Statistics Lecture 1: Introduction to Statistics

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What does the alternative hypothesis predict?

  • There will be no difference between groups.
  • There will be a random outcome.
  • There will be a correlation between variables.
  • There will be a difference between groups. (correct)

What does a p-value represent in hypothesis testing?

  • The probability that the effect measured is due to chance. (correct)
  • The confidence interval of the estimated effect.
  • The proportion of data points that are outliers.
  • The likelihood of future experiments yielding similar results.

When is a Type 1 error likely to occur?

  • When confounding variables are controlled for.
  • When the significance level is set too low.
  • When researchers incorrectly reject the null hypothesis when it is indeed true. (correct)
  • When researchers accept the null hypothesis when it is impossible.

What criterion level must the p-value be less than to reject the null hypothesis?

<p>0.05 (C)</p> Signup and view all the answers

What does internal validity refer to in research?

<p>The extent to which the researcher is testing what they claim to be testing. (B)</p> Signup and view all the answers

What is a primary weakness of using a between-subjects design?

<p>It can lead to a variety of individual differences impacting the dependent variable. (A)</p> Signup and view all the answers

Which of the following is a strength of within-subjects design?

<p>Less participant variability due to individual differences. (A)</p> Signup and view all the answers

What best describes an extraneous variable?

<p>It is a variable that is not being studied but can still influence the outcomes. (C)</p> Signup and view all the answers

How can order effects in within-subjects design be mitigated?

<p>Through the use of counterbalancing. (D)</p> Signup and view all the answers

What is a disadvantage of matched-pairs design?

<p>It is time-consuming to match participants. (C)</p> Signup and view all the answers

What is a defining characteristic of a confounding variable?

<p>It systematically influences both the independent and dependent variables. (C)</p> Signup and view all the answers

What type of design minimizes participant variable differences through pairing?

<p>Matched-pairs design. (C)</p> Signup and view all the answers

What is a potential outcome of using a between-subjects design in an experiment?

<p>Higher number of participants needed to achieve results. (C)</p> Signup and view all the answers

What characterizes a multiple regression model?

<p>It employs a plane of best fit rather than a straight line. (C)</p> Signup and view all the answers

When reporting a regression analysis in APA format, which element is NOT typically included?

<p>The mean of the dependent variable. (B)</p> Signup and view all the answers

What does a p-value less than 0.05 indicate in T-tests?

<p>The means of the two groups are statistically significant. (B)</p> Signup and view all the answers

Which statement accurately describes the t-value in T-tests?

<p>It can be negative if the sample mean is less than the hypothesized mean. (A)</p> Signup and view all the answers

What is the purpose of degrees of freedom (df) in T-tests?

<p>To indicate the number of independent values that can be estimated. (D)</p> Signup and view all the answers

Which element is NOT a part of the analysis assumptions for an independent sample T-test?

<p>Large sample sizes for both groups. (A)</p> Signup and view all the answers

Which of the following correctly describes the unstandardised coefficient in regression analysis?

<p>It represents the change in the dependent variable for a one-unit change in an independent variable. (B)</p> Signup and view all the answers

In a multiple regression equation represented as Z = ax + by + c, what does 'c' represent?

<p>The intercept of the regression plane. (D)</p> Signup and view all the answers

What does the ANOVA test in regression analysis assess?

<p>The overall significance of the regression model. (D)</p> Signup and view all the answers

How does a positive t-value in a T-test relate to group means?

<p>The sample mean is greater than the hypothesized mean. (A)</p> Signup and view all the answers

Which aspect of reliability ensures that a measurement produces consistent results across different observers?

<p>Inter-rater reliability (D)</p> Signup and view all the answers

In research design, what is the primary purpose of specifying the independent variable (IV)?

<p>To manipulate and observe its effect on the dependent variable (DV) (B)</p> Signup and view all the answers

Which of the following describes discrete variables?

<p>Variables that possess fixed values, often integers (D)</p> Signup and view all the answers

What does ecological generalisability refer to in research?

<p>The relevance of findings to real-world situations (D)</p> Signup and view all the answers

Which step comes immediately after data collection in the experimental design process?

<p>Describe the data (A)</p> Signup and view all the answers

What is meant by the term 'central tendency' in statistics?

<p>A single value that identifies the central position within a data set (B)</p> Signup and view all the answers

Which type of reliability is focused on repeating the measure over time to assess consistency?

<p>Test-retest reliability (D)</p> Signup and view all the answers

In the context of continuous variables, which of the following is an example?

<p>The height of individuals in centimeters (B)</p> Signup and view all the answers

What is a critical first step when designing an experiment?

<p>Identify the independent and dependent variables (D)</p> Signup and view all the answers

Which of the following statements best describes external reliability?

<p>It relates to the consistency of results across different studies (C)</p> Signup and view all the answers

What characterizes a deterministic model system?

<p>It delivers the same results each time when conditions are identical. (B)</p> Signup and view all the answers

What is an example of unsystematic variation?

<p>Variations resulting from factors not under statistical control. (B)</p> Signup and view all the answers

What does inferential statistics enable researchers to do?

<p>It makes predictions about a larger population based on sample data. (D)</p> Signup and view all the answers

Which method is effective for minimizing unsystematic variation?

<p>Utilizing random assignment of participants. (B)</p> Signup and view all the answers

How can statistics be misleading?

<p>Through the use of exaggerated graphics and selective data presentation. (B)</p> Signup and view all the answers

Which of the following is a key feature of a probabilistic model system?

<p>Incorporates randomness, yielding different outcomes with same conditions. (D)</p> Signup and view all the answers

What is the purpose of descriptive statistics?

<p>To provide summaries and overviews of dataset characteristics. (D)</p> Signup and view all the answers

What is often a consequence of systematic variation?

<p>It indicates reliable changes caused by independent variable manipulation. (A)</p> Signup and view all the answers

Which statement best describes the role of statistics in determining likelihood of events?

<p>Statistics helps in understanding the probabilities of various events and chance occurrences. (A)</p> Signup and view all the answers

What is NOT a component of descriptive statistics?

<p>Testing for differences (B)</p> Signup and view all the answers

Flashcards

Participant Variables

Individual differences in participants that may influence the dependent variable, rather than the independent variable.

Between-Subjects Design

A research design where each participant is exposed to only one level of the independent variable.

Within-Subjects Design

A research design where each participant experiences all levels of the independent variable.

Order Effects

Effects on performance in a within-subjects design that arise from the order in which participants experience the different levels of the independent variable.

Signup and view all the flashcards

Carryover Effects

Differences in performance caused by the influence of an earlier condition on a later condition in a within-subjects design.

Signup and view all the flashcards

Extraneous Variables

Any variable, other than the independent variable, that might influence the dependent variable.

Signup and view all the flashcards

Confounding Variable

A specific type of extraneous variable that affects both the independent variable and the dependent variable, making it difficult to determine the true effect of the independent variable.

Signup and view all the flashcards

Hypothesis

A testable prediction about the outcome of a research study.

Signup and view all the flashcards

Alternative Hypothesis

Predicts there will be a difference between groups. Example: A pill enhances alertness.

Signup and view all the flashcards

Null Hypothesis

Predicts there will be NO difference between groups. Example: There's no difference in alertness with or without the pill.

Signup and view all the flashcards

p-value

The probability of the effect being due to chance. Lower p = lower chance. (p=0.05 means there's a 5% chance the results are due to random chance.)

Signup and view all the flashcards

Statistical Test

A statistical test that tells us whether to reject or not reject the null hypothesis.

Signup and view all the flashcards

Type 1 Error (False Positive)

Error that occurs when you reject the null hypothesis when it's actually true. (You conclude there is a change when there is none).

Signup and view all the flashcards

What is statistics?

The process of using real data to identify patterns and trends in the world.

Signup and view all the flashcards

Why do you need statistics?

To understand the likelihood of events and distinguish between chance and meaningful patterns.

Signup and view all the flashcards

Deterministic Model System

A model where every run with the same conditions produces the same results. It doesn't account for random variations.

Signup and view all the flashcards

Probabilistic Model System

A model that incorporates randomness, leading to different results even with the same initial conditions.

Signup and view all the flashcards

Unsystematic Variation

Variations in data caused by unknown factors not under statistical control. Example: participants' intelligence, mood, or education levels.

Signup and view all the flashcards

Systematic Variation

Differences in performance specifically due to the manipulation of the independent variable in an experiment.

Signup and view all the flashcards

Descriptive Statistics

Summarizes and describes the characteristics of a data set, using measures like central tendency, variability, and frequency distribution.

Signup and view all the flashcards

Inferential Statistics

Uses samples to make inferences about a larger population. It involves testing for differences, correlations, and interactions.

Signup and view all the flashcards

How can stats mislead others?

A misleading presentation of data, often involving exaggeration or incomplete information, can create a skewed interpretation.

Signup and view all the flashcards

What are the three scientific methods?

The scientific methods: observation, experimentation, and modeling.

Signup and view all the flashcards

Reliability

The consistency of a task, procedure, or measurement. If a measure produces similar results when repeated, it is reliable.

Signup and view all the flashcards

Test-retest reliability

A type of reliability where a measure produces consistent scores when the same task is repeated, even if there is some time between measurements.

Signup and view all the flashcards

Inter-rater reliability

A type of reliability that assesses the consistency between different observers or raters in their judgments or measurements.

Signup and view all the flashcards

Internal reliability

A type of reliability that assesses the consistency of scores when different parts of a test or measurement are compared.

Signup and view all the flashcards

Continuous variable

Variables that can take on any value within a given range. Examples include height, weight, and temperature.

Signup and view all the flashcards

Discrete variable

Variables that can only take on specific, fixed values. Often, these are whole numbers or categories. For example, the number of students in a class.

Signup and view all the flashcards

Mode

A central tendency measure that describes the most frequent value in a dataset.

Signup and view all the flashcards

Central tendency

A single value that attempts to describe the central position of a dataset. It is often used to represent the 'typical' score.

Signup and view all the flashcards

Ordinal variable

Variables that can be ranked or ordered. Examples include finishing positions in a race or student grades.

Signup and view all the flashcards

Generalisability

This refers to the extent to which findings from a study can be applied to other groups or situations.

Signup and view all the flashcards

T-test

A statistical test comparing the means of two groups to see if the difference is significant.

Signup and view all the flashcards

Degree of freedom (df)

Measure based on sample size, indicating the number of independent values that can be estimated in an analysis. It affects the significance of the t-test result.

Signup and view all the flashcards

Independent sample t-test

Compares the means of two independent groups. Each group is exposed to a different condition or treatment.

Signup and view all the flashcards

Multiple regression

A model estimating the relationship between a dependent variable and two or more independent variables. It uses a plane of best fit instead of a line, representing how the independent variables' values influence the dependent variable.

Signup and view all the flashcards

Reporting regression in APA

Describes a regression analysis in APA style, outlining the type of analysis, relationship between variables, significance of variance, predictors, coefficients, and their impact on the dependent variable.

Signup and view all the flashcards

Multiple regression

A statistical technique that allows researchers to predict a dependent variable (DV) from multiple independent variables (IVs) simultaneously. It models the relationship between variables, providing valuable insights into how they influence each other.

Signup and view all the flashcards

Multicollinearity

Refers to a situation where two or more independent variables are highly correlated. This can inflate the significance of certain variables in multiple regression, making it difficult to pinpoint the accurate contributions of individual predictors.

Signup and view all the flashcards

R-squared in multiple regression

A statistical measure that indicates the proportion of variance in the dependent variable that is explained by the independent variables in a multiple regression model. R-squared close to 1 means the model predicts the dependent variable well.

Signup and view all the flashcards

Paired-samples t-test

A type of t-test that compares the means of two related groups. Each participant is measured twice, once under each condition.

Signup and view all the flashcards

Study Notes

Lecture 1: What is Statistics?

  • Statistics is the process of understanding patterns in real-world data, predicting likelihoods, and identifying causes of events.
  • Deterministic Model System doesn't incorporate randomness; same conditions always produce the same results.
  • Probabilistic Model System includes randomness; repeated runs with identical conditions might yield different results.
  • Unsystematic Variation represents inaccuracies or anomalies due to uncontrollable factors (e.g., participant differences).
  • Systematic Variation describes performance differences caused by manipulations.
  • Descriptive Statistics summarise and describe data characteristics using measures of central tendency (mean, median, mode) and variability
  • Inferential Statistics uses samples to make inferences about larger populations. This involves testing differences, correlations, and interactions.
  • Misleading Statistics: data may only show part of the data or use exaggerated graphics, potentially leading to inaccurate conclusions.

Lecture 2: Three Scientific Methods

  • Experiments: investigate cause-and-effect relationships by manipulating the independent variable (IV) and measuring the dependent variable (DV). Extraneous variables are controlled.
  • Quasi-Experiments: examine cause-and-effect relationships but don't use random assignment to groups. Researchers have less control over the treatment/manipulation.
  • Correlational Methods: explore associations between variables (strength and direction) but don't infer cause-and-effect relationships, only indicate a relationship.
  • Categorical Variables: classify data into distinct categories or groups, and can be nominal (with no inherent order) or ordinal (with a meaningful order).

Lecture 3: Types of Variables and Central Tendency

  • Discrete Variables: have fixed values (often integers). Examples include the number of objects.
  • Continuous Variables: can take on any value within a range. Examples include distance, height, or time.
  • Central Tendency: a single value that represents the 'central' position within a dataset; describing the typical/most frequent value in a distribution.
  • Mode: the most frequent data value.
  • Median: the middle value when data set is ordered.
  • Mean: the sum of all values divided by the number of values.

Lecture 4: Measures of Spread

  • Range: the difference between the largest and smallest values in a dataset.
  • Interquartile Range: the difference between the third (Q3) and first (Q1) quartiles; describes the spread of the middle 50% of data.
  • Variance: the measure of how spread out numbers are in a data set. It is essentially the average of the squared distances from the mean.
  • Standard Deviation: the square root of the variance, representing the average distance from the mean.

Lecture 5: Hypothesis Testing and Validity/Reliability

  • Hypothesis: a testable statement predicting the outcome of a study.
  • Alternative Hypothesis: predicts a difference between groups/conditions.
  • Null Hypothesis: predicts no difference between groups/conditions.
  • Test Statistic: used to assess the probability that the effect measured was due to chance. The p-value represents this probability.
  • Type I Error: rejecting null hypothesis when it is true.
  • Type II Error: failing to reject null hypothesis when it is false.
  • Validity: the extent to which a test measures what it claims to measure.
  • Reliability: the consistency and dependability of a measurement or test.

Lecture 6: SPSS and Correlation Tests

  • Kolmogorov-Smirnov Test: whether a data set is normally distributed.
  • Levene's Test: used to test for homogeneity of variances in data; needed in t-tests, ANOVA and other statistical methods.

Lecture 7: Correlation and Regression

  • Correlation: investigating association (strength and direction) between variables.
  • Covariance: measures the relationship between the deviations of two variables; positive covariance means that both variables move in the same direction, while negative covariance means that they move in opposite directions.
  • Pearson's Correlation: measures the strength and direction of a linear relationship between continuous variables.
  • Spearman's rank correlation: used to find the relationship between ranked scores/ordinal data.
  • Partial Correlation: the relationship between two variables when controlling the influence of other variables.
  • Regression Analysis: used to explore relationships between a dependent variable and one or more independent variables.
  • Linear Regression: a way of finding the relationship between two variables; describing change in a variable based on a single predictor variable.
  • Multiple Regression: analyzes relationships between more than one predictor variable and a dependent variable.

Lecture 8: T-Tests

  • T-tests: used to compare means of two groups to see if the differences are significant.
  • T-value: measures how reliable the result is. Larger numbers indicate more reliable results.
  • P-value: probability of observing the results if the null hypothesis being true.
  • Paired Sample T-test: compares means from the same group under different conditions (within-subjects design).
  • One Sample T-test: compares the sample mean against a known population mean.
  • Degrees of Freedom (df): calculated using sample size (N), related to how many independent observations, or values, can be changed.

Studying That Suits You

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

Quiz Team

Related Documents

Research Methods Summary PDF

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser