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Two Tailed Critical Value Formula:
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The two-tailed critical value is a statistical measure used in hypothesis testing to determine the cutoff points for rejecting the null hypothesis. It represents the values beyond which test statistics are considered statistically significant for a two-tailed test.
The calculator uses the formula:
Where:
Explanation: The formula calculates the critical value from the t-distribution for a given significance level and degrees of freedom, dividing alpha by 2 for two-tailed testing.
Details: Critical values are essential for determining statistical significance in hypothesis testing, constructing confidence intervals, and making decisions about rejecting or failing to reject null hypotheses.
Tips: Enter significance level (typically 0.05, 0.01, or 0.10) and degrees of freedom. Both values must be valid (0 < α < 1, df > 0).
Q1: What's the difference between one-tailed and two-tailed critical values?
A: One-tailed tests use α while two-tailed tests use α/2, as they account for significance in both directions of the distribution.
Q2: When should I use a two-tailed test?
A: Use two-tailed tests when you want to detect effects in either direction, or when you have no specific directional hypothesis.
Q3: How does degrees of freedom affect the critical value?
A: As degrees of freedom increase, the t-distribution approaches the normal distribution, and critical values decrease toward z-values.
Q4: What are common significance levels used?
A: α = 0.05 (95% confidence), α = 0.01 (99% confidence), and α = 0.10 (90% confidence) are most commonly used.
Q5: Can I use this for large sample sizes?
A: Yes, but for very large df (>30), the t-distribution closely approximates the normal distribution, and z-values may be used instead.