Practical Statistics for Educators - User contributions [en]

Contributions here

2025-12-16T03:41:50Z

Grigorio003: /* Student Contributors */

== Editor ==
Frank LaBanca, EdD

== Faculty Contributors ==
Karen Burke, EdD

Patricia Cosentino, EdD

Deborah Hardy, EdD

Jennifer Mitchell, EdD

== Student Contributors ==
Jennifer Blue

David Bozzuto

Ashley Brooksbank

David Ciskowski

Katie Ciskowski

Paula Connolly

Cassandra Cosentino

Lisa Daigle

Sara Dalton

Jennifer Eraca

Mary Fernand

Karen Fildes

Thomas Fox

Nicole Griffin

Kristina Hislop

Damien Holst

Kaitlyn Kakadeles

Britany Kuslis

Mykal Kuslis

Kara Kunst

Helen Knudsen

Michael Minzloff

Sandra Peña

Sheri Prendergast

Emily Rhew

John Ryan

Tania Nicole Sutherland

Joseph W. Sullivan

Scott Trungadi

Benson Casimir

Celino Grigorio

Chi square

2025-12-16T03:40:14Z

Grigorio003:

A chi square analysis is used with nominal data to determine how frequency counts are distributed for different samples. This method compares expected with observed observations. To conduct an analysis of the chi square, one must first collect the expected frequencies. After conducting a study, and gathering the observed nominal data, one must use the chi square formula. Calculate the degrees of freedom and use the chi square table to find the critical value. Next, compare the critical value to the chi square value. If the χ2 cv > χ2 , then p>.05. There would be no statistical significant difference in this case. If χ2 cv < χ2 , then p<.05. There would be statistical significant difference in this case. Lastly, one would calculate the standard residual (R) to determine which factors are the major contributors toward significance. When R>2, then this factor is a major contributor toward the chi square value.

''contributed by Chris Longo''

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In the last sentence above, it should read when the absolute value of R is greater than 2 (|R|>2), then this factor is a major contributor toward the chi square value. If the R is negative, it means there is a decrease in the data that is significant and when R is positive, it means there is an increase that is significant.

''contributed by Margie Aldrich''

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Thank you Margie. I typed that entry a while ago and didn't realize that my wording was off. Also, to add, it is important to remember that when analyzing chi square data, look at the "R" column (or calculate yourself using the formula) to determine which factors are significant. For example, in a study measuring reading achievement scores based on 4th, 5th, 6th and 7th grade teachers, also broken down by gender, you would have to look at each factor (level) individually in order to determine whether or not it is a major contributor toward significance. For example, 4th grade male teachers and 7th grade female teachers are major contributors to chi square value, based on the fact that |R|> 2.

''contributed by Chris Longo''

NOTE: To convert a data set from a pdf into an excel file, you can use acrobat.adobe.com/us/en/pdf-to-excel. Sign in with your Google account.

''contributed by Paula Connolly''

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'''When to Use Chi-Square Carefully'''

Chi-square tests require independent observations and adequately large expected frequencies. If expected counts are too small, results may be inaccurate.

Chi-square is appropriate only for categorical data.

''contribution by by Celino Grigorio''

Finding effect sizes of ANOVAs

2025-12-16T03:36:35Z

Grigorio003:

Effect size can be found under the heading Partial Eta Squared in the "Tests of Between-Subject Effects" after running a Univariate Analysis of Variance (ANOVA). Round to two decimal places. Effect size shown is .38.

''contributed by Paula Connolly''

[[File:Effect size.jpeg]]

'''Interpreting Effect Size'''

Effect size helps explain how meaningful a result is, beyond whether it is statistically significant. Larger effect sizes indicate a stronger relationship between the variables being studied.

Reporting effect size alongside p-values provides a more complete understanding of research findings, especially in educational and social science research.

''contribution by Celino Grigorio''

T-test - What is a t-test?

2025-12-16T03:32:45Z

Grigorio003:

t-tests are used to determine whether two samples are different. For example, two fifth grade classes (random samples) took the same reading pre and post-tests.
The T-Test will help us analyze whether the two means are different. This means we are comparing the mean of fifth-grade class #1 to fifth grade class #2 to see how they vary.
This will help to figure out if students are increasing performance overall or not. Also, if there is significant difference, the t-test will help us figure out if we need to investigate further to see why there is significant differences in performance (intervention, supplemental materials, delivery method of instruction, etc).

contributed by ''Tania Nicole Sutherland
''

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== A t-test is an inferential test that is used to test the difference in the mean scores of two groups. It assists teachers in determining whether an instructional plan, intervention, or policy change has quantifiable outcomes. Otherwise put, it separates the differences that occurred by chance and the differences that may have occurred due to actual treatment effects. In educational research, two types of t-tests exist. Independent Samples t-test - applied in situations when two different groups of people (e.g., students in two classrooms) are compared. Paired Samples t-test - used when the researcher wants to compare the same group of scores before an intervention and after (an example is pre-test vs. post-test). The test produces a t-value and a p-value. When p is below 05, the researchers will make a conclusion that the difference between the group means is statistically significant, which means that it is likely to be a real effect. An illustration of this is that the difference in the score of a digital-learning group versus a textbook group ( t (48) = 2.62, p =.012) would not have been due to chance. In SPSS, perform this test using Analyze - Compare Means - Independent-Samples t-test or Paired-Samples t-test. Check the Levene Test to assume that variances are equal and normality holds. Also, it is best practice to report the effect size (Cohen's d) to describe the magnitude of the difference, and not the statistical significance. T-tests provide an easy but efficient method of evaluating the teaching strategies, the use of technology, or the outcomes of the program as a teacher. They endorse an evidence-based reflection culture, which allows teachers to promote evidence-based change in instruction.
==
''contributed by Casimir007''

==Identifying the independent and dependent variables within an experimental design.
Independent variable- A factor that is controlled or changes. There can be several levels to the independent variable.
The dependent variable is the variable that changes in response to the independent variable.==
''contributed by howarth006''

===Assumptions of the t-test===

A t-test is based on several assumptions. The data should be approximately normally distributed, and the observations should be independent. For independent samples, the two groups should also have similar variances.

If these assumptions are not met, the results of the t-test may be misleading, and another statistical method may be more appropriate.

''contribution by Celino Grigorio''

An introduction to probability

2025-12-16T03:25:46Z

Grigorio003:

== Introduction to Probability ==

<big>'''Probability of an Event'''</big>

If all of the outcomes in an experiment are equally likely, then the probability of an event, ''E'', occurring is given by:

[[File:P(E)_definition.JPG]]

Note: the number of outcomes that result in event ''E'' occurring can never be negative and can never be greater than the total number of outcomes, so we know:

[[File:Range_of_P(E).JPG]]

<big>'''Theoretical Probability vs. Empirical Probability'''</big>

A probability computed by using a probability formula is called a '''''theoretical probability'''''.

A probability found by observing the actual outcomes of an experiment that is repeated many times is called '''''empirical probability'''''.

Consider rolling a 6-sided die.

We know that each outcome is equally likely, so the theoretical probabilities are as follows:

[[File:Theoretical_Probability_of_Dice.JPG]]

However, if we actually rolled a 6-sided die 600 times and recorded the outcomes, we may find that the empirical probabilities differ:

(Geogebra [https://www.geogebra.org/m/UsoH4eNl] is a great tool for simulating this experiment)

[[File:Empirical_Probability_of_Dice.JPG]]

Notice only one outcome (rolling a 5) matched the theoretical probability.

''contributed by David Ciskowski''

<big>'''What is probability?'''</big>

Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In Statistics, the probability distribution gives the possibility of each outcome of a random experiment or event. It provides the probabilities of different possible occurrences.

Consider this example:
When you flip a coin, there are only two possible outcomes. Heads or Tails. So the probability of getting heads is 1 out of 2 or 1/2 or 50%.
There is a 50% chance of getting heads and a 50% chance of getting tails.
Probability distribution maps out the likelihood of multiple outcomes in an equation or table,
If we flip the two coins twice in a row, there are four possible outcomes.
The is a distribution of
25% heads/heads
25% heads/tails
25% tails/tails
25% tails/heads

''contribution by Tania Nicole Sutherland''

<big>'''Probability in Everyday Situations'''</big>

Probability helps us describe how likely an event is to happen. We use it often in daily life, such as predicting the weather, flipping a coin, or drawing a card from a deck.

All probabilities fall between 0 and 1, where 0 means an event is impossible and 1 means it is certain. Values in between show different levels of likelihood.

Thinking about probability allows us to better understand and measure uncertainty in real-world situations.

''contribution by Celino Grigorio''

Rules of thumb for interpreting the size of a correlation coefficient

2025-12-16T03:17:54Z

Grigorio003:

Correlation is simply the relationship between two variables (x & y), varying between -1 and +1. Correlation is a descriptive measure of a central tendency and does not necessarily indicate causal relationships. When looking at graphs, an upward trend indicates a positive correlation; a downward trend indicates a negative correlation; and a scattered or messy graph indicates low to no correlation at all.

''contributed by Jennifer Blue''

{| class="wikitable"
|-
! Size of positive correlation
! Size of negative correlation
! Interpretation
|-
| .90 to 1.00
| -.90 to -1.00
| Very high positive (negative) correlation
|-
| .70 to .90
| -.70 to -.90
| High positive (negative) correlation
|-
| .50 to .70
| -.50 to -.70
| Moderate positive (negative) correlation
|-
| .30 to .50
| -.30 to -.50
| Low positive (negative) correlation
|-
| .00 to .30
| .00 to -.30
| Little, if any, correlation
|}

''contributed by Frank LaBanca EdD''

Interpreting the line of best fit can show outliers. Outliers can lead to different interpretations of data, and an easy method for spotting outliers is through a scatterplot.

''contributed by Lauren Moyer''

Recall that this is the r value, not the p value, when interpreting the r value. The Pearson correlation does not show causation. For example, if the r value has a high positive correlation between a teacher shortage and the deterioration of the ozone layer, it does not necessarily mean that the teacher shortage caused the deterioration of the ozone layer.

''contributed by Lisa Daigle''

The ruled of correlation involve understanding it coefficient (-1 to +1), where values near ±1 mean strong linear links (positive means same direction, negative means opposite) and near 0 means weak/none.

''contributed by Celino Grigorio''