Experimental Design Analysis: Hardness Testing Experiment Report

This report presents an analysis of an experimental design focused on hardness testing. The study employs a randomized block design to compare the readings produced by four different tips on a hardness testing machine. The report outlines the experimental procedure, including sample selection, data collection methods, and the identification of independent and dependent variables. It details the hypothesis testing process, including the null and alternative hypotheses, and the use of ANOVA (Analysis of Variance) to analyze the data. The report evaluates the internal and external validity of the experiment and discusses the strengths and limitations of the experimental design. The results of the ANOVA analysis are presented, along with the interpretation of the p-value and F-statistic. The conclusion summarizes the findings, indicating that there is no significant difference in the mean hardness readings among the tips, leading to the acceptance of the null hypothesis. The report concludes that tip 4 gives a higher reading as compared to the other tips.

Running head: EXPERIMENTAL DESIGN ANALYSIS 1
Experimental Design Analysis
Student’s Name
Institutional Affiliation

EXPERIMENTAL DESIGN ANALYSIS 2
Table of Contents
Introduction................................................................................................................................3
Experimental Design Procedure.................................................................................................3
Sample Used...........................................................................................................................3
Data Collection Procedure.....................................................................................................3
Strengths and Limitation of the Experiment..........................................................................4
Independent and Dependent Variables...................................................................................4
Hypothesis Testing.................................................................................................................4
Validity of the Experiment.....................................................................................................6
Conclusion..................................................................................................................................7
References..................................................................................................................................8

EXPERIMENTAL DESIGN ANALYSIS 3
Experimental Design Analysis
Introduction
There are two main factors to consider when performing an experimental design. One
of them is determining whether the study is causational or, secondly, whether it is
correlational (Montgomery, 2017). The experiment that I carried out is causational. The
experiment was based on the operation of a hardness testing machine. The machine functions
by pressing a tip into a metal test token. The depth of the resulting depression determines the
hardness of the metal tested. Therefore, this experiment was carried out to determine that
hardness of tips and if the results are different (Curtis et al., 2018). The experimental design
procedure was followed in the tests.
Experimental Design Procedure
Sample Used
For an experimental design to be successful, there should be participants in the
experiment. For this experiment, four tips were selected to be tested. The tips were selected
randomly in order to expedite an experimental design for the test. The tokens used for the
experiment may vary slightly in their hardness that is if they were obtained from nuggets of
different heat level (Sharma, 2017). Random sampling was therefore used for this particular
study because the tokens were from the same choice of materials of consideration. Otherwise,
if the tokens were from different nuggets but different heat levels then the data for the
experiment would have been shallow and therefore not significant.
Data Collection Procedure
Next is the method used to measure how the height of the subjects used in the
experiment affects how they view their value in life. Surveys or questionnaires are not viable
for this kind of experiment. This is because in this experiment, it is only readings of the

EXPERIMENTAL DESIGN ANALYSIS 4
machine that is recorded. If the experiment involved collection of data from individuals then
the use of surveys and questionnaires would have been effective. The readings recorded from
the machine were put into a table to show the results. The number of tips used for the
experiment were four therefore, the coupons presented in the table are also four.
Strengths and Limitation of the Experiment
The strength of this experiment is that it gave a brief and slight estimation of how the
depth of the depression determined the hardness of the metal used. There was no actual black
and white attitude in the reading of the results, and this allowed a more precise reading of the
tips and how their measurements were distributed. However, the research method used might
lead to uncertain data based on the different heating of the metals used for the test. Well, if
one metal is completely different from another type of metal then, this might lead to
inaccurate and skewed results (Brook, 2018).
Independent and Dependent Variables
For the experiment, the independent variable was the depth, while the dependent
variable was the readings of the depths of different tokens. The value was measured
numerically by the used the results from the survey. The control group for the experiment
was the type of tips used, while the experimental group was the resulting readings from the
depths of the tokens. This was a good indicator of whether the measurements were accurate
or not, because if they were not then the results of the experiment would have been affected
(Rouder et al., 2017). responded was doubtful or untruthful about their height, and that
would have affected the results of the experiment.
Hypothesis Testing
After the establishment of strong conceptual comprehension of the system studied, the
resulting hypothesis was written. The null hypothesis (H0), was that all the tips measured
gave the same mean reading as compared to the alternative, while the alternative hypothesis (

EXPERIMENTAL DESIGN ANALYSIS 5
H1) was that at least two tips gave different readings. The hypothesis will be tested at 5%
level of significance. If we reject the hypothesis, then we will use a confidence interval of
95%. The table below shows the way the experiment was distributed and as well as the
treatments applied. The design used in the experiment is the randomized block design. This is
whereby the four blocks show the measurements taken from the depressions made by the tips.
The number of tips is equal to the number of test coupons. The test coupons and tips are both
equal to four. The two groups contained 16 observations subjects in each category. The table
below shows the readings.
Test Token
Tip Used 1 2 3 4
1 7.3 7.4 7.6 8.0
2 7.4 7.3 7.8 7.9
3 7.2 7.4 7.5 7.7
4 7.7 7.6 7.0 7.2
The type of experimental design is not apparent from the table. This is because the
order in which the observations were recorded is not indicated, and therefore randomization
is not shown (Shiraishi & Matsuda, 2018). Next, we carry out the ANOVA analysis of the
data. The following are the results of ANOVA analysis.
ANOVA
Source of
Variation SS df MS F P-value F crit
Rows
0.02666
7 3
0.00888
9
0.10491
8
0.95417
5 4.757062663
Columns
0.01166
7 2
0.00583
3
0.06885
2
0.93419
1 5.14325285
Error 0.50833 6 0.08472

EXPERIMENTAL DESIGN ANALYSIS 6
3 2
Total
0.54666
7 11
From the analysis of variance above, we can see that degrees of freedom and the sum
of squares are as expected. The following chart shows the distribution of the measurements of
the tips.
1 2 3 4
6.4
6.6
6.8
7
7.2
7.4
7.6
7.8
8
8.2
Distribution of Readings
1 2 3 4
Validity of the Experiment
In experimental design, internal validity refers to how good an experiment is done
with regard to avoiding more than one independent variable. With more than one independent
variable, there would be inaccurate causation statements in the experiment (Fokkema et al.,
2016). External validity, on the other hand, refers to how good the ideologies presented in the
experiment would be applied in different situations (Campbell, 2017). This experiment
ensured that there was internal and external validity by keeping the measurements focused
solely on the depth made by the tips, instead of presenting a variety of queries. This, in turn,
resulted in more accurate results on the test to see if the tips produce different readings, and
this can also be used in other situations due to internal validity.

EXPERIMENTAL DESIGN ANALYSIS 7
Conclusion
After looking at the analysis of variance and the can now make conclusions about the
experiment. From the data table, there is an implication that tip 4 gives a higher reading as
compared to the other tips. The p-value from the ANOVA analysis is 0.954175, which is
greater that 0.05 level of significance. This means that we have to accept the null hypothesis
that that all the tips measured gave the same mean reading as compared to the alternative. We
therefore reject the alternative hypothesis. The p-value and the F-statistic shown by the token
column does not have any interpretation of the analysis. Therefore, we can conclude that the
mean hardness for the fourth tip is higher than that of the other tips. This means that there is
no significant difference in the means of the tips.

EXPERIMENTAL DESIGN ANALYSIS 8
References
Brook, R. J. (2018). Applied regression analysis and experimental design. Routledge.
Campbell, D. T. (2017). Factors relevant to the validity of experiments in social settings.
In Sociological methods (pp. 243-263). Routledge.
Curtis, M. J., Alexander, S., Cirino, G., Docherty, J. R., George, C. H., Giembycz, M. A., ...
& MacEwan, D. J. (2018). Experimental design and analysis and their reporting II: updated
and simplified guidance for authors and peer reviewers. British journal of
pharmacology, 175(7), 987-993.
Fokkema, T., Kveder, A., Hiekel, N., Emery, T., & Liefbroer, A. C. (2016). Generations and
Gender Programme Wave 1 data collection: An overview and assessment of sampling and
fieldwork methods, weighting procedures, and cross-sectional
representativeness. Demographic Research, 34, 499-524.
Montgomery, D. C. (2017). Design and analysis of experiments. John wiley & sons.
Rouder, J. N., Morey, R. D., Verhagen, J., Swagman, A. R., & Wagenmakers, E. J. (2017).
Bayesian analysis of factorial designs. Psychological Methods, 22(2), 304.
Sharma, G. (2017). Pros and cons of different sampling techniques. International journal of
applied research, 3(7), 749-752.
Shiraishi, T. A., & Matsuda, S. I. (2018). Closed testing procedures for all pairwise
comparisons in a randomized block design. Communications in Statistics-Theory and
Methods, 47(15), 3571-3587.