Given below are two statements:
Statement I: The p-value of a test depends on sample size.
Statement II: An important difference may not be statistically significant if the sample size is too small.
In the light of the above statements, choose the correct answer from the options given below:
Both Statement I and Statement II are true
Both statements describe how sample size interacts with statistical significance, and both are true.
Statement I is true. The p-value is not a fixed property of an effect; it depends heavily on sample size. Test statistics (such as t or z) are built with the standard error in the denominator, and the standard error shrinks as the sample grows (it is proportional to 1 divided by the square root of n). A larger sample therefore produces a larger test statistic for the same observed effect, pushing the p-value down. This is why with very large samples even a trivial, practically meaningless difference can turn out "statistically significant."
Statement II is true. This is the flip side of the same mechanism, expressed through statistical power — the probability of detecting an effect that really exists. A very small sample has low power and a large standard error, so a genuinely important difference in the population may fail to cross the significance threshold simply because there is not enough data to detect it reliably. The effect is real, but the test cannot "see" it.
Both statements correctly capture the dependence of significance on sample size, so the answer is Both Statement I and Statement II are true.
Similar Questions
Given below are two statements:
Statement I: Like correlation, statistical regression examines the association or relationship between variables.
Statement II: The primary purpose of regression is prediction.
In the light of the above statements, choose the most appropriate answer from the options given below:
Given below are two statements :
Statement I : t-tests are appropriate only when the dependent variables being measured are continuous.
Statement II : Chi-square statistic allows us to test hypotheses using both continuous and ordinal data.
In the light of the above statements, choose the most appropriate answer from the options given below :
Which of the following statistical technique will be appropriate for data analysis when the observations are available in the form of frequencies?
If data has been recorded using technical media, which among the following is a necessary step on the way to its interpretation?
Among the following, identify the continuous type of data:
If you are to calculate Spearman's rho, what kind of data you would enter?
The advantages of secondary analysis in research are:
(a) It is inexpensive.
(b) There is no need to construct a measuring instrument.
(c) Data archives are a valuable source.
(d) Useful opportunity is provided to produce valuable knowledge.
(e) Provides less time to understand data.
Which among the following softwares are used for data analysis in research?
A. SPSS
B. Microsoft Teams
C. Microsoft Excel
D. Prezi
E. PSPP
Choose the correct answer from the options given below:Given below are two statements:
Statement I: Content analysis cannot be applied to visual materials.
Statement II: It is difficult to ascertain answers to 'why?' questions through content analysis.
In the light of the above statements, choose the correct answer from the options given below:In conducting One way analysis of Variance, which of the following test statistics would be used?
Important Questions from Data Analysis
Match List-I with List-II :
List-I
List-II
(a)
The most commonly used method of computing correlation between two variables
(i)
Intra-class correlation
(b)
An ANOVA technique used for estimating reliability of a measure
(ii)
Inter-class correlation
(c)
A technique used for estimating reliability of multiple-trials tests
(iii)
Inter-tester reliability
(d)
A form of reliability that pertains to the testers
(iv)
Coefficient alpha
Select the correct option :
Given below are two statements
Statement I: Paired t-test is used to compare two related means (μ 1 and µ 2)
Statement II: The t-test is a method used for inferential statistics
In light of the above statements, choose the most appropriate answer from the options given below
Match the items of List I with the items of List II and choose the correct answer from the code given below.
List – I
List – II
a
X̅ chart
i
Number of defects
b
P chart
ii
Variations between samples
c
C chart
iii
Variations within samples
d
R chart
iv
Proportion of defectives Code
If mean, median, mode and standard deviation are known for a given data set, the Pearson's first skewness coefficient is equal to
Following are commands in SPSS-17 version for starting ANCOVA
(a) Analyze
(b) Multivariate
(c) Univariate
(d) General linear model
(e) Repeated measures
Select the correct sequence of commands from the options given below :
