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Questions and Answers
Models are a simplified representation of a ______, but not an exact replica.
Models are a simplified representation of a ______, but not an exact replica.
system
Most useful types of models take ______ form.
Most useful types of models take ______ form.
numerical
The shape of a normal distribution is often referred to as a ______ curve.
The shape of a normal distribution is often referred to as a ______ curve.
bell
In a normal distribution, data is centered symmetrically around the ______.
In a normal distribution, data is centered symmetrically around the ______.
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Empirically observed distributions are based on actual ______.
Empirically observed distributions are based on actual ______.
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The area under the curve of a probability density function will always add up to ______.
The area under the curve of a probability density function will always add up to ______.
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In a uniform distribution, the probability is uniformly spread across all possible ______.
In a uniform distribution, the probability is uniformly spread across all possible ______.
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Discrete variables have a fixed number of possible ______ for the observations.
Discrete variables have a fixed number of possible ______ for the observations.
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Changing the ______ moves the distribution along the x axis.
Changing the ______ moves the distribution along the x axis.
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Continuous variables have outcomes that can differ by arbitrarily small ______.
Continuous variables have outcomes that can differ by arbitrarily small ______.
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Samples are taken from a population to estimate the population ______.
Samples are taken from a population to estimate the population ______.
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Theoretical distributions assume a generating 'process' that follows a particular ______.
Theoretical distributions assume a generating 'process' that follows a particular ______.
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The median is the value for which half the data in the distribution fall ______ this value.
The median is the value for which half the data in the distribution fall ______ this value.
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Frequency distributions can be represented in a ______.
Frequency distributions can be represented in a ______.
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Descriptive statistics are used to summarize ______.
Descriptive statistics are used to summarize ______.
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Inferential statistics allow for making inferences about ______ of interest.
Inferential statistics allow for making inferences about ______ of interest.
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The effect size is a standardized measure used to evaluate the strength of a difference between two ______.
The effect size is a standardized measure used to evaluate the strength of a difference between two ______.
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A larger difference between groups suggests that there is a greater likelihood of a difference in the ______.
A larger difference between groups suggests that there is a greater likelihood of a difference in the ______.
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The precision of an estimate is indicated by the ______, which combines variability and sample size.
The precision of an estimate is indicated by the ______, which combines variability and sample size.
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To measure strong effects, one needs either a larger difference or ______ variability within the sample.
To measure strong effects, one needs either a larger difference or ______ variability within the sample.
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Smaller standard errors indicate that one is more ______ about their estimates.
Smaller standard errors indicate that one is more ______ about their estimates.
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Confidence intervals generated using standard error allow for a degree of ______ concerning population parameters.
Confidence intervals generated using standard error allow for a degree of ______ concerning population parameters.
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For a well-estimated mean, it is helpful to have a large sample size or ______ variability in the data.
For a well-estimated mean, it is helpful to have a large sample size or ______ variability in the data.
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Effect sizes can be categorized as small if they are less than or equal to ______.
Effect sizes can be categorized as small if they are less than or equal to ______.
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The T-test is sensitive to sample size while ______ isn't.
The T-test is sensitive to sample size while ______ isn't.
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T-distribution has heavier ______ indicating the probability of particular t-values if the null hypothesis were true.
T-distribution has heavier ______ indicating the probability of particular t-values if the null hypothesis were true.
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T-values closer to ______ are more probable if there are no group differences.
T-values closer to ______ are more probable if there are no group differences.
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A ______ is the area under the curve for values more extreme than the measured t-value.
A ______ is the area under the curve for values more extreme than the measured t-value.
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The alpha level is the threshold below which p-values are considered ______ evidence against the null hypothesis.
The alpha level is the threshold below which p-values are considered ______ evidence against the null hypothesis.
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In a two-tailed test, the sign of the test statistic is ______ and makes no assumptions about the direction of the effect.
In a two-tailed test, the sign of the test statistic is ______ and makes no assumptions about the direction of the effect.
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One should always mention some ______ measure along with the corresponding significance testing output.
One should always mention some ______ measure along with the corresponding significance testing output.
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Computing a ______ based on the samples is one of the steps in hypothesis testing.
Computing a ______ based on the samples is one of the steps in hypothesis testing.
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A Type II error is failing to obtain a statistically significant effect even though the ______ is false.
A Type II error is failing to obtain a statistically significant effect even though the ______ is false.
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The probability of missing a real effect in the population is represented by ______.
The probability of missing a real effect in the population is represented by ______.
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The complement of beta (β) is known as statistical ______.
The complement of beta (β) is known as statistical ______.
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Statistical power can be increased by increasing the magnitude of the effect, decreasing the ______ in the sample, and increasing the sample size.
Statistical power can be increased by increasing the magnitude of the effect, decreasing the ______ in the sample, and increasing the sample size.
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A Type M error occurs when there is an error in estimating the ______ of an effect.
A Type M error occurs when there is an error in estimating the ______ of an effect.
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Type S error is defined as the failure to capture the correct ______ of an effect.
Type S error is defined as the failure to capture the correct ______ of an effect.
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Increasing statistical power reduces the risk of Type II, Type M, and Type ______ errors.
Increasing statistical power reduces the risk of Type II, Type M, and Type ______ errors.
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Small sample sizes should be avoided whenever possible as they increase the risk of Type II, Type M, and Type ______ errors.
Small sample sizes should be avoided whenever possible as they increase the risk of Type II, Type M, and Type ______ errors.
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The data should be roughly normally distributed for the ______ test assumptions.
The data should be roughly normally distributed for the ______ test assumptions.
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The variance should be roughly equivalent for the groups being compared in the ______ assumption.
The variance should be roughly equivalent for the groups being compared in the ______ assumption.
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A dependence is any form of connection between ______ points.
A dependence is any form of connection between ______ points.
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For an independent t-test, every data point should come from a different ______.
For an independent t-test, every data point should come from a different ______.
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Subtracting the mean from each data point is known as ______.
Subtracting the mean from each data point is known as ______.
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Standardizing expresses each value in a distribution in terms of how many standard ______ it is away from the mean.
Standardizing expresses each value in a distribution in terms of how many standard ______ it is away from the mean.
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Violations of independence can lead to inflation of type ______ error rate.
Violations of independence can lead to inflation of type ______ error rate.
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A z-score indicates how far away a data point is from the mean in ______ units.
A z-score indicates how far away a data point is from the mean in ______ units.
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Study Notes
Models
- Models are simplified representations of a system, not exact replicas.
- Models summarize complex systems using descriptive features.
- Examples include maps, restaurant menus, and agendas.
- Most useful models are numerical.
Means and Standard Deviations
- Means and standard deviations summarize distributions.
- They provide key details about distribution features.
Distributions
- Distributions describe the position, arrangement, and frequency of occurrence within a space or time unit.
Empirically Observed Distributions
- Based on actual observations.
- All observations can be summed to create frequency distributions.
- Frequency distributions can be depicted in histograms.
- Each outcome is associated with a specific frequency value.
Theoretical Distributions
- Based entirely on theoretical considerations, not data.
- Represented by probabilities, not frequencies.
- Based on infinite observations.
- Examples include the discrete uniform distribution.
Uniform Distribution
- Discrete version of a uniform distribution.
- Probability is evenly spread across all possible outcomes.
Variables
- Characteristics that change between individuals within a study.
Qualitative Research
- Answers questions using descriptive words or phrases (e.g., marital status).
- Alternatively, responses can be numerical (e.g., number of houses owned.
- Discrete variables have a fixed number of possible outcomes.
- Continuous variables have an infinite number of possible outcomes.
Theoretical Distributions: Tools and Assumptions
- Tools for modelling empirically observed data.
- Assumes a generating process that follows a particular distribution.
- Discovering or estimating distribution properties allows for predictions of future observations.
- Different distributions are useful for modelling different processes.
Normal Distribution (Gaussian Distribution)
- A theoretical distribution depicted by a bell curve.
- Continuous data, with mean indicating the central tendency.
- Data are symmetrically centered around the mean where most data points are near the mean.
- Parameters like mean and standard deviation describe the distribution's characteristics.
- Changing the mean shifts the distribution on the x-axis.
- Changing the standard deviation stretches or squeezes the distribution.
- Mean and median are identical for normally distributed data.
- The area under the curve sums to 1.
- A given proportion (e.g., 68%) of the data falls within a particular standard deviation range.
Descriptive Statistics
- Used to summarize data.
Inferential Statistics
- Used to make inferences about populations based on samples.
Samples and Populations
- Samples are representative observations from a larger population.
- Populations are all possible observations of a particular phenomenon.
- Samples are derived from populations to estimate population parameters.
Median
- A summary statistic to divide a distribution.
- Half of the data falls above and below the median.
- Less sensitive to extreme values compared to the mean.
Range
- A summary statistic indicating the difference between the minimum and maximum values.
- Less informative as a measure of spread than other methods.
Standard Deviation
- A measure of spread in a distribution.
- Represents the average distance from the mean for data within a distribution.
- Higher standard deviations indicate greater data spread.
Boxplots
- Graphical representations summarizing data distribution.
- Displays the median, quartiles, and potential outliers.
Hypothesis Testing
- Evaluating whether differences in observations are likely due to chance.
- Key to interpret results and draw conclusions (e.g., Null Hypothesis Significance Testing).
Effect Sizes
- Quantify the magnitude of differences between groups or samples.
- Taking into account group variability and sample size increases accuracy.
- Factors like larger differences and low variability within the group increase the confidence that the measure is accurate.
Standard Error
Calculates the precision of a measured parameter.
- Combines the variability of data and sample size.
Statistical Errors
- Type I error (false positive): rejecting a true null hypothesis (falsely identifying an effect).
- Type II error (false negative): failing to reject a false null hypothesis (missing a true effect).
- Type M error: misestimating the magnitude of an effect.
- Type S error: observing an effect with the incorrect direction (opposite of the expected effect).
Multiple Comparisons
- Adjustments for testing many hypotheses, increasing the probability of type I error.
Statistical Methods for data analysis
- Independent samples t-tests: comparing means from two independent samples.
- Paired samples t-test: comparing means from two related samples (e.g., before and after).
- One-sample t-test: comparing a sample mean to a known reference.
Standardizing Data
- Z-scores (standardized scores): transform data to common units (e.g., standard deviations).
- Removing the metric of the variable allows the comparison of different variables.
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Description
Explore the essential concepts of models and distributions in statistics. This quiz covers both empirical and theoretical distributions, means, and standard deviations. Understand how these concepts summarize complex data and their applications in real-world scenarios.
