critical value

(noun)

the value corresponding to a given significance level

Related Terms

Examples of critical value in the following topics:

  • 95% Critical Values of the Sample Correlation Coefficient Table

  • Testing the Significance of the Correlation Coefficient

    • METHOD 2: Using a table of Critical Values to make a decision
    • Compare r to the appropriate critical value in the table.
    • If r < negative critical value or r > positive critical value, then r is significant.
    • The critical values are -0.532 and 0.532.
    • The critical values are -0.811 and 0.811.

  • Estimating a Population Variance

    • The value of ${ X }_{ R }^{ 2 }$represents the right-tail critical value.
    • The value of ${ X }_{ L }^{ 2 }$represents the left-tail critical value.
    • Using the values $n=30$, $\text{d.f.} = 29$ and $c=0.99$, the critical values are 52.336 and 13.121, respectively.
    • Note that these critical values are found on the chi-square critical value table, similar to the table used to find $z$-scores.
    • Using these critical values and $s=1.2$, the confidence interval for $s^2$ is as follows:

  • Try these multiple choice questions

    • No, because 0.942 is greater than the critical value of 0.707
    • Yes, because 0.942 is greater than the critical value of 0.707
    • No, because 0942 is greater than the critical value of 0.811
    • Yes, because 0.942 is greater than the critical value of 0.811

  • Hypothesis Tests with the Pearson Correlation

    • The 95% critical values of the sample correlation coefficient table shown in gives us a good idea of whether the computed value of $r$ is significant or not.
    • Compare $r$ to the appropriate critical value in the table.
    • If $r$ is not between the positive and negative critical values, then the correlation coefficient is significant.
    • The critical values associated with $df=8$ are $\pm 0.632$.
    • If $r$ is less than the negative critical value or $r$ is greater than the positive critical value, then $r$ is significant.

  • Rank Randomization for Association (Spearman's ρ)

    • Table 1 shows 5 values of X and Y.
    • Since it is hard to count up all the possibilities when the sample size is even moderately large, it is convenient to have a table of critical values.
    • From the table shown below, you can see that the critical value for a one-tailed test with 5 observations at the 0.05 level is 0.90.
    • As shown above, the probability value is 0.042.
    • Since the critical value for a two-tailed test is 1.0, Spearman's ρ is not significant in a two-tailed test.

  • Estimating the Target Parameter: Interval Estimation

    • Interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter.
    • Interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter.
    • A confidence interval for is calculated by: $\bar{x}\pm t^{*}\frac{s}{\sqrt{n}}$, where $t^*$ is the critical value for the $t(n-1)$ distribution.

  • Rank Randomization: Two Conditions (Mann-Whitney U, Wilcoxon Rank Sum)

    • First, consider how many ways the 8 values could be divided into two sets of 4.
    • Table 6 can be used to obtain the critical values for equal sample sizes of 4-10.
    • Since the sum of ranks equals 24, the probability value is somewhat above 0.05.
    • Naturally a table can only give the critical value rather than the p value itself.
    • Therefore, for practical reasons, the critical value sometimes suffices.

  • Goodness of Fit

    • A measure of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question.
    • The observed values are the data values and the expected values are the values we would expect to get if the null hypothesis was true.
    • The null hypothesis for the above experiment is that the observed values are close to the predicted values.
    • This is done in order to check if the null hypothesis is valid or not, by looking at the critical chi-square value from the table that corresponds to the calculated $\nu$.
    • The critical value for a chi-square for this example at $a = 0.05$ and $\nu=1$ is $3.84$, which is greater than $\chi ^ 2 = 0.36$.

  • Critical Thinking

    • The essential skill of critical thinking will go a long way in helping one to develop statistical literacy.
    • Statistical literacy is necessary to understand what makes a poll trustworthy and to properly weigh the value of poll results and conclusions.
    • The essential skill of critical thinking will go a long way in helping one to develop statistical literacy.
    • Critical thinking is an inherent part of data analysis and statistical literacy.
    • Interpret the role that the process of critical thinking plays in statistical literacy.