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Questions and Answers
What is the null hypothesis (H0) for an Independent-Samples t-Test?
What is the null hypothesis (H0) for an Independent-Samples t-Test?
- The means of two populations are equal. (correct)
- The samples are dependent.
- The variances of two populations are equal.
- The means of two populations are not equal.
What is required to create the sampling distribution of the difference between the means?
What is required to create the sampling distribution of the difference between the means?
- Select two random samples from one population. (correct)
- Select samples of different sizes.
- Select one random sample and compute its variance.
- Select two random samples from different populations.
What does the standard error of the difference between the means represent?
What does the standard error of the difference between the means represent?
- The maximum possible difference between the sample means.
- The average distance between the sampling distribution mean and all differences of the means. (correct)
- The margin of error in measurements.
- The actual difference between the sample means.
For which test is the standard deviation of the population known?
For which test is the standard deviation of the population known?
Which condition must be satisfied for conducting an Independent-Samples t-Test regarding the variances?
Which condition must be satisfied for conducting an Independent-Samples t-Test regarding the variances?
What decision should be made if the calculated t-value (tobt) is greater than the critical t-value (tcrit)?
What decision should be made if the calculated t-value (tobt) is greater than the critical t-value (tcrit)?
In the results, what does t(8) = 2.77, p < .05 imply about students who calculate statistics by hand compared with those who use software for calculations?
In the results, what does t(8) = 2.77, p < .05 imply about students who calculate statistics by hand compared with those who use software for calculations?
What is the estimated d calculated between the two groups of students?
What is the estimated d calculated between the two groups of students?
How is the value of r² computed based on the provided t-value and degrees of freedom?
How is the value of r² computed based on the provided t-value and degrees of freedom?
What conclusion can be drawn from the computed p-value of p < .05 in an independent t-test result?
What conclusion can be drawn from the computed p-value of p < .05 in an independent t-test result?
The pooled variance formula is used to estimate what in the context of hypothesis testing?
The pooled variance formula is used to estimate what in the context of hypothesis testing?
What does the formula for a single-sample t-test primarily compare?
What does the formula for a single-sample t-test primarily compare?
In a t-test for independent samples, what is the estimated standard error of the difference between the means based on?
In a t-test for independent samples, what is the estimated standard error of the difference between the means based on?
Which formula correctly represents the calculation of pooled variance for unequal sample sizes?
Which formula correctly represents the calculation of pooled variance for unequal sample sizes?
What is the main purpose of calculating the estimated standard error?
What is the main purpose of calculating the estimated standard error?
In the formula for the independent-samples t-test, what does the term (X1 - X2) represent?
In the formula for the independent-samples t-test, what does the term (X1 - X2) represent?
How is the t-value calculated in a single-sample t-test?
How is the t-value calculated in a single-sample t-test?
What is one of the first steps in performing a t-test?
What is one of the first steps in performing a t-test?
What is a key requirement for using the t-test with independent samples?
What is a key requirement for using the t-test with independent samples?
When calculating the t statistic in hypothesis testing, what does a higher t value indicate?
When calculating the t statistic in hypothesis testing, what does a higher t value indicate?
What do degrees of freedom in the context of t-tests refer to?
What do degrees of freedom in the context of t-tests refer to?
Flashcards
Rejecting the Null Hypothesis
Rejecting the Null Hypothesis
A statistical decision to reject a claim (the null hypothesis) when the calculated test statistic is greater than the critical value.
Retain the Null Hypothesis
Retain the Null Hypothesis
A statistical decision to maintain a claim (the null hypothesis) when the calculated test statistic is less than the critical value.
Critical Value
Critical Value
A threshold value used in hypothesis testing to decide whether to reject or retain a null hypothesis based on a calculated t-statistic.
Calculated t-statistic
Calculated t-statistic
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Effect Size (Cohen's d)
Effect Size (Cohen's d)
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Coefficient of Determination (r²)
Coefficient of Determination (r²)
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Statistical Significance (p<.05)
Statistical Significance (p<.05)
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Independent-Samples t-Test
Independent-Samples t-Test
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Homogeneity of Variance
Homogeneity of Variance
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Sampling Distribution of the Difference Between the Means
Sampling Distribution of the Difference Between the Means
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Standard Error of the Difference Between the Means
Standard Error of the Difference Between the Means
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What is the null hypothesis for the independent-samples t-test?
What is the null hypothesis for the independent-samples t-test?
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Single-Sample t-Test
Single-Sample t-Test
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Estimated Standard Error of the Mean
Estimated Standard Error of the Mean
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Estimated Standard Error of the Difference
Estimated Standard Error of the Difference
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Pooled Variance
Pooled Variance
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Why calculate pooled variance?
Why calculate pooled variance?
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Formulas for t-Tests
Formulas for t-Tests
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t-statistic (tobt)
t-statistic (tobt)
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Hypothesis Testing with Two Independent Samples
Hypothesis Testing with Two Independent Samples
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Steps of Hypothesis Testing
Steps of Hypothesis Testing
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Study Notes
Independent-Samples t-Test
- Used to compare means of two independent groups
- Assesses if there's a statistically significant difference between the groups
- Assumes homogeneity of variance (variances of the groups are similar)
- Randomly selected samples
- DV measured using ratio or interval scale
- Group means are known
Single-Sample t-Test
- Compares a sample mean to a known population mean
- Assesses if the sample mean is significantly different from the population mean
- Assumes DV is normally distributed
- Randomly selected sample
- Ratio or interval scale DV
- Population mean is known
z-Test
- Tests the difference between a sample mean and a known population mean when population standard deviation is known
- Assumes DV is measured using a ratio or interval scale, normally distributed
- Randomly selected sample
- Population mean and standard deviation are known
General Model
- Independent-Samples t-Test: Model shows relationship between sample A, sample B, population A, and population B. The null hypothesis (H0) states that there is no difference between population A and population B (μ1 - μ2 = 0). The alternative hypothesis (HA) states that there's a difference between population A and population B (μ1 - μ2 ≠ 0).
- Single-Sample t-Test and z-Test: Model shows relationship between sample, original population, and treated population. The null hypothesis (H0) states that there is no difference between samples and populations. The alternative hypothesis (HA) states that there's a difference.
Hypotheses
- Null hypothesis (H0): States no difference between groups or no relationship
- Alternative hypothesis (HA): States a difference between groups or a relationship
Steps
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Step 1: State the hypotheses
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Step 1a: Decide if it's a one-tailed or two-tailed test.
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Step 2: Set the significance level (alpha), usually .05
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Step 3: Calculate the appropriate degrees of freedom
-For Independent t-Test:df=(n₁ - 1) + (n₂ - 1)= n₁ + n₂ - 2
-For Single-Sample t-Test: df= n-1
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Step 3 (continued): Select and calculate the appropriate statistical test .Calculate Sx, Sx1-X2 etc
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Step 4: Make a decision: Determine if the test statistic is in the critical region. Draw a picture.
-If +tobt > tcrit or -tobt < -tcrit → Reject H0
-If -tcrit < tobt < +tcrit → Retain H0
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Step 5: Report the statistical results (p-value)
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Step 6: Write a conclusion: Summarize findings in words, including statistical results
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Step 7: Calculate the estimated effect size(d)
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Step 8: Calculate the percentage of variance explained (r²)
Formulas
- Independent-Samples t-Test: tobt = (X̄1 - X̄2) - (μ1 - μ2) / √S2X₁-X₂
- Single-Sample t-Test: tobt = (X̄ – μ)/SX
- Pooled Variance: Spool2 = (SS1 + SS2) / (df1 + df2)
- Estimated Standard Error: SX₁-X₂ = √((Spool2/n₁)+(Spool2/n₂))
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Description
This quiz covers the fundamentals of Independent-Samples t-Test, Single-Sample t-Test, and z-Test. It assesses your understanding of when and how to use these statistical methods, including their assumptions and applications. Test your knowledge and improve your statistical analysis skills!
