35
eNote 13 1 eNote 13 Data
eNote 13 1
eNote 13
Data
eNote 13 INDHOLD 2
Indhold
13 Data 113.1 Introduction, Randomized Blocks Design . . . . . . . . . . . . . . . . . . . 313.2 General factor structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.3 Hierarchial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1513.4 Split-plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1713.5 Analysis of covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2213.6 Random coefficient analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 2713.7 Repeated measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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) spectrosco-py was investigated as an alternative to the more cumbersome (and expensive) HPLCmethod to determine the content of active substance in tablets.
Number of observations: 10Variable Description
hplc The HPLC measurementnir The NIR predicted value
eNote 13 13.1 INTRODUCTION, RANDOMIZED BLOCKS DESIGN 3
Source
Brockhoff and Thierry-Carstensen (2003). Test set validation using simple statisticalmethods. 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 equivalentlya paired t-test.
Get the data
eNote 13 13.1 INTRODUCTION, RANDOMIZED BLOCKS DESIGN 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) spectrosco-py was investigated as an alternative to the more cumbersome (and expensive) HPLCmethod to determine the content of active substance in tablets.
Number of observations: 20 tablets
Missing values: 5 on each variable.
Variable Description
hplc The HPLC measurementnir The NIR predicted value
Source
Brockhoff and Thierry-Carstensen (2003). Test set validation using simple statisticalmethods. Submitted to: Journal of Chemometrics.
Analysis
Randomized block design analysis: ANOVA with random tablet effect and fixed met-hod (NIR/HPLC) effect.
Get the data
eNote 13 13.1 INTRODUCTION, RANDOMIZED BLOCKS DESIGN 5
Sensory evaluation of cookies
Key words:
Randomized blocks.
Description
Ten different chill or freezer storage treatments were tested on a type of cookies, andafter 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. Ateach 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. Oneassessor did not give any score for quality.
Number of observations: 260Variable Description
assessor Numbered 1-13treatm Numbered 46-55colour Sensory evaluation score of colour intensitycons Sensory evaluation score of consistencytaste Sensory evaluation score of taste intensityquality 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 fol-lowing experiment was conducted. Each of 20 planks was dried in a certain period oftime. 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: close to the topdebth 5: in the centerdebth 9: close to the bottomdebth 3: between 1 and 5debth 7: between 5 and 9
width 1: close to the sidewidth 3: in the centerwidth 2: between 1 and 3
Number of observations: 300 (20 planks)
Variable Description
plank Numbered 1-20width Numbered 1,2,3debth Numbered 1,3,5,7,9humidity 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 13.2 GENERAL FACTOR STRUCTURE 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 tem-perature on the formation of maillard reaction products was investigated. There were9 treatment combinations of the two factors and three replicates (blocks) of the experi-ment giving a total of 27 productions. The factors and levels were: water activity (ap-prox. 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. Themeasurements (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: 27Variable Description
water Numbered 1,2,3temp Values 100,110,120,140rep The block factor numbered 1,2,3maill4, maill6, maill8 Maillard concentration after 4, 6 and 8 weekstaste4, taste6, taste8 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 eachof the six variables. Repeated measures analysis for each set of three time repeated mea-surements.
Get the data
eNote 13 13.2 GENERAL FACTOR STRUCTURE 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 tem-perature on the formation of maillard reaction products was investigated. There were9 treatment combinations of the two factors and three replicates (blocks) of the experi-ment giving a total of 27 productions. The factors and levels were: water activity (ap-prox. 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. Themeasurements (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: 81Variable Description
water Numbered 1,2,3temp Values 100,110,120,140rep The block factor numbered 1,2,3storage Storage time 4,6,8maillard Maillard concentrationtaste sensory taste score
Source
The Royal Veterinary and Agricultural University, Denmark.
Analysis
Randomized block (fixed two-way treatment with interaction, random block) for eachof the six variables. Repeated measures analysis for each set of three time repeated mea-surements.
Get the data
eNote 13 13.2 GENERAL FACTOR STRUCTURE 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 or2 weeks before the packs were opened and chill stored in normal atmosphere for 0, 1 or2 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 recordedand are given in the data set below. The variable batch is a blocking variable referringto two batches of spinage.
Number of observations: 36Variable Description
batch Values A,B (blocking factor)temp Values 90,100(celcius)weeks Values 0,1,2 (pre-storage time)days Values 0,1,2 (post-chill-storage time)a measure of red colour intensityb 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 eachof the two variables.
Get the data
eNote 13 13.2 GENERAL FACTOR STRUCTURE 10
Rooting of Hibiscus
Key words:
Factor structure.
Description
The data origin from an experiment investigating the effect of conductivity in the waterbath on the rooting of Hibiscus. There were 16 water baths, four for each of the fourlevels 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 usedhere. The 30 cuttings were placed at random in the water bath. For each cutting thenumber 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: 320Variable Description
variety Values h,rbathno Numbered 1-16conduct Numbered 1-4rootno Number of roots on the cuttingrootwt 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 13.2 GENERAL FACTOR STRUCTURE 11
Desease in cucumbers
Key words:
Factor structure.
Description
A greenhouse experiment was carried out to investigate how the spread of a diseasein cucumbers depended on climate and on amount of fertilizer for two varieties. Thefollowing data are an extract from the experiment. Two climates were used, (1) changeto 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 extrahigh (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 sub-sequent days the amount of infection (in percent) was registered. From the resultingcurve 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 theperiod.There were 3 blocks each consisting of 2 sections, a section being a part of the green-house. Each section consisted of 3 plots, which were each divided into 2 subplots, eachof which had 6-8 plants. Thus there were a total of 36 subplots. Results were recordedfor each subplot.The experimental factors were randomly allocated to the different units as follows: the2 climates were allocated to the 2 sections within each block, the 3 amounts of ferti-lizer were allocated to the 3 plots within each section, and finally the 2 varieties wereallocated 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 13.2 GENERAL FACTOR STRUCTURE 12
Variable Description
block Numbered 1-3section Numbered 1-6plot Numbered 1-18climate Numbered 1,2fert Values 2.0,3.5,4.0variety Values aminex,daliborrate Rate of spread of the diseaselevel Level of infection at the end of the period
Source
Eigil de Neergard, Department of Plant Pathology, The Royal Veterinary and Agricul-tural University, Denmark.
Analysis
Get the data
eNote 13 13.2 GENERAL FACTOR STRUCTURE 13
Tractor comparison
Key words:
Factor structure.
Description
In a comparison of two tractors, five drivers used each of the tractors to plough a fieldof a certain size. The time in minutes was recorded. This was repeated on three differentdays (with the same drivers and tractors).
Number of observations: 30Variable Description
day Numbered 1,2,3tractor Numbered 1,2driver Values a,b,c,d,e,ftime Ploughing time
Source
The Royal Veterinary and Agricultural University, Denmark.
Analysis
Get the data
eNote 13 13.2 GENERAL FACTOR STRUCTURE 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 or2 weeks before the packs were opened and chill stored in normal atmosphere for 0, 1 or2 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 (someof) 7 assessors who gave a score (between 0 and 15) for each of 6 different sensoryproperties (see the list further below).There was one sesssion for each combination of batch and weeks, and at each sessionthe 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, daysafter opening, batch, temperature, session number, assessor number, and the six sensoryproperties hay flavour 1, hay flavour 2, hay taste, spinage flavour 1, spinage flavour 2,spinage taste.
Number of observations: 36Variable Description
weeks Values 0,1,2 (pre-storage time)days Values 0,1,2 (post-chill-storage time)batch Values A,B (blocking factor)temp Values 90,100(celcius)session Numbered 1-6assessor Numbered 1-7hayflav1,hayflav2,haytaste Sensory scoresspiflav1,spiflav2,spitaste Sensory scores
Source
The Royal Veterinary and Agricultural University, Denmark.
Analysis
Get the data
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 enzymelactase was measured in 20 piglets taken from 5 different litters. For each of the 20 pigletsthe lactase level was measured in three different regions. At the time the measurementwas taken the piglet was either unborn (status=1) or newborn (status=2). These dataare kindly provided by Charlotte Reinhard Bjørnvad, Department of Animal Scienceand Animal Health, Division of Animal Nutrition, Royal Veterinary and AgriculturalUniversity.Number of observations: 60Variable Description
litter Litter identification, numbered 1–5pig Piglet identification, numbered 1–22region Measurement region identification, numbered 1–3status Status identification, numbered 1,2loclact Log transformed lactase measurement
Source
Charlotte Reinhard Bjørnvad, Department of Animal Science and Animal Health, Divi-sion 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 berriesas percent of the number of flowers earlier in the season) was determined for 5 twigson each of 6 bushes for every variety. The data, which are part of a larger experimentcarried out by B. Falk PedersenNumber of observations: 120Variable Description
sort Sort identification, numbered 1–4bush Bush identification, numbered 1–24fruct Fructification (the number of berries as percent of the number of flowers earlier in the season)
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 (including0) were investigated. A split-plot design with 6 blocks was used.
Number of observations: 72Variable Description
block Values 1-6variety Values v1,v2,v3fertil Values n0,n1,n2,n3yield 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 wereslaughtered and cut in halves (right and left side). One side was then cooled by tunnel-cooling (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 registra-tions associated with tenderness are recorded below: a sensory (subjective) evaluationof tenderness (denoted tender) and the lenghts of ‘sarcomers’. Long sarcomers are su-spected to be accociated with less tender meat and could be caused by too fat cooling.
Number of observations: 48Variable Description
pigno Pig identification, numbered 73-96phgroup Values 2,3cooling Values FC,TCsarcomer lenghts of sarcomertender 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 13.4 SPLIT-PLOT 19
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 differentstorage conditions on the rancidness of steaks from cattle given the feeds, 4 cows wererandomized on the two types of feed so that 2 cows were given each type. After slaugh-tering 6 steaks from each animal were used in a storage experiment. Two types of pack-aging (A and B) were used along with 3 storage periods (2, 5, and 8 weeks). After thestorage 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:
A BAnimal Feed 2 5 8 2 5 8
1 1 2.0 2.3 2.3 0.6 2.1 2.12 2 0.8 1.7 1.4 0.4 0.8 1.23 1 1.2 2.1 2.7 0.9 1.5 1.94 2 0.4 0.9 1.3 0.1 1.1 0.9
Number of observations: 24Variable Description
animal Cow identification, numbered 1-4feed Values 1,2pack Values A,Bstorage Values 2, 5, 8 weeksLTBA rancidness measurement
Source
The Royal Veterinary and Agricultural University, Denmark.
Analysis
Split-plot with 3-way ANOVA treatment structure.
Get the data
eNote 13 13.4 SPLIT-PLOT 20
Yield of wheat
Key words:
Split-plot.
Description
An experiment with 6 varieties of wheat concerning the treatment of a fungus attackwas carried out on an experimental field with 5 blocks each consisting of 12 plots. Theexperimental design and the yield (hkg/ha) for each plot are given in the following tab-le, 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 U U U U U T T T T T Tkr sl ko an ci vu ko sl vu ci an kr
58.5 58.6 59.6 32.8 57.8 30.6 75.2 74.2 63.1 76.4 69.4 75.6
U U U U U U T T T T T Tan vu sl kr ko ci ci ko vu sl an kr
30.5 28.5 52.0 54.1 56.1 54.4 79.8 74.4 62.2 76.5 65.4 64.8
T T T T T T U U U U U Ukr ko ci an vu sl vu kr an ko ci sl
64.2 75.2 80.1 61.3 57.9 78.2 27.1 55.0 31.4 62.7 60.1 59.5
U U U U U U T T T T T Tan sl kr ci vu ko vu ko ci kr an sl
26.7 54.9 47.9 54.7 24.4 53.8 57.3 77.2 84.4 62.7 58.9 82.2
T T T T T T U U U U U Uan sl ko ci vu kr ci vu sl ko kr an
61.9 80.2 73.3 77.5 63.1 62.1 53.2 25.9 60.6 60.4 52.9 31.1
Number of observations: 60Variable Description
block Numbered 1-5treat Values U, Tvariety Values an, ci, ko, kr, sl, vuyield Measured in hkg/ha
eNote 13 13.4 SPLIT-PLOT 21
Source
The Royal Veterinary and Agricultural University, Denmark.
Analysis
Split-plot with blocks.
Get the data
eNote 13 13.5 ANALYSIS OF COVARIANCE 22
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 theweight of kidney fat was examined. A total of 16 steers in 4 blocks were used distributedwith 4 on each hormone treatment. The results can be seen in the table below where foreach steer the weight of the animal before the hormone treatment (in kg) and the weightY 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 withthe aim of reducing the random variation as described above.
Hormone treatment1 2 3 4
Weight Y Weight Y Weight Y Weight YBlock 1 560 1330 440 1280 530 1290 690 1340Block 2 470 1320 440 1270 510 1300 420 1250Block 3 410 1270 360 1270 380 1240 430 1260Block 4 500 1320 460 1280 500 1290 540 1310
Number of observations: 16Variable Description
block Numbered 1-4treat Numbered 1-4weight Initial weight (kg)Y Weight of kidney fat (gram)
Source
Mead and Curnow, 1983)[section 8.8].
Analysis
Randomized block, analysis of covariance.
eNote 13 13.5 ANALYSIS OF COVARIANCE 23
Get the data
eNote 13 13.5 ANALYSIS OF COVARIANCE 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 particularhormone in cattle was investigated. There were 9, 12, and 11 cows respectively in the3 treatment groups, and for every cow the concentration of the hormone was measu-red before the start of the experiment and again after a certain period of feeding withexperimental compositions.
Number of observations: 32Variable Description
feed Numbered 1-3initial Initial concentration measurementfinal Final concentration measurementD final-initial
Source
The Royal Veterinary and Agricultural University, Denmark.
Analysis
Analysis of covariance better than analysis of differences.
Get the data
eNote 13 13.5 ANALYSIS OF COVARIANCE 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 size3. This means that only three out of four treatments is given in each block, but in sucha way that each treatment occurs equally often (6 times) AND such that each pair oftreatments ”meet”equally often (4 times). The response is Y and the covariate is X.
Number of observations: 24Variable Description
id Observation number 1-24blk Block number 1-8trt Treatment number 1-4y Reponsex Covariate
Source
Littell et al. (1996).
Analysis
Balanced Incomplete Block, Analysis of Covariance
Get the data
eNote 13 13.5 ANALYSIS OF COVARIANCE 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 heightincrease of 2 year old trees. Each of the 11 blocks consisted of 3 plots which were rando-mized on the 3 soil treatments. The results are the average 5-year increase (in feet) foreach plot. The average starting height H (also in feet) for each plot was also recorded.
Number of observations: 33Variable Description
block Numbered 1-11treat Numbered 1-3height Starting height in feetincrease Increase in feet
Source
Freese (1967).
Analysis
Get the data
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: 100Variable Description
subjcet Numbered 1-10x x-measurementy1 Response 1y2 Response 2
Source
Per Bruun Brockhoff, The Royal Veterinary and Agricultural University, Denmark.
Analysis
Random coefficient analysis. Response y1 has highly structured (linear) patterns. Re-sponse y2 has un-structured (linear) patterns.
Get the data
eNote 13 13.6 RANDOM COEFFICIENT ANALYSIS 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 ona scale from 1 to 7. Moreover the consumers scored the degree of sweetness, bitternessand crispiness in the products. The carrots were harvested in autumn 1996 and testedin march 1997. A number of background information variables were recorded for eachconsumer:
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. 61-
Homesize: (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 13.6 RANDOM COEFFICIENT ANALYSIS 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 trainedpanel of tasters, the sensory panel, with respect to a number of sensory (taste, odour andtexture) properties. Since usually a high number of (correlated) properties(variables) areused, in this case 14, it is a common procedure to use a few, often 2, combined variablesthat contain as much of the information in the sensory variables as possible. This isachieved by extracting the first two principal components in a principal componentsanalysis(PCA) on the product-by-property panel average data matrix. In this data setthe values of the first two principal components are provided.
Number of observations: 1236Variable Description
Consumer Numbering identifying the consumersFrequency Valued 1-5 (see above)Gender Valued 1-2 (see above)Age Valued 1-4(see above)Homesize Valued 1-2 (see above)Work Valued 1-7 (see above)Income Valued 1-4 (see above)Preference preference scoreSweetness Sweetness scoreBitter Bitterness scoreCrisp Crispiness scoreSens1 First sensory principal componentSens2 First sensory principal componentProduct Product identification
eNote 13 13.6 RANDOM COEFFICIENT ANALYSIS 30
Source
Per Bruun Brockhoff, The Royal Veterinary and Agricultural University, Denmark.
Analysis
Randomized block, Random coefficient analysis.
Get the data
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 treatmentis carried out. One group of 6 pigs was given an injection (IM) and another group ofsix pigs was treated via the feed (2.5 mg/body weight). Two hours after the treatmentthe pigs were slaughtered and the concentration of enrofloxacin was determined on 5different locations in the intestine.
Number of observations: 60Variable Description
treatment factor with two (character) values: PO and IMpig pig number (1-12)position measurement position (character) (e1,e2,e3,e4,e5)conc concentration measurements
Source
The Royal Veterinary and Agricultural University, Denmark.
Analysis
Split-plot structure.
Get the data
eNote 13 13.7 REPEATED MEASURES 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 dogswere classified into two groups according to their level of histamine (intact or depleted).
Number of observations: 64Variable Description
treatm Values morphine,trimethalevel Values intact,depletdog Dog number (1–16)min Minutes after injection of morphine (0,1,3 or 5)hist Histamine concentration measurements
Morris, K.J. & Zep-
pa R. (1963): Histamine–introduced hypotension due to morphine and Arfonad in thedog, J. Surg. Res. 3, 313–317
Source
The Royal Veterinary and Agricultural University, Denmark.
Analysis
Get the data
eNote 13 13.7 REPEATED MEASURES 33
PH in pigs
Key words:
Repeated measures.
Description
To investigate the effect of injection of Porcine Growth Hormone (PGH) on pH (amongother 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 from30 minutes after until 24 hours after slaughter. There were 10 litters in the experimentbut pH was measured for only 6 of these. The data set is shown below with two linesfor each pigs. The order of the data is: treatment, litter, pig number, followed by pHmeasurements 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: 240Variable Description
treatm Values 1,2litter Values 2,4,5,6,8,10pigno Numbered 21,22,41,42,51,52,61,62,81,82,101,102min Minutes after slaughter (30,...,1440)ph pH measurements
Source
Jette Søholm Petersen, The Royal Veterinary and Agricultural University, Denmark.
Analysis
Get the data
eNote 13 13.7 REPEATED MEASURES 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 followingexperiment was carried out. The experimental unit was a cage with two rats. During theentire experimental period the rats were daily exposed to the matter under investiga-tion, in the concentration of 1, 2 or 3 units (treatment 1, 2 and 3, respectively). Once permonth during 10 months the activity of the rats was measured by placing the rats fromone cage in a chamber in which each intersection of a light beam was counted.
Number of observations: 300Variable Description
treatm 3 treatments: (1, 2 or 3) (concentrations)cage The number of the cage (30 different integers)month Month of the measurement (1,2,...,10)lnc log(count) in 57 hour period
Source
The Royal Veterinary and Agricultural University, Denmark.
Analysis
Get the data
eNote 13 13.7 REPEATED MEASURES 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 animalswere 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 weightedat the end of week 1,3,4,5,6, and 7.Number of observations: 90Variable Description
animal Number of the animal (1–15)week Week of the measurement (1,3,4,5,6,7)weight Weight (g) of the animaldose 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
