Untitled Quiz

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What does statistical inference involve?

Analyzing sample data to draw conclusions about the broader population.

What are the two main aspects of statistical inference?

Derive estimates and test hypothesis (correct)

Calculate variance and analyze data

Perform regression and run simulations

None of the above

Statistical models are always perfect representations of reality.

False

What is a test statistic?

A numerical value that summarizes sample data for the purpose of testing hypotheses. Signup and view all the answers

What is a probability distribution?

It defines the likelihood of different values for a random variable. Signup and view all the answers

What is the standard deviation?

A measure of the spread of data Signup and view all the answers

Which of these statements is true about the normal distribution?

It is a symmetrical distribution. Signup and view all the answers

A confidence interval reflects the range of values within which the population parameter is likely to fall.

True Signup and view all the answers

What does the standard error represent?

The variability of sample means across multiple samples drawn from a population. Signup and view all the answers

A higher confidence level always leads to a wider confidence interval.

True Signup and view all the answers

What is the significance level (alpha) in hypothesis testing?

The probability of rejecting a true null hypothesis. Signup and view all the answers

A p-value represents the probability of obtaining the observed data or more extreme results, assuming the null hypothesis is true.

True Signup and view all the answers

What are the steps involved in the process of NHST (Null Hypothesis Significance Testing)?

Formulating hypotheses, modeling the effect, selecting a significance level, calculating the test statistic, and interpreting the results. Signup and view all the answers

What does the p-value indicate?

The probability of obtaining the observed results if the null hypothesis is true. Signup and view all the answers

Type I error occurs when we reject a true null hypothesis.

True Signup and view all the answers

Type II error occurs when we fail to reject a false null hypothesis.

True Signup and view all the answers

What is the objective of hypothesis testing?

To determine whether there is sufficient evidence to support the alternative hypothesis and reject the null hypothesis. Signup and view all the answers

What are the advantages of using the median as a measure of central tendency?

It is not affected by outliers (extreme values), it provides more information than the mode, and it divides the data into two equal halves. Signup and view all the answers

What is a major limitation of the range as a measure of variability?

It is highly sensitive to outliers, making it unstable across different samples. Signup and view all the answers

Explain the concept of variance in statistics.

Variance measures the average squared deviation of data points from the mean, reflecting the overall spread or variability of the data. Signup and view all the answers

Standard deviation is the square root of variance.

True Signup and view all the answers

The sum of squares (SS) reflects the variability in the data and can be used to assess homogeneity (similarity) or heterogeneity (dissimilarity) of ratings.

True Signup and view all the answers

What is the purpose of a scatterplot in statistical analysis?

To visualize the relationship between two variables and examine their directionality and strength of association. Signup and view all the answers

What are some assumptions that parametric tests often require?

All of the above Signup and view all the answers

Non-parametric tests are often referred to as "distribution-free" because they make fewer assumptions about the underlying distribution of the data.

True Signup and view all the answers

What is the benefit of using a composite variable in research?

It combines information from multiple items to create a single, more comprehensive measure of a construct or concept. Signup and view all the answers

Measurement error refers to discrepancies between the observed score and the true score.

True Signup and view all the answers

What is the difference between validity and reliability in a measurement instrument?

Validity examines whether the instrument measures what it is supposed to measure, while reliability assesses the consistency of the measurements. Signup and view all the answers

The mode is particularly suitable for nominal and ordinal variables because it is not influenced by extreme values.

True Signup and view all the answers

The mean is less sensitive to outliers (extreme values) compared to the median.

False Signup and view all the answers

The chi-square test is used to analyze categorical variables with two or more levels, comparing their frequencies to assess association or dependence.

True Signup and view all the answers

What is a contingency table?

A table that displays the frequencies of two or more categorical variables simultaneously, allowing for the examination of their association or independence. Signup and view all the answers

The independent samples t-test is used to compare the means of two groups on a continuous variable.

True Signup and view all the answers

The paired-samples t-test is used to compare the means of two dependent groups on a continuous variable.

True Signup and view all the answers

One-way ANOVA is used to compare the means of three or more independent groups on a continuous variable.

True Signup and view all the answers

What is the purpose of post-hoc tests in ANOVA?

To identify which specific groups differ significantly from each other, following a significant overall F-statistic in the ANOVA. Signup and view all the answers

ANCOVA (Analysis of Covariance) is used to analyze the effect of a factor while controlling for the influence of a continuous extraneous variable.

True Signup and view all the answers

Factorial ANOVA involves two or more factors, allowing for the analysis of interaction effects, which are the combined effects of multiple factors on the outcome.

True Signup and view all the answers

What does the correlation coefficient (r) measure?

The strength and direction of the linear relationship between two continuous variables. Signup and view all the answers

The coefficient of determination (R²) represents the proportion of variance in one variable that is explained by another variable.

True Signup and view all the answers

The Pearson correlation coefficient is a non-parametric measure of association.

False Signup and view all the answers

Partial correlation is a method for examining the relationship between two variables while controlling for the influence of a third variable.

True Signup and view all the answers

Multiple regression analysis involves predicting the value of an outcome variable based on the influence of multiple independent variables.

True Signup and view all the answers

The regression coefficient in a multiple regression model represents the unique effect of a predictor variable while simultaneously controlling for the effects of other predictor variables.

True Signup and view all the answers

Multicollinearity is present when the predictor variables in a regression model are highly correlated, which can lead to problems with the reliability of the model.

True Signup and view all the answers

Autocorrelation refers to the correlation between the residuals of two adjacent observations in a time series.

True Signup and view all the answers

Homoscedasticity in regression exists when the variance of the residuals is constant across the different levels of the predictor variable.

True Signup and view all the answers

Logistic regression is a statistical technique used to predict the probability of a categorical outcome variable based on the influence of one or more continuous or categorical predictor variables.

True Signup and view all the answers

What does the concept of "moderation" refer to in regression analysis?

Moderation occurs when the effect of one predictor variable on the outcome variable varies at different levels of another predictor variable. It examines how a second variable influences the relationship between a first predictor variable and the outcome. Signup and view all the answers

Explain the difference between "Spotlight Analysis" and "Floodlight Analysis" in interaction analysis.

Spotlight Analysis examines the effect of one predictor at a specific value of another predictor (moderator), often using simple slopes, while Floodlight Analysis investigates the entire range of values for the moderator, examining the effect of the predictor across the whole spectrum of the moderator. Signup and view all the answers

In logistic regression, the "logit" is a linear transformation of the odds.

True Signup and view all the answers

The "odds ratio" in logistic regression indicates the change in the odds of the outcome resulting from a one-unit change in the predictor variable.

True Signup and view all the answers

The Hosmer and Lemeshow test is a statistical test used to assess the goodness-of-fit of a logistic regression model to the data.

True Signup and view all the answers

The "hit ratio" in logistic regression refers to the proportion of cases that are correctly classified by the model.

True Signup and view all the answers

What are some key advantages of using logistic regression?

Logistic regression is a versatile tool for predicting the probability of a categorical outcome, handling both continuous and categorical predictor variables, and can be used to analyze interactions between predictors. It is useful for analyzing a wide variety of phenomena and making predictions. Signup and view all the answers

Logistic regression requires a larger sample size compared to linear regression to achieve accurate results.

True Signup and view all the answers

Study Notes

Statistical Inference

Statistical inference uses sample data to make conclusions about a larger population.
Key aspects involve deriving estimates, testing hypotheses, and understanding the variability involved due to sampling.
Statistically model a hypothesis using a test statistic.
Obtain a random/representative sample.
Summarize sample data using a relevant test statistic.
Use the probability distribution of the test statistic to make inferences about the population.

Probability (Frequency) Distribution

It describes the likelihood of different values of a random variable.
These likelihoods are based on an underlying probability distribution.

Normal and Standard Normal Distribution

Normal distributions have a specific, symmetric, bell-shaped distribution.
68-95-99.7% (empirical rule): 68% of the data falls within one standard deviation, 95% within two standard deviations and 99.7% within three standard deviations of the mean.
Normal distributions can be standardized by converting them into a standard normal distribution with a mean of 0 and standard deviation of 1.

Sampling Error (Margin of Error)

Sampling error arises because a sample, not the whole population, is examined.
The variability of the sample statistic can be estimated theoretically using the Standard Error (SE) and the critical value from the relevant probability distribution (e.g., Z-score for confidence levels).

Parameter Estimation

Collecting data provides a sample statistic (e.g., mean).
Use a sample statistic to estimate an entire population parameter.
Variability in the sample statistic (standard deviation) can be reduced by increasing the sample size.

Confidence Level

The probability that an estimation will capture the true population parameter.
The significance level (a, or alpha) is the opposite of the confidence level.

Critical values and Conf./Sig. level

These values determine the rejection region based on pre-set confidence/significance levels, commonly 95%, 99%, 99.9%
They dictate the range of test statistics that lead to rejecting the null hypothesis.

Confidence Interval

A range of calculated values that has a specified probability of containing the true population parameter, dependent on the level of confidence.

Hypothesis Testing

A statement about a specific state of the world that is empirically testable.
It can be related to relationships between variables.
A "null" hypothesis asserts no effect.
An "alternative" hypothesis posits an effect of interest. (a particular direction/difference)

Types of Hypotheses

Directional predictions specify a direction of effect (e.g., greater than, less than).
Non-directional predicts an effect, but not its direction (e.g., different from).

Test Statistics

Numerical summaries of data that reflect the expected effect(s) of a particular test.
Dependent on the specific statistical test performed.

Type I and Type II Error

Type I error: Rejecting a true null hypothesis (false positive).
Type II error: Failing to reject a false null hypothesis (false negative).
A is the probability of a type I error; β is the probability of a type II error.

Significance Level

The maximum “risk” (probability of a Type I error) taken in hypothesis testing. Commonly set at 0.05, or 5%.
Helps define the critical values for rejecting the null hypothesis.

Test Statistic (p-value vs. critical value)

Probability of obtaining a test statistic (or bigger) if the null hypothesis is true.
The (p)-value is the probability of getting results that are extreme (or more extreme) than your observed result, if the null hypothesis is true.

Regions of Rejection

Region of sample data that would lead us to reject a null hypothesis, based on a degree of accepted probability of error.

Statistical Power

Probability of correctly rejecting a false null hypothesis.
Increases with larger sample sizes and effect sizes.

Sample Size and Statistical Significance

Larger samples decrease sampling error.

Effect Size

Magnitude of the observed effect, irrespective of sample size.
Standard ways to quantify this include Cohen's d and Pearson's r.

Key Terms

Units of analysis: "who" is being studied ("cases," "observations," etc.)
Variables: "what" is being measured
Values: The specific qualities of the variable(s), measured across participants

Data Matrix

Organized table of values for specific variables concerning specific participants/cases

Data Format and types of variables

Different questions in data collection generate different data formats and types of data
Categorical variables categorize respondents, ordinal variables rank, and continuous or interval variables measure to scale.

Variables and Constructs

Constructs are larger, more complex phenomena described in research.
Variables are specific, measurable aspects of the construct.

Forming new variables

Creating synthetic variables combining multiple individual measures of the same concept.

Measurement Error

Includes both systematic and unsystematic errors.

The Mode

The most frequent score in a set of data.
Usually appropriate for nominal/ordinal variables
Less useful for assessing variability
Useful, when identifying central tendency

The Median

The middle score in a cumulative ordered set of data.
Appropriate for ordinal/scale variables
Not sensitive to extreme values
Useful to identify the central tendency

Percentiles

Values of a variable at different quantile segments.
Useful for assessing, variability and distribution

The Mean

The simple average of all scores in a data set.
Effective for metric (scale) data
Sensitive to extreme values

Range

Difference between the highest and lowest values in a set of data.
Simple measure of dispersion.
Sensitive to extreme values

Deviance

Measuring the difference between the observed scores and a central point (e.g. mean).

Variance

Measuring the average squared difference between the observed scores and a central point (e.g. mean)
A measure of dispersion

Standard Deviation

Square root of the variance, providing a measure of dispersion but in the original unit of measurement, unaffected by scale changes.

Data Frequencies

Picture of the frequency distribution of one or more variables across participants.
Summarizes typical values, useful for identifying central tendency

Frequency Tables

Tabular summary of distributions in data, often showing frequencies and percentages, for discrete/categorical variables.

Bar Charts

Display frequency distribution of categorical variables.

Histograms

Visual representation of the distribution of the frequencies of one continuous measure.

Scatterplots

Illustrates the bivariate relationship/correlation between two variables.

Assumptions

Conditions that must be met for the results of statistical tests to be reliable and generalizable.
Includes assumptions about normality of residuals, homogeneity of variances and independence of observations

Linearity and Additivity (in regression)

Relationships between variables are linear, and the effect of predictors adds up without interactions.

Independence (in regression)

Observations, errors, and residuals in the data are independent

Normality (in regression)

Both the sampling distribution of the estimates and the residuals/errors are normally distributed

Homogeneity of Variances (Homoscedasticity)

Variance of the residuals is consistent across all levels of predictors

P-P Plot/Q-Q Plot

Plots to verify the assumed normality of distributions

Test for Normality

Kolmogorov-Smirnov and Shapiro-Wilk tests help determine if data follow a normal distribution.

Central Limit Theorem

If the sample size is large enough (n > 30), the sampling distribution of a sample statistic (e.g., mean) is approximately normal.

Homogeneity of Variance

The variance of the outcome variable is similar across different predictor groups. Measured via Levene's test or Hartley's F-max

Comparing Independent Samples

Methods for comparing two or more independent groups (e.g., t-test, ANOVA). Use different analyses for different variable types (nominal, ordinal, interval, ratio).

Comparing the Same Sample

Methods for comparing the same sample across different measures (e.g., repeated measures ANOVA, paired-samples t-test).

Third (Confounding) Variables

Controlling for additional, potentially related variables. Includes partial correlation and use of covariates in regression models.

Regression Analysis:

Predicting a continuous outcome variable from one or more predictor variables, assuming a linear relationship.

Simple Regression

Predicting a continuous outcome variable from a single predictor variable, assuming a linear relationship. Includes intercept (bo) and coefficient (b1).

Ordinary Least Squares (OLS)

Method for finding the best-fitting straight line in linear regression. (minimizes errors)

Components of the Regression Model

Partitioning the total variation present in the data
Explained variation via the model (SSM) and unexplained variation (SSR)
- Sum of Squares Total (SST) = Sum of Squares Regression(SSR) +Sum of Squared Error(SSE)

Testing the Regression Model

Using an ANOVA to determine if the regression model is a better predictor of the outcome variable compared to simply using the mean.
Assess the proportion of variability that’s explained by the model (using R^2).

Multiple Regression

Predicting an outcome variable from several predictor variables.
Using multiple predictors to enhance model accuracy and interpretation.

Methods for multiple predictors

How to choose from different procedures to include multiple predictors
Enter(forced entry), Hierarchical(blockwise), Stepwise(forward/backward)

Validity and Generalizability in Regression

Ensuring that the regression model's findings are trustworthy and applicable outside the sample dataset.

Assumptions of Regression

Requirements that must be met for valid results and generalization (includes variable types, zero variance, additivity/linearity, independence, homoscedasticity, and normality)

Multicollinearity

High correlation among predictor variables. Reduces accuracy and interpretability.

Independent Errors (Autocorrelation)

Correlated residuals across observations.

Homoscedasticity and Normality of Residuals

Uneven variances or non-normal patterns in residuals compromise regression outcomes.

Predicted Values, Observed Values, and Residuals

Visual verification of whether predicted vs actual outcomes or whether model assumptions concerning residuals were reasonable

One-Way ANOVA

Comparing means across three or more groups
- Assumes independent observations and normally distributed errors, and homogeneity of variances

Factorial ANOVA

Investigating how the effects(s) of one predictor (variable A) influence or moderate other predictors (e.g., B) on the outcome (variable Y) or investigating the combined effect of multiple predictors (e.g., A, B, A x B, etc.)
- Often uses a between-subject design, or a within-subject.
- Assumes independence of observations and normally distribution errors, with the homogeneity of variances

Two-Way ANOVA

Analyzing the effect of two or more independent variables on a dependent variable, assessing main and interaction effects
- Includes all the assumptions of one-way ANOVA

Evaluating Regression Models

Assessing the model and its generalizability (Validity or/and Generalizability), and checking the effect of individual predictors of a statistical model (evaluating how likely is an effect from a predictor variable).

Logistic Regression

Predicting categorical outcome variables from one or more predictor variables.
Assumes variables are independent, and with sufficient sample size(n>60), and the log-transformations of data follow a normal distribution

Multiple Regression: Interpretation

Interpreting the coefficients (betas) in a multiple regression model to assess the unique influence of each predictor on the outcome variable
- Using different type of variables, for instance continuous,categorical, binary

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Untitled Quiz

Choose a study mode

Podcast

Questions and Answers

What does statistical inference involve?

What are the two main aspects of statistical inference?

Statistical models are always perfect representations of reality.

What is a test statistic?

What is a probability distribution?

What is the standard deviation?

Which of these statements is true about the normal distribution?

A confidence interval reflects the range of values within which the population parameter is likely to fall.

What does the standard error represent?

A higher confidence level always leads to a wider confidence interval.

What is the significance level (alpha) in hypothesis testing?

A p-value represents the probability of obtaining the observed data or more extreme results, assuming the null hypothesis is true.

What are the steps involved in the process of NHST (Null Hypothesis Significance Testing)?

What does the p-value indicate?

Type I error occurs when we reject a true null hypothesis.

Type II error occurs when we fail to reject a false null hypothesis.

What is the objective of hypothesis testing?

What are the advantages of using the median as a measure of central tendency?

What is a major limitation of the range as a measure of variability?

Explain the concept of variance in statistics.

Standard deviation is the square root of variance.

The sum of squares (SS) reflects the variability in the data and can be used to assess homogeneity (similarity) or heterogeneity (dissimilarity) of ratings.

What is the purpose of a scatterplot in statistical analysis?

What are some assumptions that parametric tests often require?

Non-parametric tests are often referred to as "distribution-free" because they make fewer assumptions about the underlying distribution of the data.

What is the benefit of using a composite variable in research?

Measurement error refers to discrepancies between the observed score and the true score.

What is the difference between validity and reliability in a measurement instrument?

The mode is particularly suitable for nominal and ordinal variables because it is not influenced by extreme values.

The mean is less sensitive to outliers (extreme values) compared to the median.

The chi-square test is used to analyze categorical variables with two or more levels, comparing their frequencies to assess association or dependence.

What is a contingency table?

The independent samples t-test is used to compare the means of two groups on a continuous variable.

The paired-samples t-test is used to compare the means of two dependent groups on a continuous variable.

One-way ANOVA is used to compare the means of three or more independent groups on a continuous variable.

What is the purpose of post-hoc tests in ANOVA?

ANCOVA (Analysis of Covariance) is used to analyze the effect of a factor while controlling for the influence of a continuous extraneous variable.

Factorial ANOVA involves two or more factors, allowing for the analysis of interaction effects, which are the combined effects of multiple factors on the outcome.

What does the correlation coefficient (r) measure?

The coefficient of determination (R²) represents the proportion of variance in one variable that is explained by another variable.

The Pearson correlation coefficient is a non-parametric measure of association.

Partial correlation is a method for examining the relationship between two variables while controlling for the influence of a third variable.

Multiple regression analysis involves predicting the value of an outcome variable based on the influence of multiple independent variables.

The regression coefficient in a multiple regression model represents the unique effect of a predictor variable while simultaneously controlling for the effects of other predictor variables.

Multicollinearity is present when the predictor variables in a regression model are highly correlated, which can lead to problems with the reliability of the model.

Autocorrelation refers to the correlation between the residuals of two adjacent observations in a time series.

Homoscedasticity in regression exists when the variance of the residuals is constant across the different levels of the predictor variable.

Logistic regression is a statistical technique used to predict the probability of a categorical outcome variable based on the influence of one or more continuous or categorical predictor variables.

What does the concept of "moderation" refer to in regression analysis?

Explain the difference between "Spotlight Analysis" and "Floodlight Analysis" in interaction analysis.

In logistic regression, the "logit" is a linear transformation of the odds.

The "odds ratio" in logistic regression indicates the change in the odds of the outcome resulting from a one-unit change in the predictor variable.

The Hosmer and Lemeshow test is a statistical test used to assess the goodness-of-fit of a logistic regression model to the data.

The "hit ratio" in logistic regression refers to the proportion of cases that are correctly classified by the model.

What are some key advantages of using logistic regression?

Logistic regression requires a larger sample size compared to linear regression to achieve accurate results.

Study Notes

Statistical Inference

Probability (Frequency) Distribution

Normal and Standard Normal Distribution

Sampling Error (Margin of Error)

Parameter Estimation

Confidence Level

Critical values and Conf./Sig. level

Confidence Interval

Hypothesis Testing

Types of Hypotheses

Test Statistics

Type I and Type II Error

Significance Level

Test Statistic (p-value vs. critical value)

Regions of Rejection

Statistical Power

Sample Size and Statistical Significance

Effect Size

Key Terms