statistical aspects of a research project mohd ridzwan abd halim jabatan sains tanaman universiti...
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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
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
Starting a Research Project
What? Why? How?
WHAT?
What is the objective? What do you want to find out? What is the solution to the problem?
WHY?
Why do you want to study that? Is it new? Is it a problem? Is it important? Can you do it?
WHAT?
Usually your supervisor will tell or guide you
You can also suggest your own
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
HOW?
How can you find the answers? Experiments? Treatments? Statistical Methods?
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
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
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
MATERIALS & METHODS
How you conduct the study Two types of study:
Descriptive Hypothesis testing
Must include the statistical method!
DESCRIPTIVE STUDY
Getting new basic information e.g. a new crop variety, a survey No comparisons No hypothesis Descriptive statistics – mean, SD,
frequency distribution
0
20
40
60
80
100
V1 V2 V3 V4
roots
stems
leaves
Descriptive studies
Must have sampling (random, systematic, stratified)
Adequate replications Representative
Hypothesis testing
Comparing between treatments Treatments designed to meet
objectives Must have an experimental design
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!!
STEP 2
Determine your EXPERIMENTAL UNIT = the smallest unit that you apply your treatment
One pot? One plot? One plant? One animal?
STEP 3
Determine the number of REPLICATIONS = the number of experimental units in one treatment
STEP 4
Determine the EXPERIMENTAL DESIGN = how you allocate the treatments to the experimental units
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
BLOCKING
Group experimental units that are similar
Number of units in one block = number of treatments
RANDOMIZATION
Treatments must be randomized – to avoid bias
You cannot have any influence which treatment goes to which unit
+ Vita control
Comparison of padi yields with and without Vita
Problem = NO REPLICATION
+ Vita
+ Vita
+ Vita
control
control
control
Problem = NOT RANDOMIZED
+vita
+vita
+vita
control
control
control
Replication √
Randomization √
+ Vita
control+ vita
OK or not?
Problem – sampling unit treated as exp. unit!No replication!
Replication
Reps are repetition of experimental unit
Sample in an experimental unit are not replications
Four basic elements in experiments
Treatments Experimental Unit Replication Avoiding bias = Randomization
+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)
t test vs F test (ANOVA)
t test = comparing 2 treatments F test (ANOVA) = comparing 2 or > 2
treatments
Vita Kawal7.8 6.37.9 7.28.1 6.9
Jumlah 23.8 20.4Min 7.9 6.8
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
COMPLETELY RANDOMIZED DESIGN (CRD)
3 treatments
4 reps
Homogeneous units
ONE-WAY ANOVA
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
Source df SS MS F
Treatment
2 5.13 2.57 36.72**
Error 9 0.67 0.07
Total 11 5.80
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
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
Blok A
Blok B
Blok C
Blok D
RANDOMIZED COMPLETE BLOCK DESIGN (RCBD)
ANOVA RCBD
Source df SS MS F
Treatment
2
Block 3
Error 6
Total 11
Program SAS
Proc Anova; Class trt blok; Model hasil=trt blok; Means trt blok/lsd; Run;
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
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
Allocate treatments randomly if CRD
Source df
Variety (V) 3
Irrigation (I) 2
V x I 6
Error
Total 47
Main effects
Interaction
ANOVA FOR CRD FACTORIAL
Block 1
Block 2
Block 3
RCBD FACTORIAL
12 treatments randomized in each block
Block 4
Source df
Block 3
Variety (V) 3
Irrigation (I) 2
V x I 6
Error
Total 47
SPLIT-PLOT EXPERIMENT
Two or more factors The factors use unequal plot size Use only when necessary
V3 V4 V1 V2
I2 I1 I3
I3 I2 I1
I1 I3 I2Main Plot
Sub Plot
Block 1
Block 2
Block 3
Block 4
Source df
Block (B)
Irrigation (I)
B x I (error A)
Variety (V)
V x I
Error (B)
Total
ANOVA FOR SPLIT PLOT
Make a checklist
Treatments = refer to objectives Experimental unit No of replications Design = randomization Statistical test
TERIMA KASIH