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I am trying to find a n-back (also known as 1-back/one-back) test made in MATLAB. In case you know how to make one (for instance by using psychtoolbox) or have some code you would like to share, that would be very appreciated.

Basically anything that could help me is appreciated, as long as it is connected to MATLAB.

## Chi Square Test

Chi-square (or χ2) tests draw inferences and test for relationships between categorical variables, that is a set of data points that fall into discrete categories with no inherent ranking.

There are three types of Chi-square tests, tests of goodness of fit, independence and homogeneity. All three tests also rely on the same formula to compute a test statistic.

All three function by deciphering relationships between observed sets of data and theoretical—or “expected”—sets of data that align with the null hypothesis.

##### What is the chi-square goodness of fit test?

###### What is the chi-square goodness of fit test?

The Chi-square goodness of fit test is used to compare a randomly collected sample containing a single, categorical variable to a larger population. This test is most commonly used to compare a random sample to the population from which it was potentially collected.

The test begins with the creation of a null and alternative hypothesis. In this case, the hypotheses are as follows:

**Null Hypothesis (Ho)**: The collected data is consistent with the population distribution.

**Alternative Hypothesis (Ha)**: The collected data is not consistent with the population distribution.

The next step is to create a contingency table that represents how the data would be distributed if the null hypothesis were exactly correct.

The sample’s overall deviation from this theoretical/expected data will allow us to draw a conclusion, with more severe deviation resulting in smaller p-values.

##### What is the chi-square test of independence?

###### What is the chi-square test of independence

The Chi-square test for independence looks for an association between two categorical variables within the same population. Unlike the goodness of fit test, the test for independence does not compare a single observed variable to a theoretical population, but rather two variables within a sample set to one another.

The hypotheses for a Chi-square test of independence are as follows:

**Null Hypothesis (Ho)**: There is no association between the two categorical variables in the population of interest.

**Alternative Hypothesis (Ha)**: There is no association between the two categorical variables in the population of interest.

The next step is to create a contingency table of expected values that reflects how a data set that perfectly aligns the null hypothesis would appear.

The simplest way to do this is to calculate the marginal frequencies of each row and column the expected frequency of each cell is equal to the marginal frequency of the row and column that corresponds to a given cell in the observed contingency table divided by the total sample size.

##### What is a contingency table?

###### What is a contingency table?

Contingency table (also known as two-way tables) are grids in which Chi-square data is organized and displayed. They provide a basic picture of the interrelation between two variables and can help find interactions between them.

In contingency tables, one variable and each of its categories are listed vertically and the other variable and each of its categories are listed horizontally.

Additionally, including column and row totals, also known as “marginal frequencies”, will help facilitate the Chi-square testing process.

In order for the Chi-square test to be considered trustworthy, each cell of your expected contingency table must have a value of at least five.

Each Chi-square test will have one contingency table representing observed counts (see Fig. 1) and one contingency table representing expected counts (see Fig. 2).

*Figure 1.* Observed table (which contains the observed counts).

To obtain the expected frequencies for any cell in any cross- tabulation in which the two variables are assumed independent, multiply the row and column totals for that cell and divide the product by the total number of cases in the table.

*Figure 2.* Expected table (what we expect the two-way table to look like if the two categorical variables are independent).

##### How do you calculate the chi square statistic?

###### How do you calculate the chi square statistic?

- Calculate the expected frequencies and the observed frequencies.
- For each observed number in the table subtract the corresponding expected number (O — E).
- Square the difference (O —E)².
- Divide the squares obtained for each cell in the table by the expected number for that cell (O - E)² / E.
- Sum all the values for (O - E)² / E. This is the chi square statistic.

##### What is the chi square statistic?

###### What is the chi square statistic?

The chi-square statistic tells you how much difference exists between the observed count in each table cell to the counts you would expect if there were no relationship at all in the population.

A **very small** chi square test statistic means means there is a high correlation between the observed and expected values. Therefore, the sample data is a good fit for what would be expected in the general population.

In theory, if the observed and expected values were equal (no difference) then the chi-square statistic would be zero — but this is unlikely to happen in real life.

A **very large** chi square test statistic means that the sample data (observed values) does not fit the population data (expected values) very well. In other words, there isn't a relationship.

##### How to report a chi square test result (APA)?

###### How to report a chi square test result (APA)?

To report a chi square output in an APA style results section, always rely on the following template:

χ2 ( degrees of freedom , N = sample size ) = chi-square statistic value ,

p=pvalue .

In the case of the above example, the results would be written as follows:

A chi-square test of independence showed that there was a significant association between gender and post graduation education plans,

χ2(4, N = 101) = 54.50, p < .001.

###### APA Style Rules

- Do not use a zero before a decimal when the statistic cannot be greater than 1 (proportion, correlation, level of statistical significance).
- Report exact p values to two or three decimals (e.g.,
*p*= .006, p = .03). - However, report p values less than .001 as “
*p*< .001.” - Put a space before and after a mathematical operator (e.g., minus, plus, greater than, less than, equals sign).
- Do not repeat statistics in both the text and a table or figure.

##### How is the p-value interpreted?

###### How is the p-value interpreted?

For a chi-square test, a p-value that is less than or equal to the .05 significance level indicates that the observed values are different to the expected values.

Thus, low p-values (p< < .05) indicate a likely difference between the theoretical population and the collected sample. You can conclude that a relationship exists between the categorical variables.

Remember that *p*-values do not indicate the odds that the null hypothesis is true, but rather provides the probability that one would obtain the sample distribution observed (or a more extreme distribution) if the null hypothesis was in fact true.

A level of confidence necessary to accept the null hypothesis can never be reached. Therefore, conclusions must choose to either fail to reject the null or accept the alternative hypothesis, depending on the calculated p-value.

##### Using SPSS to Perform a Chi-Square Test

###### Using SPSS to Perform a Chi-Square Test

The four steps below show you how to analyse your data using a

chi-square goodness-of-fittest in SPSS (when you have hypothesised that you have equal expected proportions).

**Step 1**: Analyze > Nonparametric Tests > Legacy Dialogs > Chi-square. on the top menu as shown below:

**Step 2**: Move the variable indicating categories into the “Test Variable List:” box.

**Step 3**: If you want to test the hypothesis that all categories are equally likely, click “OK.”

**Step 4**: Specify the expected count for each category by first clicking the “Values” button under “Expected Values.”

**Step 5**: Then, in the box to the right of “Values,” enter the expected count for category 1 and click the “Add” button. Now enter the expected count for category 2 and click “Add.” Continue in this way until all expected counts have been entered.

**Step 6**: Then click “OK.”

The four steps below show you how to analyse your data using a

chi-square test of independencein SPSS Statistics.

**Step 1**: Open the Crosstabs dialog (Analyze > Descriptive Statistics > Crosstabs).

**Step 2**: Select the variables you want to compare using the chi square test. Click one variable in the left window and then click the arrow at the top to move the variable. Select the row variable, and the column variable.

**Step 3**: Click Statistics (a new pop up window will appear). Check Chi-square, then click Continue.

**Step 4**: (Optional) Check the box for Display clustered bar charts.

**Step 5**: Click OK.

##### What is the chi-square test for homogeneity?

###### What is the chi-square test for homogeneity?

The Chi-square test for homogeneity is organized and executed exactly the same as the test for independence. The main difference to remember between the two is that the test for independence looks for an association between two categorical variables within the same population, while the test for homogeneity determines if the distribution of a variable is the same in each of several populations (thus allocating population itself as the second categorical variable).

The hypotheses for a Chi-square test of independence are as follows:

**Null Hypothesis (Ho)**: There is no difference in the distribution of a categorical variable for several populations or treatments.

**Alternative Hypothesis (Ha)**: There is a difference in the distribution of a categorical variable for several populations or treatments.

The difference between these two tests can be a bit tricky to determine especially in practical applications of a Chi-square test. A reliable rule of thumb is to determine how the data was collected.

If the data consists of only one random sample with the observations classified according to two categorical variables, it is a test for independence. If the data consists of more than one independent random sample, it is a test for homogeneity.

##### About the Author

Ben is a senior at Harvard College studying History and Science with a minor in Global Health and Health Policy. Ben is most interested in the intersections between psychology and history and hopes to pursue a career in the field of mental healthcare.

## MATLAB n-back test - Psychology

**SPSS, SAS, MATLAB, and R Programs for Determining**

**the Number of Components and Factors Using**

**Parallel Analysis and Velicer's MAP Test**

O'Connor, B. P. (2000). SPSS and SAS programs for determining the number of components using parallel analysis and Velicer's MAP test. *Behavior Research Methods, Instrumentation, and Computers, 32,* 396-402.

Popular statistical software packages do not have the proper procedures for determining the number of components or factors in correlation matrices. Parallel analysis and Velicer's minimum average partial (MAP) test are validated procedures that are widely recommended by statisticians. This paper described brief and efficient programs for conducting parallel analyses and the MAP test using SPSS, SAS, and MATLAB.

**The parallel analysis programs have been revised:**

Parallel analyses of both principal components and common/principal axis factors can now be conducted. The common/principal axis factor parallel analyses produce results that are essentially identical to those yielded by Montanelli and Humphreys's equation (1976, Psychometrika, vol. 41, p. 342). If your eventual goal is to conduct a principal components analysis on your data, then run the parallel analyses using the principal components option in the programs below. Unfortunately, when the eventual goal is conduct a common/principal axis factor analysis on your data, the experts disagree on whether principal component eigenvalues or common/principal axis factor eigenvalues should be used to determine the number of factors. Some (e.g., Montanelli, Humphreys, Gorsuch, Widaman) argue that if the eventual goal is to conduct a common/principal axis factor analysis, then communalities should be placed on the diagonal of a correlation matrix before extracting the eigenvalues that are then examined to determine the number of factors. Others do not follow this procedure: They extract and examine principal component eigenvalues to determine the number of common/principal axis factors!? The latter procedure was recommended by Cattell and it is the procedure that he used in his scree tests. It is also the procedure used in the SPSS and SAS factor analysis routines. The present programs permit both kinds of analyses.

The programs named "rawpar" conduct parallel analyses after first reading a raw data matrix, wherein the rows of the data matrix are cases/individuals and the columns are variables. The "rawpar" programs can run parallel analyses based on either normally distributed random data generation or on permutations of the original raw data set. In the latter case, the distributions of the original raw variables are exactly preserved in the permuted versions used in the parallel analyses. Permutations of the raw data set are thus highly accurate and most relevant, especially in cases where the raw data are not normally distributed.

SPSS: | SAS: | MATLAB: | |

map.sps | map.sas | map.m | for Velicer's MAP test |

parallel.sps | parallel.sas | parallel.m | for parallel analysis |

rawpar.sps | rawpar.sas | rawpar.m | for parallel analysis using raw data |

There is an R package named "EFA.dimensions" on the R CRAN site that runs these and other analyses.

Run these commands to install and use the package:

# example command for trial data:

MAP(data_RSE, corkind='polychoric') # MAP test on the Rosenberg Self-Esteem Scale

## Conclusion

Overall, the N-back is an important and valuable tool for learning more about learning – particularly with regards to working memory. The tool has a long history of use and is easily set up. While some of the claims made about the test are subject to controversy, it’s currently the only psychological test that has been shown to offer some degree of transference for cognitive abilities. The test will undoubtedly be used well into the future, as an incisive method to investigate working memory. These tests could benefit from using a varied and integrative approach, ensuring that the N-back task continues to yield insights.

If you want to know more about how to use the N-back test in iMotions, or would like to learn about how iMotions can help your research, then feel free to contact us. We’ve also previously talked about other psychological tests, such as gaze-contingency tasks, and the Stroop test, check them out through the links!

I hope you’ve enjoyed reading our article about the N-back test! If you’d like to learn more about how to perform great research, then check out our free pocket guide below!

## MATLAB n-back test - Psychology

The classical cognitive psychological test: n-back paradigm.

We are planning for a cognitive training project, which contains an fMRI pre-test and an fMRI post-test with the same test paradigm: **n back test**. Based on the previous experience, we decided to use **Psychtoolbox** to program the stimuli presentation process. We use **Github** to host our codes for this test.

It is easy to use these codes to start an experiment. Simply start a MATLAB (please use the latest version, or at least version larger than R2017b ) session, and type

then a graphical user interface (GUI) called **测验向导** will appear (see below).

With this GUI, you can add and modify user, start practice and testing part of experiment. Especially when you click on **新用户**, a user register wizard will pop up:

## Abstract

It is clear that the cognitive resources invested in standing are greater than in sitting, but six of eight previous studies suggested that there is no difference in cognitive performance. This study investigated the effects of sitting and standing workstations on the physical workload and cognitive performance under variable cognitive demand conditions. Fifteen participants visited two times for testing sitting and standing workstations, and were asked to play two difficulty levels of Tetris game for 40 min while kinematic variables, CoP regularity, CoP SD, and cognitive performances were captured every 5 min. Results revealed a more neural posture in standing than in sitting, but using the standing workstation degraded attention and executive function. The CoP SD was 7 times greater in standing, but the CoP regularity was 1/4 in sitting, denoting greater attentional investment while engaged at the standing workstation.

## Acute sleep deprivation in humans

### Working memory

Working memory is a layered system of information storage for optimum cognitive functioning and represents the ability to store and use information for a short period of time ( Chai et al., 2018 García et al., 2020 ). The N-back task and the Digit Span Task (DST) are commonly used to measure the effect of sleep loss on working memory. N-back tasks involve the continuous sequences of stimuli (e.g., images or letters), presented one-by-one in which participants must determine if the currently presented stimulus is the same as the stimulus presented n trails before (e.g., 1, 2, or 3) ( Kirchner, 1958 ). The DST involves memorization of a sequence of numbers that participants must recite forward or backward ( Blackburn and Benton, 1957 Wechsler, 1981 ). After TSD, both N-back and DST performance are impaired ( Choo et al., 2005 Alhola and Polo-Kantola, 2007 Linde and Bergstrom, 1992 Quigley et al., 2000 ). The working memory deficits caused by sleep loss include difficulty maintaining focus on relevant cues ( Goel et al., 2009 Krause et al., 2017 ) and in memorizing the temporal order of information ( Harrison and Horne, 2000 ). Following acute TSD, memory performance does not return to baseline after two nights of recovery, thus exemplifying the lingering detrimental impact of sleep deprivation ( Chai et al., 2020 ).

## Verification, Validation, and Test

### Verify and validate embedded systems using Model-Based Design

Engineering teams use Model-Based Design with MATLAB ® and Simulink ® to design complex embedded systems and generate production-quality C, C++, and HDL code. MathWorks tools use simulation testing and formal methods-based static analysis to complement Model-Based Design with rigor and automation to find errors earlier and achieve higher quality.

With MATLAB and Simulink, you can:

- Trace requirements to architecture, design, tests, and code
- Prove that your design meets requirements and is free of critical run-time errors
- Check compliance and measure quality of models and code
- Generate test cases automatically to increase test coverage
- Produce reports and artifacts, and certify to standards (such as DO-178 and ISO 26262).

“Compared with our past experience with hand-coding, Model-Based Design enabled us to reduce labor costs by 30%, cut testing costs by 20%, and increase productivity by more than 30%. We completed ECU development ahead of schedule while establishing our in-house software development team.”

Daming Li, Weichai Power

### Using MATLAB and Simulink for Verification and Validation

## Conclusion

Overall, the N-back is an important and valuable tool for learning more about learning – particularly with regards to working memory. The tool has a long history of use and is easily set up. While some of the claims made about the test are subject to controversy, it’s currently the only psychological test that has been shown to offer some degree of transference for cognitive abilities. The test will undoubtedly be used well into the future, as an incisive method to investigate working memory. These tests could benefit from using a varied and integrative approach, ensuring that the N-back task continues to yield insights.

If you want to know more about how to use the N-back test in iMotions, or would like to learn about how iMotions can help your research, then feel free to contact us. We’ve also previously talked about other psychological tests, such as gaze-contingency tasks, and the Stroop test, check them out through the links!

I hope you’ve enjoyed reading our article about the N-back test! If you’d like to learn more about how to perform great research, then check out our free pocket guide below!

## Abstract

It is clear that the cognitive resources invested in standing are greater than in sitting, but six of eight previous studies suggested that there is no difference in cognitive performance. This study investigated the effects of sitting and standing workstations on the physical workload and cognitive performance under variable cognitive demand conditions. Fifteen participants visited two times for testing sitting and standing workstations, and were asked to play two difficulty levels of Tetris game for 40 min while kinematic variables, CoP regularity, CoP SD, and cognitive performances were captured every 5 min. Results revealed a more neural posture in standing than in sitting, but using the standing workstation degraded attention and executive function. The CoP SD was 7 times greater in standing, but the CoP regularity was 1/4 in sitting, denoting greater attentional investment while engaged at the standing workstation.

## MATLAB n-back test - Psychology

The classical cognitive psychological test: n-back paradigm.

We are planning for a cognitive training project, which contains an fMRI pre-test and an fMRI post-test with the same test paradigm: **n back test**. Based on the previous experience, we decided to use **Psychtoolbox** to program the stimuli presentation process. We use **Github** to host our codes for this test.

It is easy to use these codes to start an experiment. Simply start a MATLAB (please use the latest version, or at least version larger than R2017b ) session, and type

then a graphical user interface (GUI) called **测验向导** will appear (see below).

With this GUI, you can add and modify user, start practice and testing part of experiment. Especially when you click on **新用户**, a user register wizard will pop up:

## Appendix

Figures 1𠄵 were obtained using simulations which hypothesized a virtual listener performing a 3*AFC* task. The responses of the virtual listener were modulated by the following psychometric function:

where *p*_{c} is the proportion of correct responses of the listener as a function of the level of the stimulus *x*. In the equation, γ and λ are the chance rate in the 3*AFC* task (i.e., 33%) and the lapse rate of the virtual listener (λ = 2% in all simulations), respectively. α is the psychometric function midpoint (i.e., it corresponds to the average between γ and λ, i.e., α = 65.5% in the simulated experiments) and β is the psychometric function slope (β = 1 in all simulations).

The following Table A1 reports the theoretical threshold of the virtual listeners as a function of the various *p-target*s tracked by the procedures:

**Table A1. p-targets and corresponding thresholds of the virtual listener used in the simulations**.

Keywords: auditory perception, psychoacoustics, matlab toolbox, staircase, pest, maximum likelihood estimation

Citation: Soranzo A and Grassi M (2014) PSYCHOACOUSTICS: a comprehensive MATLAB toolbox for auditory testing. *Front. Psychol*. **5**:712. doi: 10.3389/fpsyg.2014.00712

Received: 22 April 2014 Paper pending published: 04 June 2014

Accepted: 19 June 2014 Published online: 21 July 2014.

Shevaun D. Neupert, North Carolina State University, USA

Robert Schlauch, University of Minnesota, USA

Copyright © 2014 Soranzo and Grassi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

This research was supported in part by a Grant-in-Aid (No. 19K09452) for Scientific Research (C) from the Japan Society for the Promotion of Science, and a research grant from Kanae Foundation for the Promotion of Medical Science.

### Affiliations

Department of Neurosurgery, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8655, Japan

Kazuhiko Takabatake, Naoto Kunii, Hirofumi Nakatomi, Seijiro Shimada, Kei Yanai, Megumi Takasago & Nobuhito Saito

You can also search for this author in PubMed Google Scholar

You can also search for this author in PubMed Google Scholar

You can also search for this author in PubMed Google Scholar

You can also search for this author in PubMed Google Scholar

You can also search for this author in PubMed Google Scholar

You can also search for this author in PubMed Google Scholar

You can also search for this author in PubMed Google Scholar

### Contributions

NK, SS, and HN conceptualized this research. KT performed data curation. KT analyzed data. KT, NK, SS, MT, KY, and HN interpreted data. KT and NK drafted the manuscript. HN and NS supervised and revised the manuscript.

### Corresponding author

## Chi Square Test

Chi-square (or χ2) tests draw inferences and test for relationships between categorical variables, that is a set of data points that fall into discrete categories with no inherent ranking.

There are three types of Chi-square tests, tests of goodness of fit, independence and homogeneity. All three tests also rely on the same formula to compute a test statistic.

All three function by deciphering relationships between observed sets of data and theoretical—or “expected”—sets of data that align with the null hypothesis.

##### What is the chi-square goodness of fit test?

###### What is the chi-square goodness of fit test?

The Chi-square goodness of fit test is used to compare a randomly collected sample containing a single, categorical variable to a larger population. This test is most commonly used to compare a random sample to the population from which it was potentially collected.

The test begins with the creation of a null and alternative hypothesis. In this case, the hypotheses are as follows:

**Null Hypothesis (Ho)**: The collected data is consistent with the population distribution.

**Alternative Hypothesis (Ha)**: The collected data is not consistent with the population distribution.

The next step is to create a contingency table that represents how the data would be distributed if the null hypothesis were exactly correct.

The sample’s overall deviation from this theoretical/expected data will allow us to draw a conclusion, with more severe deviation resulting in smaller p-values.

##### What is the chi-square test of independence?

###### What is the chi-square test of independence

The Chi-square test for independence looks for an association between two categorical variables within the same population. Unlike the goodness of fit test, the test for independence does not compare a single observed variable to a theoretical population, but rather two variables within a sample set to one another.

The hypotheses for a Chi-square test of independence are as follows:

**Null Hypothesis (Ho)**: There is no association between the two categorical variables in the population of interest.

**Alternative Hypothesis (Ha)**: There is no association between the two categorical variables in the population of interest.

The next step is to create a contingency table of expected values that reflects how a data set that perfectly aligns the null hypothesis would appear.

The simplest way to do this is to calculate the marginal frequencies of each row and column the expected frequency of each cell is equal to the marginal frequency of the row and column that corresponds to a given cell in the observed contingency table divided by the total sample size.

##### What is a contingency table?

###### What is a contingency table?

Contingency table (also known as two-way tables) are grids in which Chi-square data is organized and displayed. They provide a basic picture of the interrelation between two variables and can help find interactions between them.

In contingency tables, one variable and each of its categories are listed vertically and the other variable and each of its categories are listed horizontally.

Additionally, including column and row totals, also known as “marginal frequencies”, will help facilitate the Chi-square testing process.

In order for the Chi-square test to be considered trustworthy, each cell of your expected contingency table must have a value of at least five.

Each Chi-square test will have one contingency table representing observed counts (see Fig. 1) and one contingency table representing expected counts (see Fig. 2).

*Figure 1.* Observed table (which contains the observed counts).

To obtain the expected frequencies for any cell in any cross- tabulation in which the two variables are assumed independent, multiply the row and column totals for that cell and divide the product by the total number of cases in the table.

*Figure 2.* Expected table (what we expect the two-way table to look like if the two categorical variables are independent).

##### How do you calculate the chi square statistic?

###### How do you calculate the chi square statistic?

- Calculate the expected frequencies and the observed frequencies.
- For each observed number in the table subtract the corresponding expected number (O — E).
- Square the difference (O —E)².
- Divide the squares obtained for each cell in the table by the expected number for that cell (O - E)² / E.
- Sum all the values for (O - E)² / E. This is the chi square statistic.

##### What is the chi square statistic?

###### What is the chi square statistic?

The chi-square statistic tells you how much difference exists between the observed count in each table cell to the counts you would expect if there were no relationship at all in the population.

A **very small** chi square test statistic means means there is a high correlation between the observed and expected values. Therefore, the sample data is a good fit for what would be expected in the general population.

In theory, if the observed and expected values were equal (no difference) then the chi-square statistic would be zero — but this is unlikely to happen in real life.

A **very large** chi square test statistic means that the sample data (observed values) does not fit the population data (expected values) very well. In other words, there isn't a relationship.

##### How to report a chi square test result (APA)?

###### How to report a chi square test result (APA)?

To report a chi square output in an APA style results section, always rely on the following template:

χ2 ( degrees of freedom , N = sample size ) = chi-square statistic value ,

p=pvalue .

In the case of the above example, the results would be written as follows:

A chi-square test of independence showed that there was a significant association between gender and post graduation education plans,

χ2(4, N = 101) = 54.50, p < .001.

###### APA Style Rules

- Do not use a zero before a decimal when the statistic cannot be greater than 1 (proportion, correlation, level of statistical significance).
- Report exact p values to two or three decimals (e.g.,
*p*= .006, p = .03). - However, report p values less than .001 as “
*p*< .001.” - Put a space before and after a mathematical operator (e.g., minus, plus, greater than, less than, equals sign).
- Do not repeat statistics in both the text and a table or figure.

##### How is the p-value interpreted?

###### How is the p-value interpreted?

For a chi-square test, a p-value that is less than or equal to the .05 significance level indicates that the observed values are different to the expected values.

Thus, low p-values (p< < .05) indicate a likely difference between the theoretical population and the collected sample. You can conclude that a relationship exists between the categorical variables.

Remember that *p*-values do not indicate the odds that the null hypothesis is true, but rather provides the probability that one would obtain the sample distribution observed (or a more extreme distribution) if the null hypothesis was in fact true.

A level of confidence necessary to accept the null hypothesis can never be reached. Therefore, conclusions must choose to either fail to reject the null or accept the alternative hypothesis, depending on the calculated p-value.

##### Using SPSS to Perform a Chi-Square Test

###### Using SPSS to Perform a Chi-Square Test

The four steps below show you how to analyse your data using a

chi-square goodness-of-fittest in SPSS (when you have hypothesised that you have equal expected proportions).

**Step 1**: Analyze > Nonparametric Tests > Legacy Dialogs > Chi-square. on the top menu as shown below:

**Step 2**: Move the variable indicating categories into the “Test Variable List:” box.

**Step 3**: If you want to test the hypothesis that all categories are equally likely, click “OK.”

**Step 4**: Specify the expected count for each category by first clicking the “Values” button under “Expected Values.”

**Step 5**: Then, in the box to the right of “Values,” enter the expected count for category 1 and click the “Add” button. Now enter the expected count for category 2 and click “Add.” Continue in this way until all expected counts have been entered.

**Step 6**: Then click “OK.”

The four steps below show you how to analyse your data using a

chi-square test of independencein SPSS Statistics.

**Step 1**: Open the Crosstabs dialog (Analyze > Descriptive Statistics > Crosstabs).

**Step 2**: Select the variables you want to compare using the chi square test. Click one variable in the left window and then click the arrow at the top to move the variable. Select the row variable, and the column variable.

**Step 3**: Click Statistics (a new pop up window will appear). Check Chi-square, then click Continue.

**Step 4**: (Optional) Check the box for Display clustered bar charts.

**Step 5**: Click OK.

##### What is the chi-square test for homogeneity?

###### What is the chi-square test for homogeneity?

The Chi-square test for homogeneity is organized and executed exactly the same as the test for independence. The main difference to remember between the two is that the test for independence looks for an association between two categorical variables within the same population, while the test for homogeneity determines if the distribution of a variable is the same in each of several populations (thus allocating population itself as the second categorical variable).

The hypotheses for a Chi-square test of independence are as follows:

**Null Hypothesis (Ho)**: There is no difference in the distribution of a categorical variable for several populations or treatments.

**Alternative Hypothesis (Ha)**: There is a difference in the distribution of a categorical variable for several populations or treatments.

The difference between these two tests can be a bit tricky to determine especially in practical applications of a Chi-square test. A reliable rule of thumb is to determine how the data was collected.

If the data consists of only one random sample with the observations classified according to two categorical variables, it is a test for independence. If the data consists of more than one independent random sample, it is a test for homogeneity.

##### About the Author

Ben is a senior at Harvard College studying History and Science with a minor in Global Health and Health Policy. Ben is most interested in the intersections between psychology and history and hopes to pursue a career in the field of mental healthcare.

## Acute sleep deprivation in humans

### Working memory

Working memory is a layered system of information storage for optimum cognitive functioning and represents the ability to store and use information for a short period of time ( Chai et al., 2018 García et al., 2020 ). The N-back task and the Digit Span Task (DST) are commonly used to measure the effect of sleep loss on working memory. N-back tasks involve the continuous sequences of stimuli (e.g., images or letters), presented one-by-one in which participants must determine if the currently presented stimulus is the same as the stimulus presented n trails before (e.g., 1, 2, or 3) ( Kirchner, 1958 ). The DST involves memorization of a sequence of numbers that participants must recite forward or backward ( Blackburn and Benton, 1957 Wechsler, 1981 ). After TSD, both N-back and DST performance are impaired ( Choo et al., 2005 Alhola and Polo-Kantola, 2007 Linde and Bergstrom, 1992 Quigley et al., 2000 ). The working memory deficits caused by sleep loss include difficulty maintaining focus on relevant cues ( Goel et al., 2009 Krause et al., 2017 ) and in memorizing the temporal order of information ( Harrison and Horne, 2000 ). Following acute TSD, memory performance does not return to baseline after two nights of recovery, thus exemplifying the lingering detrimental impact of sleep deprivation ( Chai et al., 2020 ).

## Verification, Validation, and Test

### Verify and validate embedded systems using Model-Based Design

Engineering teams use Model-Based Design with MATLAB ® and Simulink ® to design complex embedded systems and generate production-quality C, C++, and HDL code. MathWorks tools use simulation testing and formal methods-based static analysis to complement Model-Based Design with rigor and automation to find errors earlier and achieve higher quality.

With MATLAB and Simulink, you can:

- Trace requirements to architecture, design, tests, and code
- Prove that your design meets requirements and is free of critical run-time errors
- Check compliance and measure quality of models and code
- Generate test cases automatically to increase test coverage
- Produce reports and artifacts, and certify to standards (such as DO-178 and ISO 26262).

“Compared with our past experience with hand-coding, Model-Based Design enabled us to reduce labor costs by 30%, cut testing costs by 20%, and increase productivity by more than 30%. We completed ECU development ahead of schedule while establishing our in-house software development team.”

Daming Li, Weichai Power

### Using MATLAB and Simulink for Verification and Validation

## MATLAB n-back test - Psychology

**SPSS, SAS, MATLAB, and R Programs for Determining**

**the Number of Components and Factors Using**

**Parallel Analysis and Velicer's MAP Test**

O'Connor, B. P. (2000). SPSS and SAS programs for determining the number of components using parallel analysis and Velicer's MAP test. *Behavior Research Methods, Instrumentation, and Computers, 32,* 396-402.

Popular statistical software packages do not have the proper procedures for determining the number of components or factors in correlation matrices. Parallel analysis and Velicer's minimum average partial (MAP) test are validated procedures that are widely recommended by statisticians. This paper described brief and efficient programs for conducting parallel analyses and the MAP test using SPSS, SAS, and MATLAB.

**The parallel analysis programs have been revised:**

Parallel analyses of both principal components and common/principal axis factors can now be conducted. The common/principal axis factor parallel analyses produce results that are essentially identical to those yielded by Montanelli and Humphreys's equation (1976, Psychometrika, vol. 41, p. 342). If your eventual goal is to conduct a principal components analysis on your data, then run the parallel analyses using the principal components option in the programs below. Unfortunately, when the eventual goal is conduct a common/principal axis factor analysis on your data, the experts disagree on whether principal component eigenvalues or common/principal axis factor eigenvalues should be used to determine the number of factors. Some (e.g., Montanelli, Humphreys, Gorsuch, Widaman) argue that if the eventual goal is to conduct a common/principal axis factor analysis, then communalities should be placed on the diagonal of a correlation matrix before extracting the eigenvalues that are then examined to determine the number of factors. Others do not follow this procedure: They extract and examine principal component eigenvalues to determine the number of common/principal axis factors!? The latter procedure was recommended by Cattell and it is the procedure that he used in his scree tests. It is also the procedure used in the SPSS and SAS factor analysis routines. The present programs permit both kinds of analyses.

The programs named "rawpar" conduct parallel analyses after first reading a raw data matrix, wherein the rows of the data matrix are cases/individuals and the columns are variables. The "rawpar" programs can run parallel analyses based on either normally distributed random data generation or on permutations of the original raw data set. In the latter case, the distributions of the original raw variables are exactly preserved in the permuted versions used in the parallel analyses. Permutations of the raw data set are thus highly accurate and most relevant, especially in cases where the raw data are not normally distributed.

SPSS: | SAS: | MATLAB: | |

map.sps | map.sas | map.m | for Velicer's MAP test |

parallel.sps | parallel.sas | parallel.m | for parallel analysis |

rawpar.sps | rawpar.sas | rawpar.m | for parallel analysis using raw data |

There is an R package named "EFA.dimensions" on the R CRAN site that runs these and other analyses.

Run these commands to install and use the package:

# example command for trial data:

MAP(data_RSE, corkind='polychoric') # MAP test on the Rosenberg Self-Esteem Scale

Bravo, excellent idea

cool pictures

There is something about that, and it's a good idea. I support you.

Mudrenee morning evening.