※Normal distribution: The majority of experimental values have a central tendency,
with values increasing and decreasing away from a central value, presenting a
symmetrical bell curve. If samples are normally distributed, statistical analysis is
possible. However, if the mean is skewed, some amount of error is possible.
⑦Null hypothesis: A hypotheses of no difference between the populations being
compared. To determine whether or not there are differences between
populations, a null hypothesis of “no difference” is used. An alternative hypothesis (the hypothesis that there is a difference in) is adopted if the null hypothesis is
rejected.
⑧Confidence interval significant probability: The probability (possibility) that the
null hypothesis is supported from the results produced from a real specimen. It is
said that there is a significant difference when this probability is less than 5% (i.e.,
the null hypothesis is rejected as almost impossible). It is denoted as “α” or “p”
and expressed as either a probability (p ¼ 0.01) or a percentage (p ¼ 1%).
2. Difference Between Test Types and Their Uses
Tests are divided into analyses of variance (ANOVA) for judging the difference
among groups, the Student’s t-test for judging the difference between two groups,
and multivariate techniques. The t-test is used to examine whether there is a
difference between the population means between two independent groups, such
as A and B. For three groups such as A, B, and C, for which μ represents the mean, it
would be a serious mistake to simply repeat the t-test as below. In this case,
multivariate techniques must be used.
• Between A and B, is there a difference in the value? (μ A ¼ μ B )
• Between A and C, is there a difference in the value? (μ A ¼ μ C )
• Between B and C, is there a difference in the value? (μ B ¼ μ C )
• Why must the t-test not simply be repeated for multiple groups?
In the case of an examination with 5% confidence intervals, the probability (of a
type I error) to dismiss the null hypothesis, H 0 , by mistake is 0.05, assuming that the
H 0 of μA ¼ μB is true. When separate data analyses are performed for various
problems associated with a certain sample, three H 0 will be considered the truth
when analyses are performed three times, and the probability of type I errors
occurring somewhere in the article will become unexpectedly high, at 1 À
(0.95 Â 0.95 Â 0.95) ¼ 0.14. When the same analyses are performed 10 times,
the probability of a type I error becomes 0.40. Furthermore, a more serious problem
occurs when different tests are based on the same data. For example, if a t-test of A is
performed among the three groups, A, B, and C, comparisons are performed between
A vs. B, B vs. C, and C vs. A. Unfortunately, a sample mean of A will then be higher
than the true average; in the case of A vs. B and A vs. C, H 0 becomes easy to reject.
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K. Kakazu et al.
with values increasing and decreasing away from a central value, presenting a
symmetrical bell curve. If samples are normally distributed, statistical analysis is
possible. However, if the mean is skewed, some amount of error is possible.
⑦Null hypothesis: A hypotheses of no difference between the populations being
compared. To determine whether or not there are differences between
populations, a null hypothesis of “no difference” is used. An alternative hypothesis (the hypothesis that there is a difference in) is adopted if the null hypothesis is
rejected.
⑧Confidence interval significant probability: The probability (possibility) that the
null hypothesis is supported from the results produced from a real specimen. It is
said that there is a significant difference when this probability is less than 5% (i.e.,
the null hypothesis is rejected as almost impossible). It is denoted as “α” or “p”
and expressed as either a probability (p ¼ 0.01) or a percentage (p ¼ 1%).
2. Difference Between Test Types and Their Uses
Tests are divided into analyses of variance (ANOVA) for judging the difference
among groups, the Student’s t-test for judging the difference between two groups,
and multivariate techniques. The t-test is used to examine whether there is a
difference between the population means between two independent groups, such
as A and B. For three groups such as A, B, and C, for which μ represents the mean, it
would be a serious mistake to simply repeat the t-test as below. In this case,
multivariate techniques must be used.
• Between A and B, is there a difference in the value? (μ A ¼ μ B )
• Between A and C, is there a difference in the value? (μ A ¼ μ C )
• Between B and C, is there a difference in the value? (μ B ¼ μ C )
• Why must the t-test not simply be repeated for multiple groups?
In the case of an examination with 5% confidence intervals, the probability (of a
type I error) to dismiss the null hypothesis, H 0 , by mistake is 0.05, assuming that the
H 0 of μA ¼ μB is true. When separate data analyses are performed for various
problems associated with a certain sample, three H 0 will be considered the truth
when analyses are performed three times, and the probability of type I errors
occurring somewhere in the article will become unexpectedly high, at 1 À
(0.95 Â 0.95 Â 0.95) ¼ 0.14. When the same analyses are performed 10 times,
the probability of a type I error becomes 0.40. Furthermore, a more serious problem
occurs when different tests are based on the same data. For example, if a t-test of A is
performed among the three groups, A, B, and C, comparisons are performed between
A vs. B, B vs. C, and C vs. A. Unfortunately, a sample mean of A will then be higher
than the true average; in the case of A vs. B and A vs. C, H 0 becomes easy to reject.
66
K. Kakazu et al.