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