-Carstensen (2003). Test set validation using simple statistical methods. Submitted to: Journal of Chemometrics. Analysis Randomized block design analysis: ANOVA with random tablet effect and fixed method (NIR/HPLC) effect. Get the data

eNote 13


5

Sensory evaluation of cookies Key words: Randomized blocks. Description Ten different chill or freezer storage treatments were tested on a type of cookies, and after storage the cookies were evaluated by a sensory panel composed of 13 assessors. Each assessor tasted the cookies in randomized order, and tasted each type twice. At each test the assessor gave a score for each of the properties: colour, consistency, taste, quality (combined). The score was an integer between 1 and 11 with 11 as the best. One assessor did not give any score for quality. Number of observations: 260 Variable Description assessor treatm colour cons taste quality

Numbered 1-13 Numbered 46-55 Sensory evaluation score of colour intensity Sensory evaluation score of consistency Sensory evaluation score of taste intensity Sensory evaluation score of quality

Source The Royal Veterinary and Agricultural University, Denmark. Analysis Randomized block (fixed treatment, random assessor) for each of the four properties. Get the data

eNote 13

13.2 GENERAL FACTOR STRUCTURE

6

13.2 General factor structure Drying of beech wood planks Key words: Factor structure, Randomized blocks with two-way full factorial treatment structure. Description To investigate the effect of drying of beech wood on the humidity percentage, the following experiment was conducted. Each of 20 planks was dried in a certain period of time. Then the humidity percentage was measured in 5 debths (1,3,5,7,9) and 3 widths (1,2,3) for each plank: debth 1: debth 5: debth 9: debth 3: debth 7:

close to the top in the center close to the bottom between 1 and 5 between 5 and 9

width 1: width 3: width 2:

close to the side in the center between 1 and 3

Number of observations: 300 (20 planks) Variable

Description

plank width debth humidity

Numbered 1-20 Numbered 1,2,3 Numbered 1,3,5,7,9 Humidity percentage

Source The Royal Veterinary and Agricultural University, Denmark. Analysis Randomized block (fixed two-way treatment with interaction, random assessor) Get the data

eNote 13


7

Maillard reaction in milk powder Key words: Factor structure, Randomized blocks with two-way full factorial treatment structure, repeated measurements. Description In an experiment with production of milk powder the effect of water activity and temperature on the formation of maillard reaction products was investigated. There were 9 treatment combinations of the two factors and three replicates (blocks) of the experiment giving a total of 27 productions. The factors and levels were: water activity (approx. 0.15, 0.25 and 0.10, coded as 1, 2, 3 in the data set), and temperature (100 C, 110 C, 120 C, 140 C). The 27 samples were stored and measurements were made after 4, 6 and 8 weeks. The measurements (response variables) were: concentration of maillard reaction products (which may give a bad taste), and sensory evaluation of taste (high = good taste). Number of observations: 27 Variable Description water temp rep maill4, maill6, maill8 taste4, taste6, taste8

Numbered 1,2,3 Values 100,110,120,140 The block factor numbered 1,2,3 Maillard concentration after 4, 6 and 8 weeks sensory taste score after 4, 6 and 8 weeks

Source The Royal Veterinary and Agricultural University, Denmark. Analysis Randomized block (fixed two-way treatment with interaction, random block) for each of the six variables. Repeated measures analysis for each set of three time repeated measurements. Get the data

eNote 13


8

Maillard reaction in milk powder, version II Key words: Factor structure, Randomized blocks with two-way full factorial treatment structure, repeated measurements. Description In an experiment with production of milk powder the effect of water activity and temperature on the formation of maillard reaction products was investigated. There were 9 treatment combinations of the two factors and three replicates (blocks) of the experiment giving a total of 27 productions. The factors and levels were: water activity (approx. 0.15, 0.25 and 0.10, coded as 1, 2, 3 in the data set), and temperature (100 C, 110 C, 120 C, 140 C). The 27 samples were stored and measurements were made after 4, 6 and 8 weeks. The measurements (response variables) were: concentration of maillard reaction products (which may give a bad taste), and sensory evaluation of taste (high = good taste). Number of observations: 81 Variable Description water temp rep storage maillard taste

Numbered 1,2,3 Values 100,110,120,140 The block factor numbered 1,2,3 Storage time 4,6,8 Maillard concentration sensory taste score

Source The Royal Veterinary and Agricultural University, Denmark. Analysis Randomized block (fixed two-way treatment with interaction, random block) for each of the six variables. Repeated measures analysis for each set of three time repeated measurements. Get the data

eNote 13


9

Colour of spinage Key words: Factor structure, Randomized blocks with three-way full factorial treatment structure. Description Spinage heated to 90 or 100 degrees Celcius was vacuum packed and stored for 0, 1 or 2 weeks before the packs were opened and chill stored in normal atmosphere for 0, 1 or 2 days. Then the colour was measured on a Hunter Lab. Two of the colour coordinates, a and b (measuring respectively something like red and yellow colour), were recorded and are given in the data set below. The variable batch is a blocking variable referring to two batches of spinage. Number of observations: 36 Variable Description batch temp weeks days a b

Values A,B (blocking factor) Values 90,100(celcius) Values 0,1,2 (pre-storage time) Values 0,1,2 (post-chill-storage time) measure of red colour intensity measure of yellow colour intensity

Source The Royal Veterinary and Agricultural University, Denmark. Analysis Randomized block (fixed three-way treatment with interaction, random block) for each of the two variables. Get the data

eNote 13


10

Rooting of Hibiscus Key words: Factor structure. Description The data origin from an experiment investigating the effect of conductivity in the water bath on the rooting of Hibiscus. There were 16 water baths, four for each of the four levels of conductivity: 0.5, 1.0, 1.5 and 2.0 micro-Siemens per square meter (coded as 1, 2, 3, 4 in the data set). There were 10 cuttings of each of two varieties (Red rosa-sinensis, and Holiday) in each water bath, but only data from the latter two varieties are used here. The 30 cuttings were placed at random in the water bath. For each cutting the number roots (rootno) and the weight of roots (rootwt) were registered after 28 days. The four conductivity treatments were randomized on the 16 water baths. Number of observations: 320 Variable Description variety bathno conduct rootno rootwt

Values h,r Numbered 1-16 Numbered 1-4 Number of roots on the cutting Weight of the roots on the cutting

Source Lise Bertram, The Royal Veterinary and Agricultural University, Denmark. Analysis Split-plot for each of the two variables. Get the data

eNote 13


11

Desease in cucumbers Key words: Factor structure. Description A greenhouse experiment was carried out to investigate how the spread of a disease in cucumbers depended on climate and on amount of fertilizer for two varieties. The following data are an extract from the experiment. Two climates were used, (1) change to day temperature 3 hours before sunrise, and (2) normal change to day temperature. Three amounts of fertilizer were applied, normal (2.0 units), high (3.5 units), and extra high (4.0 units). The two varieties were Aminex and Dalibor. At a certain time the plants were ‘standardized’ to have equally many leaves, and then (on day 0, say) the plants were contaminated with the disease. On 8 particular subsequent days the amount of infection (in percent) was registered. From the resulting curve of infection two summary measures were calculated (in a way not specified here), namely the rate of spread of the disease, and the level of infection at the end of the period. There were 3 blocks each consisting of 2 sections, a section being a part of the greenhouse. Each section consisted of 3 plots, which were each divided into 2 subplots, each of which had 6-8 plants. Thus there were a total of 36 subplots. Results were recorded for each subplot. The experimental factors were randomly allocated to the different units as follows: the 2 climates were allocated to the 2 sections within each block, the 3 amounts of fertilizer were allocated to the 3 plots within each section, and finally the 2 varieties were allocated to the 2 subplots within each plot. Thus, in summary, there were 3 blocks 2 sections per block (given 2 different climates) 3 plots per section (given 3 different amounts of fertilizer) 2 subplots per plot (with 2 different varieties) Number of observations: 36

eNote 13


Variable

Description

block section plot climate fert variety rate level

Numbered 1-3 Numbered 1-6 Numbered 1-18 Numbered 1,2 Values 2.0,3.5,4.0 Values aminex,dalibor Rate of spread of the disease Level of infection at the end of the period

12

Source Eigil de Neerg˚ard, Department of Plant Pathology, The Royal Veterinary and Agricultural University, Denmark. Analysis Get the data

eNote 13


13

Tractor comparison Key words: Factor structure. Description In a comparison of two tractors, five drivers used each of the tractors to plough a field of a certain size. The time in minutes was recorded. This was repeated on three different days (with the same drivers and tractors). Number of observations: 30 Variable Description day tractor driver time

Numbered 1,2,3 Numbered 1,2 Values a,b,c,d,e,f Ploughing time

Source The Royal Veterinary and Agricultural University, Denmark. Analysis Get the data

eNote 13


14

Sensory evaluation of spinage Key words: General factor structure. Description Spinage heated to 90 or 100 degrees Celcius was vacuum packed and stored for 0, 1 or 2 weeks before the packs were opened and chill stored in normal atmosphere for 0, 1 or 2 days. The variable batch is a blocking variable referring to two batches of spinage. The products from each treatment combination from each batch were assessed by (some of) 7 assessors who gave a score (between 0 and 15) for each of 6 different sensory properties (see the list further below). There was one sesssion for each combination of batch and weeks, and at each session the assessors evaluated the same 6 products (6 combinations of days and temperature). Note that not all assessors were present at all sessions. The results, with one line per evaluation, are given in the order: weeks of storage, days after opening, batch, temperature, session number, assessor number, and the six sensory properties hay flavour 1, hay flavour 2, hay taste, spinage flavour 1, spinage flavour 2, spinage taste. Number of observations: 36 Variable weeks days batch temp session assessor hayflav1,hayflav2,haytaste spiflav1,spiflav2,spitaste

Description Values 0,1,2 (pre-storage time) Values 0,1,2 (post-chill-storage time) Values A,B (blocking factor) Values 90,100(celcius) Numbered 1-6 Numbered 1-7 Sensory scores Sensory scores


eNote 13

13.3 HIERARCHIAL

15

13.3 Hierarchial Lactase in piglets Key words: Hierarchial Description As part of a larger study of the intestinal health in newborn piglets, the gut enzyme lactase was measured in 20 piglets taken from 5 different litters. For each of the 20 piglets the lactase level was measured in three different regions. At the time the measurement was taken the piglet was either unborn (status=1) or newborn (status=2). These data are kindly provided by Charlotte Reinhard Bjørnvad, Department of Animal Science and Animal Health, Division of Animal Nutrition, Royal Veterinary and Agricultural University. Number of observations: 60 Variable Description litter pig region status loclact

Litter identification, numbered 1–5 Piglet identification, numbered 1–22 Measurement region identification, numbered 1–3 Status identification, numbered 1,2 Log transformed lactase measurement

Source Charlotte Reinhard Bjørnvad, Department of Animal Science and Animal Health, Division of Animal Nutrition, Royal Veterinary and Agricultural University. Analysis Two or three layer hierarchial model with mean value depending on region and status. Get the data

eNote 13

13.3 HIERARCHIAL

16

Fructification of blueberries Key words: Hierarchial Description In an experiment with 4 varieties of blueberries the fructification (the number of berries as percent of the number of flowers earlier in the season) was determined for 5 twigs on each of 6 bushes for every variety. The data, which are part of a larger experiment carried out by B. Falk Pedersen Number of observations: 120 Variable Description sort bush fruct

Sort identification, numbered 1–4 Bush identification, numbered 1–24 Fructification (the number of berries as percent of the number of flowers earli

Source B. Falk Pedersen, The Royal Veterinary and Agricultural University, Denmark. Analysis Two layer hierarchial model with sort as systematic effect. Get the data

eNote 13

13.4 SPLIT-PLOT

17

13.4 Split-plot Effect of nitrogen fertilizer on yield of oats Key words: Split-plot Description Three different varieties of oats and four different levels of nitrogen fertilizer (including 0) were investigated. A split-plot design with 6 blocks was used. Number of observations: 72 Variable Description block variety fertil yield

Values 1-6 Values v1,v2,v3 Values n0,n1,n2,n3 yield measurement

Source The Royal Veterinary and Agricultural University, Denmark. Analysis Split-plot structure. Get the data

eNote 13

13.4 SPLIT-PLOT

18

Tenderness of pork-meat paragraphKey words: Split-plot Description To investigate the effect of the cooling process on the tenderness of meat, 24 porks were slaughtered and cut in halves (right and left side). One side was then cooled by tunnelcooling (a very quick cooling denoted ‘TC’ below) and the other side by (conventional) fast cooling (denoted ‘FC’ below). Furthermore the pigs were divided into two groups: 12 pigs with high pH (ph-group 3) and 12 pigs with low pH (ph-group 2). Two registrations associated with tenderness are recorded below: a sensory (subjective) evaluation of tenderness (denoted tender) and the lenghts of ‘sarcomers’. Long sarcomers are suspected to be accociated with less tender meat and could be caused by too fat cooling. Number of observations: 48 Variable Description pigno phgroup cooling sarcomer tender

Pig identification, numbered 73-96 Values 2,3 Values FC,TC lenghts of sarcomer sensory evaluation of tenderness

Source Anders Juul Møller, The Royal Veterinary and Agricultural University, Denmark. Analysis Split-plot for each of the two variables. Get the data

eNote 13

19

13.4 SPLIT-PLOT

Rancidness of steaks Key words: Split-plot Description In order to investigate the effect of two different types of feed (1 and 2) and 6 different storage conditions on the rancidness of steaks from cattle given the feeds, 4 cows were randomized on the two types of feed so that 2 cows were given each type. After slaughtering 6 steaks from each animal were used in a storage experiment. Two types of packaging (A and B) were used along with 3 storage periods (2, 5, and 8 weeks). After the storage period the rancidness of each steak was determined by an LTBA-measurement. The data, which are part of a larger experiment, are given in the following table:

Animal 1 2 3 4

Feed 1 2 1 2

2 2.0 0.8 1.2 0.4

A 5 2.3 1.7 2.1 0.9

8 2.3 1.4 2.7 1.3

2 0.6 0.4 0.9 0.1

B 5 2.1 0.8 1.5 1.1

Number of observations: 24 Variable Description animal feed pack storage LTBA

Cow identification, numbered 1-4 Values 1,2 Values A,B Values 2, 5, 8 weeks rancidness measurement

Source The Royal Veterinary and Agricultural University, Denmark. Analysis Split-plot with 3-way ANOVA treatment structure. Get the data

8 2.1 1.2 1.9 0.9

eNote 13

20

13.4 SPLIT-PLOT

Yield of wheat Key words: Split-plot. Description An experiment with 6 varieties of wheat concerning the treatment of a fungus attack was carried out on an experimental field with 5 blocks each consisting of 12 plots. The experimental design and the yield (hkg/ha) for each plot are given in the following table, where the treatment (T=treated, U=untreated) and the variety (an=anja, ci=citadel, ko=kosack, kr=kraka, sl=sleipner, vu=vuka) are also given. U kr 58.5

U sl 58.6

U ko 59.6

U an 32.8

U ci 57.8

U vu 30.6

T ko 75.2

T sl 74.2

T vu 63.1

T ci 76.4

T an 69.4

T kr 75.6

U an 30.5

U vu 28.5

U sl 52.0

U kr 54.1

U ko 56.1

U ci 54.4

T ci 79.8

T ko 74.4

T vu 62.2

T sl 76.5

T an 65.4

T kr 64.8

T kr 64.2

T ko 75.2

T ci 80.1

T an 61.3

T vu 57.9

T sl 78.2

U vu 27.1

U kr 55.0

U an 31.4

U ko 62.7

U ci 60.1

U sl 59.5

U an 26.7

U sl 54.9

U kr 47.9

U ci 54.7

U vu 24.4

U ko 53.8

T vu 57.3

T ko 77.2

T ci 84.4

T kr 62.7

T an 58.9

T sl 82.2

T an 61.9

T sl 80.2

T ko 73.3

T ci 77.5

T vu 63.1

T kr 62.1

U ci 53.2

U vu 25.9

U sl 60.6

U ko 60.4

U kr 52.9

U an 31.1

Number of observations: 60 Variable Description block treat variety yield

Numbered 1-5 Values U, T Values an, ci, ko, kr, sl, vu Measured in hkg/ha

eNote 13

13.4 SPLIT-PLOT

Source The Royal Veterinary and Agricultural University, Denmark. Analysis Split-plot with blocks. Get the data

21

eNote 13

22

13.5 ANALYSIS OF COVARIANCE

13.5 Analysis of covariance Hormone treatment of steers Key words: Randomized block, analysis of covariance. Description In an experiment with steers the influence of 4 hormone treatments (1,2,3,4) on the weight of kidney fat was examined. A total of 16 steers in 4 blocks were used distributed with 4 on each hormone treatment. The results can be seen in the table below where for each steer the weight of the animal before the hormone treatment (in kg) and the weight Y of kidney fat (in gram) a suitable time period after the hormone treatment is given. The weight of the animal before the hormone treatment is recorded as a covariate with the aim of reducing the random variation as described above.

Block 1 Block 2 Block 3 Block 4

1 Weight 560 470 410 500

Y 1330 1320 1270 1320

Hormone treatment 2 3 Weight Y Weight Y 440 1280 530 1290 440 1270 510 1300 360 1270 380 1240 460 1280 500 1290

Number of observations: 16 Variable Description block treat weight Y

Numbered 1-4 Numbered 1-4 Initial weight (kg) Weight of kidney fat (gram)

Source Mead and Curnow, 1983)[section 8.8]. Analysis Randomized block, analysis of covariance.

4 Weight 690 420 430 540

Y 1340 1250 1260 1310

eNote 13

Get the data


23

eNote 13


24

Concentration of a hormone in cattle Key words: Analysis of covariance, baseline measurements Description In an experiment the effect of 3 feed compositions on the concentration of a particular hormone in cattle was investigated. There were 9, 12, and 11 cows respectively in the 3 treatment groups, and for every cow the concentration of the hormone was measured before the start of the experiment and again after a certain period of feeding with experimental compositions. Number of observations: 32 Variable Description feed initial final D

Numbered 1-3 Initial concentration measurement Final concentration measurement final-initial

Source The Royal Veterinary and Agricultural University, Denmark. Analysis Analysis of covariance better than analysis of differences. Get the data

eNote 13


25

BIB example with different slopes Key words: Balanced Incomplete Block, Analysis of Covariance Description Four treatments were given to 24 experimental units partitioned into 8 blocks of size 3. This means that only three out of four treatments is given in each block, but in such a way that each treatment occurs equally often (6 times) AND such that each pair of treatments ”meet”equally often (4 times). The response is Y and the covariate is X. Number of observations: 24 Variable Description id blk trt y x

Observation number 1-24 Block number 1-8 Treatment number 1-4 Reponse Covariate

Source Littell et al. (1996). Analysis Balanced Incomplete Block, Analysis of Covariance Get the data

eNote 13


26

Growth of trees Key words: Analysis of covariance, baseline measurements Description In a block design 3 soil treatments were compared with respect to the 5-year height increase of 2 year old trees. Each of the 11 blocks consisted of 3 plots which were randomized on the 3 soil treatments. The results are the average 5-year increase (in feet) for each plot. The average starting height H (also in feet) for each plot was also recorded. Number of observations: 33 Variable Description block treat height increase Source Freese (1967). Analysis Get the data

Numbered 1-11 Numbered 1-3 Starting height in feet Increase in feet

eNote 13

13.6 RANDOM COEFFICIENT ANALYSIS

27

13.6 Random coefficient analysis Constructed data Key words: Random coefficient analysis. Description Two different responses were recorded for 10 different x-values on each of 10 subjects. Number of observations: 100 Variable Description subjcet x y1 y2

Numbered 1-10 x-measurement Response 1 Response 2

Source Per Bruun Brockhoff, The Royal Veterinary and Agricultural University, Denmark. Analysis Random coefficient analysis. Response y1 has highly structured (linear) patterns. Response y2 has un-structured (linear) patterns. Get the data

eNote 13


28

Consumer preference mapping of carrots Key words: Random coefficient analysis. Description In a consumer study 103 consumers scored their preference of 12 danish carrot types on a scale from 1 to 7. Moreover the consumers scored the degree of sweetness, bitterness and crispiness in the products. The carrots were harvested in autumn 1996 and tested in march 1997. A number of background information variables were recorded for each consumer: Frequency: ”How often do you eat carrots?” 1. Once a week or more 2. Once every 2 weeks 3. once every 3 weeks 4. At least once a month 5. Less than once a month Gender: 1. male 2. female Age: 1. -25 y 2. 26-40 y 3. 41-60 4. 61Homesize: (number of persons in the household) 1. 1 or 2 persons 2. 3 or more persons Work: (7 different types of employment) 1. Unskilled worker (no education)

eNote 13


29

2. Skilled worker (with education) 3. Office worker 4. Housewife (or man) 5. independent businessman/self-employed 6. Student 7. Retired Income: (of the household) 1. <150.000 DKK 2. 150.000-300.000 DKK 3. 300.000-500.000 DKK 4. >500.000 DKK In addition to the consumer survey, the carrot products were evaluated by a trained panel of tasters, the sensory panel, with respect to a number of sensory (taste, odour and texture) properties. Since usually a high number of (correlated) properties(variables) are used, in this case 14, it is a common procedure to use a few, often 2, combined variables that contain as much of the information in the sensory variables as possible. This is achieved by extracting the first two principal components in a principal components analysis(PCA) on the product-by-property panel average data matrix. In this data set the values of the first two principal components are provided. Number of observations: 1236 Variable Description Consumer Frequency Gender Age Homesize Work Income Preference Sweetness Bitter Crisp Sens1 Sens2 Product

Numbering identifying the consumers Valued 1-5 (see above) Valued 1-2 (see above) Valued 1-4(see above) Valued 1-2 (see above) Valued 1-7 (see above) Valued 1-4 (see above) preference score Sweetness score Bitterness score Crispiness score First sensory principal component First sensory principal component Product identification

eNote 13


Source Per Bruun Brockhoff, The Royal Veterinary and Agricultural University, Denmark. Analysis Randomized block, Random coefficient analysis. Get the data

30

eNote 13

13.7 REPEATED MEASURES

31

13.7 Repeated measures Enrofloxacin treatments of pigs Key words: Two-sample completely randomized, Randomized Blocks, repeated measurements. Description The effect on pigs of the antibiotics enrofloxacin may depend on the way the treatment is carried out. One group of 6 pigs was given an injection (IM) and another group of six pigs was treated via the feed (2.5 mg/body weight). Two hours after the treatment the pigs were slaughtered and the concentration of enrofloxacin was determined on 5 different locations in the intestine. Number of observations: 60 Variable Description treatment pig position conc

factor with two (character) values: PO and IM pig number (1-12) measurement position (character) (e1,e2,e3,e4,e5) concentration measurements

Source The Royal Veterinary and Agricultural University, Denmark. Analysis Split-plot structure. Get the data

eNote 13


32

Histamine response in dogs Key words: Repeated measures, analysis of covariance(baseline). Description In an experiment with 16 dogs the blood histamine concentration was measured 0, 1, 3, and 5 minutes after injection of morphine or trimethaphane. Before injection the dogs were classified into two groups according to their level of histamine (intact or depleted). Number of observations: 64 Variable Description treatm Values morphine,trimetha Morris, K.J. & Zeplevel Values intact,deplet dog Dog number (1–16) min Minutes after injection of morphine (0,1,3 or 5) hist Histamine concentration measurements pa R. (1963): Histamine–introduced hypotension due to morphine and Arfonad in the dog, J. Surg. Res. 3, 313–317 Source The Royal Veterinary and Agricultural University, Denmark. Analysis Get the data

eNote 13


33

PH in pigs Key words: Repeated measures. Description To investigate the effect of injection of Porcine Growth Hormone (PGH) on pH (among other things) a block experiment was carried out with two pigs from each of 6 litters (= blocks). There were two treatments: 1) control 2) pgh (daily injection with 0.08 mg Porcine Growth Hormone) Apart from several other measurements the pH in the meat was measured 20 times from 30 minutes after until 24 hours after slaughter. There were 10 litters in the experiment but pH was measured for only 6 of these. The data set is shown below with two lines for each pigs. The order of the data is: treatment, litter, pig number, followed by pH measurements at 30, 45, 60, 75, 90, 105, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 480, 1440 minutes after slaughter. Number of observations: 240 Variable Description treatm litter pigno min ph

Values 1,2 Values 2,4,5,6,8,10 Numbered 21,22,41,42,51,52,61,62,81,82,101,102 Minutes after slaughter (30,...,1440) pH measurements

Source Jette Søholm Petersen, The Royal Veterinary and Agricultural University, Denmark. Analysis Get the data

eNote 13


34

Activity of rats Key words: Repeated measures. Description To investigate the effect of a certain type of exposure on the activity of rats, the following experiment was carried out. The experimental unit was a cage with two rats. During the entire experimental period the rats were daily exposed to the matter under investigation, in the concentration of 1, 2 or 3 units (treatment 1, 2 and 3, respectively). Once per month during 10 months the activity of the rats was measured by placing the rats from one cage in a chamber in which each intersection of a light beam was counted. Number of observations: 300 Variable Description treatm cage month lnc

3 treatments: (1, 2 or 3) (concentrations) The number of the cage (30 different integers) Month of the measurement (1,2,...,10) log(count) in 57 hour period


eNote 13


35

Growth of guinea pigs Key words: Repeated measurements Description In an investigation of the effect of vitamin E on the growth of guinea pigs 15 animals were observed for 7 weeks. In week one they were given a growth inhibiting substance. In the beginning of week five they received different amounts of vitamin E (dosage 0,1, or 2). there were five animals in each treatment group, and each animal were weighted at the end of week 1,3,4,5,6, and 7. Number of observations: 90 Variable Description animal week weight dose

Number of the animal (1–15) Week of the measurement (1,3,4,5,6,7) Weight (g) of the animal Dose of vitamin E (0,1,2)

Source Crowder, M.J. & Hand, D.J. (1990). Analysis of repeated measures. Chapman & Hall, London. Analysis Various models for repeated measurements Get the data

Data - Technical University of Denmark

Recommend Documents