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Statistical Aspects of a Statistical Aspects of a Research ProjectResearch Project
Mohd Ridzwan Abd HalimMohd Ridzwan Abd HalimJabatan Sains TanamanJabatan Sains TanamanUniversiti Putra MalaysiaUniversiti Putra Malaysia
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Outline
What, why and how The need for statistics Two types of study
Decriptive Hypothesis testing
Treatments, Experimental units and Replications
Experimental Design and Analysis
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Starting a Research Project
What? Why? How?
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WHAT?
What is the objective? What do you want to find out? What is the solution to the problem?
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WHY?
Why do you want to study that? Is it new? Is it a problem? Is it important? Can you do it?
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WHAT?
Usually your supervisor will tell or guide you
You can also suggest your own
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WHY?
You must SEARCH, READ, ASK and obtain information*
FIND OUT what others have done You must be CONVINCED that it is
IMPORTANT to know
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HOW?
How can you find the answers? Experiments? Treatments? Statistical Methods?
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Why do we need to use Statistical
Methods? Makes results of study valid and
acceptable Helps in deriving conclusions from
results Provides degree of confidence in the
conclusion made
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What happens if you don’t use
statistical methods
Your results will not be accepted You cannot make a valid conclusion You cannot answer any question
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What you need to do
Determine what you want to find out = OBJECTIVE/S
READ and understand the topic = LITERATURE REVIEW, JUSTIFICATION
Determine what you must do = MATERIALS AND METHODS
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MATERIALS & METHODS
How you conduct the study Two types of study:
Descriptive Hypothesis testing
Must include the statistical method!
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DESCRIPTIVE STUDY
Getting new basic information e.g. a new crop variety, a survey No comparisons No hypothesis Descriptive statistics – mean, SD,
frequency distribution
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0
20
40
60
80
100
V1 V2 V3 V4
roots
stems
leaves
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Descriptive studies
Must have sampling (random, systematic, stratified)
Adequate replications Representative
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Hypothesis testing
Comparing between treatments Treatments designed to meet
objectives Must have an experimental design
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STEP 1
Determine your treatments: fertilizer? variety? hormone? Method?
Are you studying ONE factor only – SIMPLEST
Are you studying 2 factors – FACTORIAL experiment – more difficult
Are you studying 3 factors – DON’T!!
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STEP 2
Determine your EXPERIMENTAL UNIT = the smallest unit that you apply your treatment
One pot? One plot? One plant? One animal?
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STEP 3
Determine the number of REPLICATIONS = the number of experimental units in one treatment
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STEP 4
Determine the EXPERIMENTAL DESIGN = how you allocate the treatments to the experimental units
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CRD vs RCBD
To BLOCK or NOT TO BLOCK?? If experimental units are
HOMOGENEOUS = don’t need blocking = CRD
If experimental units are HETEROGENOUS = need BLOCKING = RCBD
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BLOCKING
Group experimental units that are similar
Number of units in one block = number of treatments
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RANDOMIZATION
Treatments must be randomized – to avoid bias
You cannot have any influence which treatment goes to which unit
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+ Vita control
Comparison of padi yields with and without Vita
Problem = NO REPLICATION
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+ Vita
+ Vita
+ Vita
control
control
control
Problem = NOT RANDOMIZED
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+vita
+vita
+vita
control
control
control
Replication √
Randomization √
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+ Vita
control+ vita
OK or not?
Problem – sampling unit treated as exp. unit!No replication!
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Replication
Reps are repetition of experimental unit
Sample in an experimental unit are not replications
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Four basic elements in experiments
Treatments Experimental Unit Replication Avoiding bias = Randomization
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+vita 7.8 t
Control 6.3 t
Control 7.2 t
Control 6.9 t
+vita 7.9 t
+vita 8.1 t
Homogeneous units
Independent t test
One-way ANOVA
Completely Randomized Design (CRD)
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t test vs F test (ANOVA)
t test = comparing 2 treatments F test (ANOVA) = comparing 2 or > 2
treatments
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Vita Kawal7.8 6.37.9 7.28.1 6.9
Jumlah 23.8 20.4Min 7.9 6.8
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Ladang A
Ladang B
Ladang C
Paired t test
Randomized Complete Block Design (RCBD)
Two-way ANOVA
4.5 4.0
5.6 5.9
5.2 3.3
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COMPLETELY RANDOMIZED DESIGN (CRD)
3 treatments
4 reps
Homogeneous units
ONE-WAY ANOVA
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T1 T2 T3
4.2 3.5 4.9
3.9 3.3 5.1
4.1 3.8 4.7
4.4 3.0 5.3
Min 4.15 3.40 5.00
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Source df SS MS F
Treatment
2 5.13 2.57 36.72**
Error 9 0.67 0.07
Total 11 5.80
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Comparison between treatment
means LSD (least
significant difference)
Min
T3 5.3 a
T1 4.4 b
T2 3.0 crstlsd2
*05.0
=0.12
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Program dengan SAS
Data varieti; Input trt hasil; Cards; T1 4.2 T1 3.9 Data ; Proc anova; Class trt; Model hasil=trt; Means trt/lsd; run
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Blok A
Blok B
Blok C
Blok D
RANDOMIZED COMPLETE BLOCK DESIGN (RCBD)
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ANOVA RCBD
Source df SS MS F
Treatment
2
Block 3
Error 6
Total 11
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Program SAS
Proc Anova; Class trt blok; Model hasil=trt blok; Means trt blok/lsd; Run;
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FACTORIAL EXPERIMENTS
Looks at 2 or more factors in one experiment:
Example: Effects of variety – V1, V2, V3, V3 Effects of Irrigation – I1, I2, I3 4 x 3 factorial 12 treatment combinations
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Treatment Combinations
VARIETIES
IRRIGATION V1 V2 V3 V4
I1 V1I1 V2I1 V3I1 V4I1
I2 V1I2 V2I2 V3I2 V4I2
I3 V1I3 V2I3 V3I3 V4I3
12 TREATMENTS X 4 REPS = 48 PLOTS
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Allocate treatments randomly if CRD
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Source df
Variety (V) 3
Irrigation (I) 2
V x I 6
Error
Total 47
Main effects
Interaction
ANOVA FOR CRD FACTORIAL
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Block 1
Block 2
Block 3
RCBD FACTORIAL
12 treatments randomized in each block
Block 4
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Source df
Block 3
Variety (V) 3
Irrigation (I) 2
V x I 6
Error
Total 47
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SPLIT-PLOT EXPERIMENT
Two or more factors The factors use unequal plot size Use only when necessary
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V3 V4 V1 V2
I2 I1 I3
I3 I2 I1
I1 I3 I2Main Plot
Sub Plot
Block 1
Block 2
Block 3
Block 4
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Source df
Block (B)
Irrigation (I)
B x I (error A)
Variety (V)
V x I
Error (B)
Total
ANOVA FOR SPLIT PLOT
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Make a checklist
Treatments = refer to objectives Experimental unit No of replications Design = randomization Statistical test
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TERIMA KASIH