Topic 3 Comparing Distributions ,Effect Sizes And Statistical Power Flashcards
(110 cards)
1
Q
Describe the purpose of analyzing two conditions in statistics.
A
The purpose is to analyze the differences between scores in two conditions.
2
Q
Explain the difference between between-participants and within-participants designs.
A
Between-participants design involves different groups of participants providing scores in each condition, while within-participants design involves the same group performing in both conditions.
3
Q
Define the t-test in the context of analyzing two conditions.
A
The t-test is a parametric statistical test used to analyze the difference between the means of two groups.
4
Q
How does the t-test assume data distribution?
A
The t-test assumes that data are drawn from a normally distributed population.
5
Q
What should be considered if the assumption of normality is violated in a t-test?
A
If the assumption is violated, non-parametric equivalents should be considered.
6
Q
List foundational concepts required to understand the t-test.
A
Foundational concepts include the mean, standard deviation, standard error, z-scores, normal distribution, assumptions of parametric tests, probability distributions, one- and two-tailed hypotheses, statistical significance, and confidence intervals.
7
Q
Describe the components involved in the analysis of two conditions.
A
Components include descriptive statistics, graphical illustrations, effect size, confidence limits around the means, and inferential tests like t-tests.
8
Q
Explain the significance of effect size in the analysis of two conditions.
A
Effect size measures how much differences in a dependent variable are due to the independent variable.
9
Q
What is the role of descriptive statistics in a two-group design analysis?
A
Descriptive statistics provide means, medians, standard deviations, and confidence intervals to summarize the data.
10
Q
How are graphical representations used in analyzing two conditions?
A
Graphical representations, such as box and whisker plots and histograms, help in understanding participant behavior.
11
Q
What insights can be gained from summary statistics in SPSS for a two-group design?
A
Summary statistics provide means, standard deviations, and confidence intervals in tables, offering a clear overview of the data.
12
Q
Describe the findings of the NOISE/NO NOISE study regarding word recall.
A
Participants in the NO NOISE condition recalled a mean of 13.8 words, while those in the NOISE condition recalled a mean of 7.3 words.
13
Q
Explain the concept of confidence limits around the mean.
A
Confidence limits are the upper and lower bounds of an interval estimate, indicating where the population mean is likely to fall.
14
Q
What are point estimates and how do they relate to sample means?
A
Point estimates are sample means that serve as estimates of population means, but they can vary with repeated experiments.
15
Q
How do confidence intervals provide more information than point estimates?
A
Confidence intervals provide a range of scores within which the population mean is likely to fall, offering a more informative estimate.
16
Q
Describe the importance of confidence intervals in research.
A
Confidence intervals allow researchers to generalize from a particular sample to the population and provide a more comprehensive and realistic view of the results.
17
Q
Explain what a 95% confidence interval indicates.
A
A 95% confidence interval implies that if a study were replicated 100 times, 95 of those calculated intervals would contain the true population parameter.
18
Q
How can confidence intervals be visually represented?
A
Confidence intervals can be graphically represented using error bar charts.
19
Q
What are the confidence intervals for the NOISE and NO NOISE conditions?
A
For the NOISE condition, the 95% CI is 5.7–8.8; for the NO NOISE condition, it is 12.1–15.6.
20
Q
Define the measure of effect in research.
A
The measure of effect quantifies differences between means, providing a standardised comparison of the magnitude of the difference.
21
Q
How are standardized differences expressed?
A
Differences between means can be expressed in terms of standard deviations, allowing for a standardized comparison.
22
Q
What does an effect size (d) represent?
A
Effect size (d) is a measure of the magnitude of the difference between conditions.
23
Q
How is effect size (d) calculated?
A
Effect size (d) is calculated using the formula: d = (mean 1 - mean 2) / mean SD.
24
Q
Explain the relationship between overlap and effect size.
A
A large overlap between two group distributions indicates a relatively small effect size, while a small overlap indicates a large effect size.
25
What are Cohen's guidelines for interpreting effect size (d)?
Cohen's guidelines are: Small effect: d = 0.20 (85% overlap), Medium effect: d = 0.50 (67% overlap), Large effect: d = 0.80 (53% overlap).
26
Describe the primary goal of the t-test.
The primary goal of the t-test is to determine if there is a statistically significant difference between the means of two conditions.
27
What are the two sources of variance considered in a t-test?
The two sources of variance are within-participants variance (variation within each condition) and between-participants variance (variation between the conditions).
28
Explain the sampling distribution logic in the context of the t-test.
If no true difference exists in the population (null hypothesis is true), the distribution of differences between sample means would be centered around zero.
29
How does a t-test convert observed differences?
A t-test converts the observed difference into a test statistic (t-value) and compares it to a probability distribution to find the likelihood of obtaining such a difference by sampling error alone.
30
What information does SPSS output provide regarding t-tests?
SPSS output provides means of the two conditions, their difference, confidence intervals for the difference, the t-value, and its associated probability value.
31
How should findings from a t-test be reported?
Findings should be reported by stating the test statistic (t) with the degrees of freedom (df) in brackets, followed by the probability value (p) at the chosen significance level.
32
Define the test statistic in the context of statistical tests.
The test statistic is the calculated value of the statistical test that has been undertaken.
33
What are degrees of freedom in statistical analysis?
Degrees of freedom refer to the number of scores that are free to vary in the analysis when calculating a statistic.
34
Define p value in hypothesis testing.
The p value is the probability of a test statistic, assuming the null hypothesis is true. A very small p value (e.g., .02763) indicates that the null hypothesis should be rejected.
35
Explain the significance of a small p value in hypothesis testing.
A small p value suggests that the observed data is unlikely under the null hypothesis, leading researchers to reject the null hypothesis.
36
Describe the difference between a one-tailed and a two-tailed test.
A one-tailed test predicts a specific direction of difference between two samples, while a two-tailed test predicts a difference without specifying the direction.
37
How is the p value adjusted in a one-tailed hypothesis test using SPSS output?
In a one-tailed hypothesis test, the probability value from the 'Sig. (2-tailed)' column in SPSS output is halved.
38
Explain the concept of equality of variance in statistical testing.
Equality of variance refers to the assumption that the populations from which samples are drawn have the same variance, which is crucial for parametric tests.
39
What is the role of Levene's Test in hypothesis testing?
Levene's Test assesses whether the assumption of equal variances is met for the data being analyzed.
40
Define test statistic in the context of statistical analysis.
A test statistic is the calculated value derived from a statistical test that is used to determine whether to reject the null hypothesis.
41
What are degrees of freedom in statistical calculations?
Degrees of freedom represent the number of scores that are free to vary in an analysis, indicating how many scores are needed to determine the rest.
42
Describe the output provided by SPSS for an independent t-test.
SPSS output for an independent t-test includes means of the two conditions, the difference between them, confidence intervals, and degrees of freedom.
43
Explain the importance of confidence intervals in statistical analysis.
Confidence intervals provide a range within which the true population mean is likely to fall, offering a more realistic view of results than a single point estimate.
44
How are degrees of freedom calculated for an independent t-test?
For an independent t-test, degrees of freedom are calculated as (n1 - 1) + (n2 - 1), where n1 and n2 are the number of participants in each group.
45
What does a confidence limit indicate in the context of mean differences?
Confidence limits indicate the range within which the true population mean difference is expected to fall, enhancing the generalizability of the results.
46
Describe the significance of the observed mean difference in hypothesis testing.
The observed mean difference must be substantial enough to be considered important, not just statistically significant, in hypothesis testing.
47
Describe the importance of including degrees of freedom (DF) in statistical reports.
DF should always be included in reports, typically in brackets alongside the t-value and p-value, indicating the number of scores that are free to vary in the analysis.
48
Define degrees of freedom in the context of statistical analysis.
Degrees of freedom refers to the number of scores that are free to vary in the analysis, calculated as the number of observations minus the number of parameters estimated.
49
Explain how degrees of freedom affect statistical calculations.
Estimating a mean results in the loss of one degree of freedom, which is why calculations often involve dividing by 'n - 1' instead of 'n'.
50
What does standard deviation measure in a dataset?
Standard deviation measures the degree to which scores in a dataset deviate around the mean.
51
How is the standard error of the mean (SEM) utilized in statistics?
The standard error of the mean is used in the construction of confidence intervals and measures the extent to which sample means vary from the mean of the sample means.
52
Describe the measure of effect in the context of the independent t-test.
The measure of effect quantifies the difference between two sample means to determine if the observed difference is statistically significant and large enough to be important.
53
Define effect size and its significance in statistical analysis.
Effect size measures the magnitude of the difference between conditions or the strength of a relationship, providing context beyond statistical significance.
54
How is Cohen's d calculated?
Cohen's d is calculated by dividing the difference between two means (x1 - x2) by the mean standard deviation.
55
Interpret a Cohen's d value of 2.45.
A Cohen's d of 2.45 is considered a very large effect size, indicating a substantial difference between the two means.
56
What are the guidelines for interpreting Cohen's d values?
Small effect: d = 0.2 (85% overlap), Medium effect: d = 0.5 (67% overlap), Large effect: d = 0.8 (53% overlap).
57
Explain the relationship between effect size and the overlap of distributions.
A small difference between groups results in substantial overlap of their score distributions, while a large difference leads to less overlap.
58
What does a larger standard deviation indicate about a dataset?
A larger standard deviation indicates more variability within the data.
59
How does the standard error of the mean contribute to statistical analysis?
The standard error of the mean provides insight into how much sample means vary, aiding in the construction of confidence intervals.
60
Discuss the role of effect sizes in interpreting research findings.
Effect sizes provide a meaningful way to interpret findings beyond just statistical significance, highlighting the practical importance of results.
61
Describe the related t-test and its alternative name.
The related t-test, also known as the paired t-test, is used when the same participants perform under both conditions of an experiment.
62
Explain the sensitivity of the related t-test compared to the independent t-test.
The related t-test is more sensitive than the independent t-test because each participant is tested against themselves, leading to reduced within-participants variance and a larger t-value.
63
How does the number of participants in a related design compare to an independent design for equivalent statistical power?
A related design with 20 participants is statistically equivalent to an independent design requiring 40 participants (20 in each condition).
64
Define a one-tailed hypothesis in the context of a related t-test.
A one-tailed hypothesis, or directional hypothesis, is made when a specific direction of difference between variables or conditions is predicted.
65
What is a two-tailed hypothesis and when is it used in a related t-test?
A two-tailed hypothesis, or bi-directional prediction, is used when a difference or relationship is predicted, but the exact direction is not known.
66
Explain the concept of order effects in within-participants designs.
Order effects occur when the order in which conditions are completed leads to differences in the dependent variable that are not due to the independent variable manipulation, influenced by factors like practice, fatigue, or boredom.
67
What is counterbalancing and how does it address order effects?
Counterbalancing is a method where different participants complete the conditions in different orders to mitigate order effects.
68
Provide an example of a study that could use a related t-test.
An example is comparing the verbal IQ (VIQ) and performance IQ (PIQ) of people with chronic illness.
69
What information does the SPSS Output - Paired Samples Statistics provide?
It confirms the number of pairs (N), names of the variables, mean, standard deviation, and standard error mean for each condition.
70
Interpret the mean VIQ and PIQ from the example provided in the content.
In the example, the mean VIQ is 94.875, which is lower than the mean PIQ of 109.100 for the group.
71
What does the SPSS Output - Paired Samples Correlations table indicate?
It shows the correlation between the two conditions, with a strong and positive relationship (correlation = 0.680, p < 0.001) observed for VIQ and PIQ.
72
What key information does the SPSS Output - Paired Samples Test provide?
It provides the mean difference, standard deviation of the differences, standard error mean of the differences, and the 95% confidence interval of the difference.
73
Calculate the mean paired difference between VIQ and PIQ from the example.
The mean paired difference between VIQ and PIQ is -14.2250.
74
What does the 95% confidence interval of the difference indicate?
It indicates the range within which we are 95% confident the true population mean difference lies; if it includes zero, it suggests no difference between groups.
75
Analyze the significance of the 95% confidence interval provided in the example.
In the example, the 95% confidence interval for the estimated population mean difference is between -17.4195 and -11.0305, which does not include zero, suggesting a real difference exists.
76
Define t-value in the context of a t-test.
The t-value is the calculated value of the t-test, representing the test statistic used to determine the significance of the results.
77
Explain the significance of the p-value in hypothesis testing.
The p-value indicates the probability of obtaining the observed t-value by chance if the null hypothesis is true, helping to assess the likelihood of a result occurring due to sampling error.
78
Describe the concept of degrees of freedom in statistical analysis.
Degrees of freedom (df) refer to the number of scores that are free to vary in the analysis, typically calculated as the number of observations minus the number of parameters estimated.
79
How should inferential statistics be reported in research results?
Inferential statistics should be reported by clearly stating the test used, the significance level, the precise value of the statistic, degrees of freedom, the p-value, and whether the result is statistically significant.
80
What is the purpose of using inferential statistics in data analysis?
The purpose of using inferential statistics is to analyze data and draw conclusions about a population based on sample data, allowing researchers to determine if observed differences are statistically significant.
81
Do you need to include all digits from statistical output when reporting t-values or p-values?
No, it is recommended to report t-values and p-values to no more than two and three decimal places, respectively, avoiding the inclusion of all digits from statistical output.
82
Explain the difference between findings and interpretations in research results.
Findings refer to the results obtained from statistical analysis, while interpretations involve discussing the implications and meaning of those results, which should be reserved for the Discussion section.
83
How can you succinctly report the outcome of a t-test in research findings?
"You can report the outcome by stating the test type, degrees of freedom, t-value, p-value, and whether the result is statistically significant, e.g., "t(42) = 2.23
84
What does a p-value of less than 0.001 indicate in hypothesis testing?
A p-value of less than 0.001 indicates a very low probability of the observed result occurring by chance, suggesting that the observed differences are likely to represent a real difference in the population.
85
Define the term 'test statistic' in statistical analysis.
The test statistic is the calculated value from a statistical test that is used to determine whether to reject the null hypothesis based on the data.
86
Describe the significance of the p-value in statistical tests.
The p-value indicates the probability of observing the data, or something more extreme, if the null hypothesis is true. A lower p-value suggests stronger evidence against the null hypothesis.
87
Explain the concept of power in statistical testing.
Power is the ability of a statistical test to detect a significant effect when one exists, calculated as 1 - β, where β is the probability of making a Type II error.
88
Define Type II error in the context of hypothesis testing.
Type II error occurs when a statistical test fails to reject a false null hypothesis, meaning an effect exists but is not detected.
89
How does effect size influence the power of a study?
A larger effect size is easier to detect and requires less power, while a smaller effect size is harder to detect and requires more power to identify.
90
What is the relationship between significance level and power?
A stricter significance level (lower alpha) can reduce the power of a test, making it harder to detect an effect, while a more lenient level increases power.
91
Explain the importance of clarity and accuracy in the Results section of a research paper.
Clarity and accuracy ensure that the data and analysis outcomes are presented in a way that is easily understood, allowing readers to grasp the main features and implications without confusion.
92
Describe the role of post-experimental interviews in research studies.
Post-experimental interviews help investigate participants' awareness of the experimental hypotheses, providing insights into their understanding and perceptions of the study.
93
How should multiple data sets and analyses be reported in a research paper?
They should be reported as a unit, starting with a description of the data, followed by detailed analysis outcomes in order of importance, beginning with central predictions.
94
What is the purpose of using chi-square tests in research?
Chi-square tests are used to determine if there is a statistically significant association between categorical variables.
95
Explain the significance of an alpha level of .05 in hypothesis testing.
An alpha level of .05 indicates a 5% risk of concluding that a difference exists when there is none, serving as a threshold for statistical significance.
96
Describe the importance of understanding power before conducting experiments.
Understanding power helps researchers determine the likelihood of detecting an effect, guiding study design and interpretation of results, especially when no effect is found.
97
What should be included in a basic Results section of a research paper?
A basic Results section should include clear data presentation, descriptive statistics, and the outcomes of inferential analyses, ensuring clarity on what is being discussed.
98
Describe the impact of lowering the alpha level on Type I error and study power.
Lowering the alpha level (e.g., from 0.05 to 0.02) reduces the chance of making a Type I error, but it also decreases the power of the study to detect a real effect.
99
Explain how sample size affects the power of a study.
A larger sample size increases the power of a study, making it more likely to detect a true effect.
100
Discuss the potential issues with relying solely on p-values in research.
Relying too heavily on p-values without considering sample size can lead to misleading conclusions, especially if the sample size is small, resulting in wide confidence intervals.
101
Define the difference between between-participants and within-participants designs in terms of statistical power.
Within-participants designs generally have more statistical power than between-participants designs because each participant serves as their own control, reducing within-participant variance.
102
How does the choice between one-tailed and two-tailed tests affect sample size requirements?
One-tailed tests require smaller sample sizes compared to two-tailed tests, which need larger sample sizes to compensate for the loss of power.
103
What factors are needed to calculate the power of a study?
To calculate the power of a study, you need the number of participants, the effect size, and a criterion probability value (e.g., p = 0.10).
104
Explain the significance of a power level of 0.7 in research.
A power level of 0.7 indicates a 70% chance of detecting an effect if one exists, which is considered a good threshold for research studies.
105
Describe the concept of confidence intervals in research.
Confidence intervals provide a range within which the true population parameter is likely to fall, offering a more comprehensive estimate than a single point estimate.
106
Discuss the importance of confidence intervals in generalizing research findings.
Confidence intervals allow researchers to generalize from their sample to the population, providing a fuller picture of results than just reporting a sample mean.
107
What does it indicate if a confidence interval for the difference between two means includes zero?
If a confidence interval includes zero, it suggests that there is likely no real difference between the groups in the population.
108
Explain how confidence intervals enhance the understanding of data compared to hypothesis testing alone.
Confidence intervals provide a clearer and more intuitive understanding of data, indicating how seriously to take sample means as estimates of population means.
109
How can confidence intervals be constructed around different statistics?
Confidence intervals can be constructed around various statistics, including means, the size of a difference between two means, correlation coefficients, and t-statistics.
110
Describe the relationship between power and the width of confidence intervals.
A narrower confidence interval is more useful than a wide one, and tests with greater power tend to have narrower confidence intervals.
