According to Navarro (2020), what are the four primary questions that descriptive statistics help to answer?
They answer questions about typical values, data spread, extreme values, and the shape of the distribution.
Which measure of central tendency is calculated by adding all values and dividing by the number of values?
The mean (average).
What is the primary disadvantage of using the mean to describe the central tendency of a dataset?
It can be pulled too far by extreme values, also known as outliers.
Term: Median
Definition: The middle value in a dataset that has been ordered from smallest to largest.
What is a key advantage of using the median as a measure of central tendency?
It is not affected by outliers and represents the central value well, even in skewed data.
The _____ is the most frequently occurring value in a dataset and is best used for categorical data.
mode
In statistics, what does understanding the variability or 'spread' of the data tell you about the people or items being measured?
It indicates whether they are very similar (low spread) or very different (high spread).
How is the 'range' of a dataset calculated?
By subtracting the smallest value from the largest value.
The Interquartile Range (IQR) is calculated using the formula ____ - ____.
$Q3 - Q1$
Which measure of variability is less sensitive to outliers and works well with the median?
The Interquartile Range (IQR).
What is the most important and commonly used measure of spread that is calculated as the square root of the variance?
The standard deviation.
A small standard deviation (SD) indicates that the data points tend to _____ the mean.
cluster tightly around
According to the Empirical Rule for normally distributed data, what percentage of values lie within 1 standard deviation of the mean?
Approximately 68%.
According to the Empirical Rule, approximately 95% of values in a normal distribution fall within how many standard deviations of the mean?
Two standard deviations.
A data distribution with a long tail extending to the right is described as having a _____ skew.
positive
What does it mean if a dataset's skewness value is greater than 2?
It indicates that the data is seriously skewed.
A distribution that is very pointy with heavy tails is described as positive or _____.
leptokurtic
What does a Z-score represent?
It indicates how many standard deviations a specific value is above or below the mean.
What type of data visualization is described as a 'smooth version of a histogram' and is great for seeing the true shape of the data?
A density plot.
A boxplot is a graphical representation that shows the median, IQR, whiskers, and ____.
outliers
In research, what is the term for the entire group you want to study?
The population.
In research, the _____ is a smaller group that is actually measured to make guesses about the population.
sample
What is a sampling distribution?
It is the distribution formed by calculating the mean from many different samples taken from the same population.
What does the Standard Error (SE) measure?
It measures how accurate your sample mean is as an estimate of the true population mean.
What is the core idea of the Central Limit Theorem?
The sampling distribution of the mean becomes normal as the sample size gets large, even if the original data is not normal.
What does a very wide confidence interval suggest about your sample or data?
It suggests the sample is small and/or the data is noisy, leading to an imprecise estimate.
Why is it critical to perform assumption testing before using inferential statistics like a t-test or ANOVA?
If assumptions are broken, the p-values become wrong and the results cannot be trusted.
On a QQ Plot used for checking normality, what does it mean if the data points fall on the straight line?
It means the data is normally distributed.
What statistical test is used to check if data is normally distributed, where p > 0.05 indicates normality?
The Shapiro-Wilk test.
Why is it advised to check both a QQ plot and a Shapiro-Wilk test for normality, especially with large samples?
Because large samples often fail the Shapiro-Wilk test even when the data appears visually normal on a QQ plot.
The assumption that different groups in a study have a similar spread or variance is known as _____.
homogeneity of variance
Which statistical test is used to check for homogeneity of variance between groups?
Levene's Test.
In Levene's Test, a p-value of p < 0.05 indicates that the group variances are _____.
not equal
If the assumption of homogeneity of variance is violated, what alternative tests should be used for comparing groups?
Welch's t-test or Welch ANOVA.
For which type of statistical analysis is the assumption of homoscedasticity, where residuals have equal spread, required?
Regression.
What does a 'good' residual plot look like when checking regression assumptions?
It shows random dots scattered around zero with no discernible pattern, curve, or funnel shape.
What is the primary purpose of Null Hypothesis Significance Testing (NHST)?
It helps decide whether an observed effect in data is real or could simply be due to chance.
What does the null hypothesis ($H_0$) typically state?
It states that there is no difference or no effect between the groups or variables being studied.
In hypothesis testing, what question does the p-value answer?
It answers how likely it is to get the observed result if the null hypothesis were true.
In NHST, if the p-value is less than the alpha level ($p < \alpha$), what decision is made about the null hypothesis?
The null hypothesis is rejected.
A two-sided hypothesis expects a difference but does not specify the ____.
direction
When is a one-sample t-test the appropriate statistical procedure?
It is used when comparing a single sample mean to a known or hypothesized value.
If the normality assumption for a one-sample t-test is violated (p < 0.05 on Shapiro-Wilk), what non-parametric test should be used instead?
The Wilcoxon signed-rank test.
Which statistical test is used for comparing the means of two separate, unrelated groups?
The independent samples t-test.
In an independent samples t-test, what does a large t-score signify?
It signifies that the two groups being compared are very different from each other.
When is a paired-samples t-test used?
It is used when comparing the means of the same group of individuals at two different points in time or under two different conditions.
What is the primary use of an Analysis of Variance (ANOVA)?
It is used to compare the means of three or more groups.
If an ANOVA result is significant (p < 0.05), what does this indicate?
It indicates that at least one group is different from the others, but not which specific groups differ.
After a significant ANOVA result, what type of tests must be performed to determine which specific groups differ from each other?
Post-hoc tests.
When is a Chi-square test the appropriate statistical analysis?
It is used when examining the relationship between two categorical variables.
In a Chi-square test, the null hypothesis ($H_0$) states that there is no _____ between the variables.
association
Term: Eta Squared ($\eta^2$)
Definition: An effect size for ANOVA that measures the proportion of total variance explained by the independent variable.
What is a major disadvantage of using Eta Squared ($\eta^2$) as an effect size?
It tends to overestimate the population effect, especially when sample sizes are small.
Which ANOVA effect size is considered best for comparing results across different studies and is commonly used in multifactorial ANOVA?
Partial Eta Squared ($\eta p^2$).
Term: Omega Squared ($\omega^2$)
Definition: An effect size for ANOVA that measures the proportion of population variance explained by the independent variable.
Which ANOVA effect size is considered the least biased and most accurate for population estimates, particularly with small samples?
Omega Squared ($\omega^2$).
A positive skew indicates that the tail of the distribution points to the _____.
right
A negative skew indicates that the tail of the distribution points to the _____.
left
For a regression analysis, the assumption of _____ states that the relationship between variables is linear.
linearity
An S-shape on a QQ plot suggests that the data is ____.
skewed
What are the key assumptions for an independent samples t-test?
Independent groups, continuous dependent variable, normally distributed data, and homogeneity of variances.
What are the key assumptions for conducting an ANOVA?
Categorical IV, continuous DV, independence of observations, normality, no major outliers, and homogeneity of variances.
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