Here I used to data file from the researcher Udara Rathnayake who undergraduate at University of Ruhuna Sri Lanka. I basically carry out the MINITAB17 statistical software to analyze this data.

The researcher has used light intensity (as treatment with 3 different levels: 5W, 10W, 15W) for measure germination potential how they are significantly differing. 

He has measured different responses. Such as,

Seedling length (Root and Shoot separately)

Germination percentage (with dark control group)

 

1.     The effect of 4 type of light intensity on seeding length (Total length with shoot & root)

 

Replication

5W

10W

15W

1

7.86

6.06

4.535

2

7.83

6.065

4.215

3

7.86

5.875

4.67

4

7.655

6.305

4.94

MINITAB output:

 

Analysis of Variance (ANOVA)

 

Source  DF   Adj SS   Adj MS  F-Value  P-Value

Factor   2  20.6623  10.3311   235.46    0.000

Error    9   0.3949   0.0439

Total   11  21.0571

 

Hypothesis

 

·        Null hypothesis (H0)   :- There is same effect of 3 type of light intensity on seeding length.

·        Alternative hypothesis (H1)   :-The effects on seeding of light intensities are not all the same. (At least on pair of light intensities are different)

 

Conclusions

 

Since p value (0.000) is less than the significance value (0.005), we can reject the null hypothesis. That is different type of light intensities significantly differ on seeding length.

Therefore, at 5% significance level (even at 1%), we have sufficient evidence to say that 3 types of light intensities have significant effect on seeding length.

 

Mean comparisons

 

Tukey Pairwise Comparisons

 

Tukey Simultaneous Tests for Differences of Means

 

Difference  Difference       SE of                             Adjusted

of Levels     of Means  Difference       95% CI       T-Value   P-Value

10W - 5W        -1.725       0.148  (-2.139, -1.311)   -11.65     0.000

15W - 5W        -3.211       0.148  (-3.625, -2.798)   -21.68     0.000

15W - 10W       -1.486       0.148  (-1.900, -1.073)   -10.03     0.000

 

In here all p values of different comparisons are less than the significant value. So that is in hypothetically,

H0   :- mean i = mean j

H1   :- mean i ≠ mean j       for some i & j,   (  : mean of each treatment)

 

Since all p values (0.000) are less than the significance value (0.05), we can reject the null hypothesis.

Therefore, at 5% significance level, we have sufficient evidence to say that all light intensities have significantly different effect on seeding length.

 

Grouping Information Using the Tukey Method and 95% Confidence

 

Factor  N    Mean  Grouping

5W      4  7.8013  A

10W     4  6.0762    B

15W     4   4.590      C

 

Means that do not share a letter are significantly different.

 

So any treatment group doesn’t have shared letter. That means all light intensities have significantly different effect on seeding length.

 

 

2.     The effect of 4 type of light intensity on germination percentage (with dark control treatment group)

 

Replications

5W

10W

15W

DARK (Control)

1

90

88

100

58

2

90

90

100

58

3

94

88

100

56

4

90

88

98

50

MINITAB output:

 

Analysis of Variance (ANOVA)

 

Source  DF   Adj SS   Adj MS  F-Value  P-Value

Factor   3  4484.75  1494.92   294.08    0.000

Error   12    61.00     5.08

Total   15  4545.75

 

Hypothesis

 

·        Null hypothesis (H0)   :- There is same effect of 4 type of light intensity on germination.

·        Alternative hypothesis (H1)   :-The effects on germination of light intensities are not all the same. (At least on pair of light intensities are different)

 

 

 

Conclusions

 

Since p value (0.000) is less than the significance value (0.05), we can reject the null hypothesis. That is different type of light intensities significantly differ on germination.

Therefore, at 5% significance level (even at 1%), we have sufficient evidence to say that 4 types of light intensities have significant effect on germination.

 

Mean comparisons

 

Dunnett Multiple Comparisons with a Control

 

Dunnett Simultaneous Tests for Level Mean - Control Mean

 

                      Difference       SE of                           Adjusted

Difference of Levels    of Means  Difference      95% CI      T-Value   P-Value

5W - DARK (Contro          35.50        1.59  (31.22, 39.78)    22.27     0.000

10W - DARK (Contro         33.00        1.59  (28.72, 37.28)    20.70     0.000

15W - DARK (Contro         44.00        1.59  (39.72, 48.28)    27.60     0.000

 

In here all p values of different comparisons with control group are less than the significant value. So that is in hypothetically,

H0   :- mean i = mean control

H1   :- mean i ≠ mean control    for some i,    (  : mean of each treatment)

 

Since all p values (0.000) are less than the significance value (0.05), we can reject the null hypothesis.

Therefore, at 5% significance level, we have sufficient evidence to say that all light intensities have significantly different effect with control group on germination.

 

 

Grouping Information Using the Dunnett Method and 95% Confidence

 

Factor                    N    Mean  Grouping

DARK (Control) (control)  4   55.50  A

15W                       4  99.500

5W                        4   91.00

10W                       4  88.500

 

Means not labeled with the letter A are significantly different from the control level mean.

 

So any treatment group doesn’t have the letter (A). That means all light intensities have significantly different effect with control group on germination.