Podcast
Questions and Answers
When is it appropriate to use a z-test to compare a sample mean against a population?
When is it appropriate to use a z-test to compare a sample mean against a population?
- When comparing the means of two independent samples.
- When the population variance (or SD) is unknown and must be estimated.
- When both the population mean and variance (or SD) are known. (correct)
- When the population mean is unknown but the sample variance is known.
A paired-samples t-test should be used if there are 2 groups that are independent from each other.
A paired-samples t-test should be used if there are 2 groups that are independent from each other.
False (B)
Under what circumstance is a single-sample t-test most appropriate?
Under what circumstance is a single-sample t-test most appropriate?
- When comparing means from two independent samples with unknown variances.
- When the population mean is known, but the population variance is unknown. (correct)
- When neither the population mean nor the variance is known.
- When the population mean and variance are both known.
What is a key characteristic of data suitable for a repeated measures t-test?
What is a key characteristic of data suitable for a repeated measures t-test?
In a repeated measures design, the participants in each group must be completely different.
In a repeated measures design, the participants in each group must be completely different.
What does a matched-samples design primarily aim to achieve?
What does a matched-samples design primarily aim to achieve?
Which type of t-test is used to compare the means of two independent groups?
Which type of t-test is used to compare the means of two independent groups?
When conducting a t-test, if the calculated $t_{obt}$ exceeds the critical value $t_{crit}$, you should ______ the null hypothesis.
When conducting a t-test, if the calculated $t_{obt}$ exceeds the critical value $t_{crit}$, you should ______ the null hypothesis.
What is the primary purpose of calculating the pooled variance in an independent samples t-test?
What is the primary purpose of calculating the pooled variance in an independent samples t-test?
In an independent groups t-test, what does the degrees of freedom (df) represent?
In an independent groups t-test, what does the degrees of freedom (df) represent?
In hypothesis testing, how does increasing the sample size typically affect the likelihood of detecting a statistically significant effect, assuming an effect truly exists?
In hypothesis testing, how does increasing the sample size typically affect the likelihood of detecting a statistically significant effect, assuming an effect truly exists?
A directional conceptual hypothesis indicates the ______ of the difference between groups or conditions.
A directional conceptual hypothesis indicates the ______ of the difference between groups or conditions.
Participants are tested on their memory performance before and after a specific intervention. Which statistical test is most appropriate to determine if there is a significant change in memory performance?
Participants are tested on their memory performance before and after a specific intervention. Which statistical test is most appropriate to determine if there is a significant change in memory performance?
Match each statistical test to its appropriate scenario:
Match each statistical test to its appropriate scenario:
Why is it important to control for individual differences in experimental designs?
Why is it important to control for individual differences in experimental designs?
A negative t value indicates that a mistake has been made in the calculations.
A negative t value indicates that a mistake has been made in the calculations.
In factorial designs, what is the primary advantage of using a within-subjects (repeated measures) factor?
In factorial designs, what is the primary advantage of using a within-subjects (repeated measures) factor?
Explain how failing to reject the null hypothesis could still be a valuable outcome in a research study.
Explain how failing to reject the null hypothesis could still be a valuable outcome in a research study.
The standard error of the mean is influenced by both the standard deviation and the ______ size.
The standard error of the mean is influenced by both the standard deviation and the ______ size.
When is it most appropriate to use a one-tailed t-test instead of a two-tailed t-test?
When is it most appropriate to use a one-tailed t-test instead of a two-tailed t-test?
What does 'statistical power' refer to?
What does 'statistical power' refer to?
If a study has low statistical power, any statistically insignificance findings are definitive proof that there is no effect.
If a study has low statistical power, any statistically insignificance findings are definitive proof that there is no effect.
As alpha increases, what happens to the statistical power of a test?
As alpha increases, what happens to the statistical power of a test?
Rounding intermediate values during calculations by hand can lead to ______ in the final result.
Rounding intermediate values during calculations by hand can lead to ______ in the final result.
When the population variance is unknown, which test statistic should be used to test hypotheses about a single population mean?
When the population variance is unknown, which test statistic should be used to test hypotheses about a single population mean?
In hypothesis testing, the p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the one computed from your sample data, assuming what?
In hypothesis testing, the p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the one computed from your sample data, assuming what?
What is the purpose of running Levene's test before conducting an independent samples t-test?
What is the purpose of running Levene's test before conducting an independent samples t-test?
Which of the following is a key assumption of repeated measures t-tests?
Which of the following is a key assumption of repeated measures t-tests?
Match the following terms with their correct definitions:
Match the following terms with their correct definitions:
Flashcards
Single-sample t-test
Single-sample t-test
Compare a sample mean to a population mean.
Repeated Measures t-test
Repeated Measures t-test
Analyzes paired scores to determine if differences are significantly different from zero.
Independent groups t-test
Independent groups t-test
Compares the means of two independent samples to determine if they differ significantly.
Single sample t-test
Single sample t-test
Signup and view all the flashcards
Matched pairs design
Matched pairs design
Signup and view all the flashcards
Repeated measures t-test
Repeated measures t-test
Signup and view all the flashcards
Pooled Variance
Pooled Variance
Signup and view all the flashcards
Independent groups t-test
Independent groups t-test
Signup and view all the flashcards
P Value
P Value
Signup and view all the flashcards
Study Notes
Z-Tests and T-Tests
- A z-test is for comparing a single sample mean to a population when the population mean and variance/SD are known.
- In practice, population variance/SD is rarely known.
- Population variance must be estimated from the sample variance.
- A single sample t-test compares a single sample mean against a population mean.
- The population mean is known.
- The population variance/SD is unknown and estimated from the sample.
Single Sample T-Test Example
- A psychology tutor investigates if students daydream differently than normal during tutorials.
- The average daydreaming time is 32 minutes in a 2-hour period.
- Self-reported daydreaming times were taken from 10 students during a two hour tutorial: 27, 31, 35, 25, 23, 30, 34, 26, 19, 40.
- The null hypothesis (H0) states that time spent daydreaming does not differ between the class and the general population; μ = 32.
- The alternative hypothesis (H1) states that time spent daydreaming differs between the class and the general population; μ ≠32.
- Sum of squares (SSX) formula is Σ(X – X)² which equals 352 in this example.
- Variance (s²) is calculated as SSX / (N-1), resulting in 39.111 in this example.
- Standard deviation is the square root of the variance, s = √39.111 = 6.254.
- Standard error of the mean (SEM) is calculated as sX = s/√N = 6.254 / √10 = 1.978.
- The t-value calculation is t = (X̄ – μ) / sX = (29 – 32) / 1.978 = -1.517.
- Compare the calculated t-value (tobt) to the critical t-value (tcrit) from a t-table with degrees of freedom (df) = N - 1 = 9.
- With df = 9, tcrit = ±2.262.
- The statistical decision involves comparing the absolute value of the calculated t-value to the critical t-value.
- Since |tobt| = |-1.517| < |tcrit| = 2.262, retain the null hypothesis (H0).
- The single-sample t-test shows the time spent daydreaming (in minutes) does not differ significantly between the class (M = 29.0) and the general population (M = 32.0), t(9) = -1.52, ns.
Repeated Measures T-Test
- Used to analyze paired scores to determine if differences are significantly different from zero.
- Paired scores can be from the same participant/subject or closely matched pairs.
- Matched-samples design pairs participants matched in some way ie twins.
Repeated Measures T-Test Example
- A Department of Health campaign tries to reduce people's smoking habits.
- 10 participants record the average number of cigarettes smoked per day before and after the campaign.
- The effectiveness of the campaign in reducing smoking is assessed.
- The null hypothesis (H0) states that the number of cigarettes smoked after the campaign does not differ from the number smoked before.
- The alternative hypothesis (H1) states that the number of cigarettes smoked after the campaign does differ from the number smoked before.
- Statistically, H0: μD = 0 and H1: μD ≠0.
- The t-statistic is calculated as t = (D – μ) / sD.
- Transform data into difference scores (D), then calculate the mean difference score (DÌ„).
- Subtract the average difference score from each difference score, square the result, and sum these squared differences: SS D = Σ(D – D̄)².
- SD = √(SS D / (N-1)).
- sD = SD/√N.
- Finally, calculate the t-value as t = (D̄ - μ) / sD.
- Use t-tables to find tcrit with df = N - 1. Finally compare tobt to tcrit.
- Decision: Comparing tobt (0.751) to tcrit (2.262).
- Since |tobt (9)| = 0.751 < |tcrit (9)| = 2.262, retain H0.
- The repeated measures t-test shows there was no significant difference in the number of cigarettes smoked before (M = 28.7) and after (M = 28.0) the smoking reduction campaign, t(9) = 0.75, ns.
Independent Groups T-Test
- An independent-groups t-test compares the means of two independent samples to determine if those means differ significantly.
- Scores are always drawn from different participants or subjects.
Independent Groups T-Test Example
- Hypothesis: memory for pictures is better than memory for words.
- Eight randomly selected students view 30 slides with words.
- Another eight students view slides with the objects described by those words.
- After viewing, students take a recall test.
- The number of correctly recalled items is recorded.
- H0: Memory for words and pictures does not differ ; μ1 = μ2 or μ1 – μ2 = 0.
- H1: Memory for words and pictures does differ; μ1 ≠μ2 or μ1 – μ2 ≠0.
- The t-statistic is: t = (X̄1 – X̄2) / sX1-X2.
- Calculate the mean (XÌ„) and sum of squares (SS) for each group
- Calculate the pooled variance: s2p = (SSX1 + SSX2) / (N1 + N2 - 2)
- The standard error of the difference is: sX1-X2 = √( s2p * (1/N1 + 1/N2 ) ).
- The calculated t-value is: t = 2.211.
- df = N1 + N2 - 2 = 16-2 = 14
- The critical t-value is: tcrit = ± 2.145
- Decision: |tobt(14) = 2.211| > |tcrit(14) = 2.145| which means that we reject H0.
- The independent-groups t-test revealed memory, for pictures (M=20.1) was significantly better than memory for words (M = 15.3), t(14) = 2.21, p < .05.
Another Way to Pool Variance
- A nurse investigates the impact of a lead smelter on lead levels in local children's blood.
- Ten children near the smelter and seven children from an unpolluted area are selected.
- The average lead level near the smelter is 18.40 (SD = 3.17).
- The average lead level in the unpolluted area is 12.14 (SD = 3.18).
- The pooled variance is: s2p = ( (N1-1)s12 + (N2-1)s22 ) / (N1+N2-2) = 10.074.
- Standard error of the difference between the means is: sX1-X2 = 1.565
- Calculate t: t = (X̄1 – X̄2) / sX1-X2, which yields a t-value of 4.000.
- Make a statistical decision: df = 10 + 7 - 2 = 15
- Compare |tobt(15) = 4.000| > |tcrit(15) = 2.131| to reject HO.
- Blood lead levels were higher in children living close to the smelter (M = 18.4) than in children living in an unpolluted area (M = 12.1) with t(15) = 4.00, p < .05.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
