Podcast
Questions and Answers
When is a single-sample t-test appropriately used?
When is a single-sample t-test appropriately used?
- When comparing two samples where each participant is in only one sample.
- When comparing a sample mean to a population mean and the population standard deviation is unknown. (correct)
- When comparing two samples where each participant is in both samples.
- When comparing a sample mean to a population mean and the population standard deviation is known.
In what study design is a paired-samples t-test suitable?
In what study design is a paired-samples t-test suitable?
- Any design where the population standard deviation is unknown.
- Any design where there are more than two samples.
- A between-groups design.
- A within-groups design. (correct)
What distinguishes the independent-samples t-test from other types of t-tests?
What distinguishes the independent-samples t-test from other types of t-tests?
- It compares a sample mean to a known population mean.
- It compares two means in a between-groups design. (correct)
- It compares a sample mean to a known population mean when the population standard deviation is known.
- It compares two means in a within-groups design.
What does the independent-samples t-test require regarding participant assignment?
What does the independent-samples t-test require regarding participant assignment?
What type of distribution does the independent-samples t-test use for comparison?
What type of distribution does the independent-samples t-test use for comparison?
What does the independent-samples t-test require in terms of standard error?
What does the independent-samples t-test require in terms of standard error?
In the context of hypothesis testing, if we assume the null hypothesis is true for an independent-samples t-test, what value would we expect for the difference between the population means $(\mu_X - \mu_Y)$?
In the context of hypothesis testing, if we assume the null hypothesis is true for an independent-samples t-test, what value would we expect for the difference between the population means $(\mu_X - \mu_Y)$?
Which of the following is NOT a step in calculating independent-samples t-tests?
Which of the following is NOT a step in calculating independent-samples t-tests?
What is the purpose of identifying the populations, distribution, and assumptions in the first step of an independent-samples t-test?
What is the purpose of identifying the populations, distribution, and assumptions in the first step of an independent-samples t-test?
In the context of hypothesis testing, what does stating the null hypothesis involve?
In the context of hypothesis testing, what does stating the null hypothesis involve?
What does determining the characteristics of the comparison distribution involve in an independent-samples t-test?
What does determining the characteristics of the comparison distribution involve in an independent-samples t-test?
What is the purpose of determining critical values or cutoffs in the context of an independent-samples t-test?
What is the purpose of determining critical values or cutoffs in the context of an independent-samples t-test?
What does calculating the test statistic achieve in an independent-samples t-test?
What does calculating the test statistic achieve in an independent-samples t-test?
In hypothesis testing, what action do you take when the test statistic falls within the critical region?
In hypothesis testing, what action do you take when the test statistic falls within the critical region?
Consider the scenario where one group rates a wine bottle at 6.23, and another rates it at 8.11. To determine if these means are significantly different, what statistical test would be appropriate, assuming participants were only in one of the two groups?
Consider the scenario where one group rates a wine bottle at 6.23, and another rates it at 8.11. To determine if these means are significantly different, what statistical test would be appropriate, assuming participants were only in one of the two groups?
If you aim to avoid overgeneralizing the results from a non-random sample in an independent-samples t-test, what assumption is most immediately affected?
If you aim to avoid overgeneralizing the results from a non-random sample in an independent-samples t-test, what assumption is most immediately affected?
In an independent-samples t-test, when variances between groups aren't exactly equal, what general rule is often applied regarding the relative size of these variances?
In an independent-samples t-test, when variances between groups aren't exactly equal, what general rule is often applied regarding the relative size of these variances?
In hypothesis testing for an independent-samples t-test, what does the research hypothesis propose?
In hypothesis testing for an independent-samples t-test, what does the research hypothesis propose?
What does calculating the pooled variance achieve in an independent-samples t-test?
What does calculating the pooled variance achieve in an independent-samples t-test?
After calculating the pooled variance, what's the subsequent step in determining the standard error of the difference?
After calculating the pooled variance, what's the subsequent step in determining the standard error of the difference?
What does the variance of the difference represent in the context of an independent-samples t-test?
What does the variance of the difference represent in the context of an independent-samples t-test?
What is the purpose of calculating the 'standard error of the difference' in an independent samples t-test?
What is the purpose of calculating the 'standard error of the difference' in an independent samples t-test?
Given a two-tailed test with an alpha level of .05 and degrees of freedom of 41, what is the critical t-value ($t_{crit}$)?
Given a two-tailed test with an alpha level of .05 and degrees of freedom of 41, what is the critical t-value ($t_{crit}$)?
In an independent-samples t-test, if the calculated t-statistic ($t_{obt}$) is -0.67 and the critical t-value ($t_{crit}$) for a two-tailed test at alpha = 0.05 is +/- 2.021, what decision should be made?
In an independent-samples t-test, if the calculated t-statistic ($t_{obt}$) is -0.67 and the critical t-value ($t_{crit}$) for a two-tailed test at alpha = 0.05 is +/- 2.021, what decision should be made?
When reporting the results of an independent-samples t-test, what p-value would you typically report if there is no significant difference between the means?
When reporting the results of an independent-samples t-test, what p-value would you typically report if there is no significant difference between the means?
How is the reporting of an independent-samples t-test commonly structured when the t-statistic is -0.67 and degrees of freedom ($df$) are 41?
How is the reporting of an independent-samples t-test commonly structured when the t-statistic is -0.67 and degrees of freedom ($df$) are 41?
If a 95% confidence interval (CI) for the difference between means includes zero, what does this suggest about the statistical significance of the difference?
If a 95% confidence interval (CI) for the difference between means includes zero, what does this suggest about the statistical significance of the difference?
What does Cohen's d measure?
What does Cohen's d measure?
How is Cohen's d calculated?
How is Cohen's d calculated?
According to Cohen's guidelines, what value of $d$ represents a 'small' effect size?
According to Cohen's guidelines, what value of $d$ represents a 'small' effect size?
In the wine-tasting example, the calculate Cohen's $d$ is -0.21. How is this interpreted?
In the wine-tasting example, the calculate Cohen's $d$ is -0.21. How is this interpreted?
What does a small effect size (e.g., d = 0.20) imply about the amount of overlap between the distributions of two groups?
What does a small effect size (e.g., d = 0.20) imply about the amount of overlap between the distributions of two groups?
When interpreting the results of an independent-samples t-test, what components are typically included in the final write-up?
When interpreting the results of an independent-samples t-test, what components are typically included in the final write-up?
Which of the following indicates the greatest probability of superiority?
Which of the following indicates the greatest probability of superiority?
Flashcards
Independent-samples t-test
Independent-samples t-test
Compares two means in a between-groups design.
Single-sample t test
Single-sample t test
Used when comparing a sample mean to a population mean when the population standard deviation is unknown.
Paired-samples t test
Paired-samples t test
Used when comparing two samples and every participant is in both samples (within-groups design).
The Distribution
The Distribution
Signup and view all the flashcards
Steps for Calculating t Tests
Steps for Calculating t Tests
Signup and view all the flashcards
Null hypothesis
Null hypothesis
Signup and view all the flashcards
Research hypothesis
Research hypothesis
Signup and view all the flashcards
Mean
Mean
Signup and view all the flashcards
Standard Deviation
Standard Deviation
Signup and view all the flashcards
Compute pooled variance
Compute pooled variance
Signup and view all the flashcards
Alpha level
Alpha level
Signup and view all the flashcards
Critical values
Critical values
Signup and view all the flashcards
Test statistic
Test statistic
Signup and view all the flashcards
Make a decision
Make a decision
Signup and view all the flashcards
Use p > 0.05
Use p > 0.05
Signup and view all the flashcards
Use p < 0.05
Use p < 0.05
Signup and view all the flashcards
95% Confidence Interval (CI)
95% Confidence Interval (CI)
Signup and view all the flashcards
Cohen's d
Cohen's d
Signup and view all the flashcards
Small Effect Size
Small Effect Size
Signup and view all the flashcards
Medium Effect Size
Medium Effect Size
Signup and view all the flashcards
Large Effect Size
Large Effect Size
Signup and view all the flashcards
Study Notes
- There are three types of t tests
Single-Sample t Test
- Compares a sample mean to a population mean
- Used when the population standard deviation is unknown
Paired-Samples t Test
- Compares two samples where every participant is in both samples
- Used in a within-groups design
Independent-Samples t Test
- Compares two samples where every participant is in only one sample
- Used in a between-groups design
Independent-Samples t Test Explained
- Compares two means in a between-groups design
- Participants are assigned to only one of two groups
- Uses a distribution of differences between means
- Requires estimation of appropriate standard error
Distribution of Differences Between Means
- Assumes knowledge of population parameters
- Null hypothesis (H₀) is true (μX - μY = 0)
- In Population X: μ = 50, σ = 25, and N = 1,000,000
- In Population Y: μ = 50, σ = 25, and N = 1,000,000
- Random samples of 50 scores are taken from each population
- The mean of each sample is computed
- Difference computed: Mx - My
- The process repeats 10,000 times
Steps for Calculating Independent-Samples t Tests
- Step 1: Identify the populations, distribution, and assumptions
- Step 2: State the null and research hypotheses
- Step 3: Determine the characteristics of the comparison distribution
- Step 4: Determine critical values or cutoffs
- Step 5: Calculate the test statistic
- Step 6: Make a decision
Independent t-test Example: Wine Tasting Experiment
- A researcher wants to determine if knowing the price of wine influences taste ratings
- Participants taste and rate a bottle on a scale of 1-10 (1 = hate it, 10 = love it)
- One group is told the wine costs $12.00, and the other group is told the wine costs $80.00
- The $12 group gives a mean rating of 6.23, while the $80 group gives a mean rating of 8.11
- Goal: Determine if ratings are significantly different at a 5% significance level
Step 1: Wine Tasting Example
- Population 1: People told they are drinking $12 wine
- Population 2: People told they are drinking $80 wine
- The distribution of differences is between means (not mean difference scores)
Independent-Samples t Test - Assumptions
- Dependent variable is a scale variable (Interval ratings on a scale of 1-10)
- Random samples were not attained, so be cautious about overgeneralizing
- Check normal populations; if distributions don't look too different, then the data is ok
- There is equal variance
Step 2: State Null and Research Hypotheses
- Null hypothesis: On average, people rate $12 wine equally to $80 wine (H₀: μ₁ = μ₂)
- Research hypothesis: On average, people rate $12 wine differently than $80 wine (H₁: μ₁ ≠ μ₂)
Step 3: Comparison Distribution Characteristics
- Mean of distribution of differences between means: μX - μY = 0
- Compute sample variances (Variance of X = 84.64, Variance of Y= 73.96)
- Compute the pooled variance: dfX = N - 1 = 25, dfY = N - 1 = 16, df total= dfx + dfy = 41
Computation of Pooled Variance
- A weighted average of the two estimates of variance - one from each sample
- s² pooled = (dfX/df total) s² X + (dfY /df total) s²Y = (25/41)84.64 + (16/41)73.96
- s² pooled = (.61)84.64 + (.39)73.96 = 51.63 + 28.84 = 80.47
Estimation of Variance
- Estimate of Variance of X = S² Mx = S² pooled /Nx = 80.47/26 = 3.10
- Estimate of Variance of Y = S² My = S² pooled /Ny = 80.47/17 = 4.73
Variance of the Difference
- S² difference = S² Mx+ S² My= 3.10 + 4.73 = 7.83
Standard Error of the Difference
- Sdifference = √S² difference = √7.83 = 2.80
Step 4: Determine Critical Values or Cutoffs
- Alpha level = 0.05
- Two-tailed test
- df total= 41
- t crit= +/- 2.021
Step 5: Calculate the Test Statistic (tobt)
- t = (Mx – My) – (μχ – μγ)/Sdifference
- t = (6.23-8.11)/2.80 = -1.88/2.80 = -0.67
Step 6: Make a Decision
- Is tobt (-0.67) > tcrit (+/-2.021)? No - we cannot reject the null hypothesis
Reporting t Statistics
- Use p > 0.05 if there is no difference between means
- Use p < 0.05 if there is a difference between means
- t(41) = -0.67, p>0.05
95% Confidence Interval (CI) for Differences Between Means
-
(Mx - My)lower = -t(Sdifference) + (Mx - My) sample= -2.021 (2.80)+(-1.88)
- = -5.66 - 1.88 = -7.54
-
(Mx - My)upper = t(Sdifference) + (Mx - My) sample= +2.021 (2.80) + (-1.88)
- = 5.66 + (-1.88) = 3.78
-
Because 95% CI = [-7.54, 3.78] contains μ of 0, this confirms that there is no significant difference
Cohen's d Effect Size
- Spooled = √s2pooled
- Cohen's d = (Mx - My)/ Spooled
- Small is 0.20
- Medium is 0.50
- Large is 0.80
- Spooled = √s2pooled = √80.47 = 8.97
- Cohen's d = (6.23-8.11)/8.97 = -1.88/8.97 = -0.21 - Small Effect
Final Report
- The Independent t-test of wine ratings indicates no statistically significant difference between wines said to be worth $12.00 (M = 6.23, SD = 9.20) and $80.00 (M = 8.11, SD = 8.60), t(41) = -0.67, p > .05, d = -0.21, 95%CI [-7.54, 3.78]
- This is a small effect size according to Cohen's (1988) guidelines, and the population mean does fall within the Confidence Interval
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
