Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Inferential Stats in Educational Research: Samples to Populations & Hypothesis Testing - P, Study notes of History of Education

State University of New York at Geneseo (SUNY)History of Education
Prof. Kathryn Rommel-Esham

An overview of inferential statistics, its role in educational research, and the concepts of probability, normal distribution, hypothesis testing, levels of significance, and errors. It covers the use of t-tests and analysis of variance (anova) for comparing means, as well as post hoc tests and ancova for adjusting initial group differences. Additionally, it introduces nonparametric tests and chi-square for analyzing nominal data.

Typology: Study notes

Pre 2010

Uploaded on 08/16/2009

koofers-user-946
koofers-user-946 🇺🇸

10 documents

1 / 21

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
1
Inferential Statistics
Katie Rommel-Esham
Education 504
Probability
•Probability is the scientific way of stating the degree
of confidence we have in predicting something
•Tossing coins and rolling dice are examples of
probability experiments
•The concepts and procedures of inferential statistics
provide us with the language we need to address the
probabilistic nature of the research we conduct in the
field of education
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14
pf15

Partial preview of the text

Download Inferential Stats in Educational Research: Samples to Populations & Hypothesis Testing - P and more Study notes History of Education in PDF only on Docsity!

Inferential Statistics

Katie Rommel-Esham Education 504

Probability

  • Probability is the scientific way of stating the degree of confidence we have in predicting something
  • Tossing coins and rolling dice are examples of probability experiments
  • The concepts and procedures of inferential statistics provide us with the language we need to address the probabilistic nature of the research we conduct in the field of education

From Samples to Populations

  • Probability comes into play in educational research when we try to estimate a population mean from a sample mean
  • Samples are used to generate the data, and inferential statistics are used to generalize that information to the population, a process in which error is inherent
  • Different samples are likely to generate different means. How do we determine which is “correct?”

The Role of the Normal Distribution

  • If you were to take samples repeatedly from the same population, it is likely that, when all the means are put together, their distribution will resemble the normal curve
  • The resulting normal distribution will have its own mean and standard deviation
  • This distribution is called the sampling distribution and the corresponding standard deviation is known as the standard error

The Probability-Inferential Statistics

Connection

  • Armed with this information, a researcher can be fairly certain that, 68% of the time, the population mean that is generated from any given sample will be within 1 standard deviation of the mean of the sampling distribution

Hypotheses Revisited

  • Research hypothesis: the research prediction that is tested
  • Null hypothesis: a statement of “no difference” between the means of two populations
  • The null hypothesis is a technical necessity of inferential statistics
  • The research hypothesis is more important than the null hypothesis when conceiving and designing research

How does all this fit together?

  • Researchers use inferential statistics to determine the probability that the null hypothesis is untrue
  • Recall that if the null hypothesis is untrue, that is if it is “not true that there is no difference,” the most plausible conclusion is that there is indeed a difference
  • We never prove that anything is true, we only fail to disprove

Levels of Significance

  • Used to indicate the chance that we are wrong in rejecting the null hypothesis
  • Also called the level of probability or p level
  • p =.01, for example, means that the probability of finding the stated difference as a result of chance is only 1 in 100

Interpreting Level of Significance

  • Researchers generally look for levels of significance equal to or less than.
  • If the desired level of significance is achieved, the null hypothesis is rejected and the result is that there is a “statistically significant” difference in the means

Some notes on p -values

  • Acceptable levels of significance are situation specific
  • p = .05 is fine for most educational research
  • p = .05 is not an acceptable level if we are considering the error in a test concerning usage of a drug that might cause death

t -tests

  • The most common statistical procedure for determining the level of significance when two means are compared
  • Generates a number that is used to determine the p -level of rejecting the null hypothesis
  • Assumes equal variability in both data sets

Calculating the t statistic

  • As the difference between the means increases, and the error decreases, the t -statistic gets larger
  • The denominator represents the standard error of measurement between the means (the amount of error inherent in estimating population means from sample means)

Variations on the t

  • An independent samples t-test is used when the groups have no relationship to one another, as would an experimental group and control group
  • You may also encounter literature that references a dependent sample, paired, correlated, or matched t- test
  • These are used if the subjects in the two groups are matched in some way, as they would be matched with themselves in a pretest-posttest situation

Analysis of Variance (ANOVA)

  • Similar to a t -test, but used when there are more than two groups being compared
  • ANOVA is an extension of the t -test
  • Addresses the question "Is there a significant difference between any two population means?”

How ANOVA Works

  • Analysis of variance allows a researcher to examine differences in all population means simultaneously rather than conducting a series of t -tests
  • It uses variances (rather than means) of groups to calculate a value that reflects the degree of differences in the means

Interpreting ANOVA

  • Produces an F statistic (or F ratio) which is analogous to the t-statistic
  • A "1x4 ANOVA" is a one-way (i.e. one independent variable) ANOVA that is comparing four group means

2x3 ANOVA

High ability readers Average ability readers Low ability readers Reading Program # Reading Program #

Interpretation

  • In this example, three groups are being compared on two variables
  • A related research question might be “How do the two reading programs affect the reading achievement of low, average, and high ability readers?”

Another way to look

at the same thing…

Reading Program # Reading Program # Low (^) Average High Low (^) Average High

Then what?

  • Once the analysis of variance is complete, we still need to know where the difference lies, as it only tells us there is a difference in two or more of the means

For example,

  • Two groups are pretested, group A’s mean is higher. The same two groups are posttested, group A’s mean is still higher.
  • Is the higher posttest mean due to the fact that group A’s pretest mean was higher (i.e. are they “smarter?”)
  • ANCOVA adjusts for these initial pretest score differences

Multivariate Analyses

  • Used to investigate problems in which the researcher is interested in studying more than one dependent variable

An Example

  • “Attitudes towards science” is a complex construct that might involve things like enjoying science, valuing science, attitudes towards different branches of science (Earth Science, Biology, Chemistry), lab work, science field trips, etc.
  • Multivariate methods allow researchers to look at each of these components separately

Multivariate Tests

ANCOVA MANCOVA ANOVA MANOVA t -test Hotelling’s T^2 Univariate Test Multivariate Test

Nonparametric Procedures

  • If the assumptions associated with parametric procedures are not met, then nonparametric procedures are used
  • Most parametric procedures have analogous nonparametric procedures Parametric and Nonparametric Analogs Kruskal-Wallis one-way ANOVA of ranks One-way ANOVA Wilcoxon matched-pairs signed ranks test Dependent samples t-test Mann-Whitney U test Independent samples t-test Parametric Nonparametric

Chi-Square

  • Nonparametric procedure used when data are in nominal form
  • It is a way of answering questions about relationship based on frequencies of observations in categories

An Example

  • What is the relationship between year in college (freshman, sophomore, junior, senior) and use of campus counseling services?
  • Responses to this question will involve a count of how many in each group use the counseling service
  • The independent variable is year in college which has four categories