#finding correlation coefficient

[correlationcoefficien]

Understanding Correlation Coefficient: A Tool for My Browser App Store Users

Learn what correlation coefficient is and how it can help you make informed decisions in My Browser App Store. Read on for a comprehensive guide.

Understanding Correlation Coefficient: A Tool for My Browser App Store Users

What is Correlation Coefficient?

Correlation coefficient is a statistical measure that measures the relationship between two variables. In simpler terms, it tells you how closely two variables are related. Correlation coefficient ranges from -1 to 1. If the correlation coefficient is 1, it means that the two variables are perfectly positively correlated. If the correlation coefficient is -1, it means that the two variables are perfectly negatively correlated. A correlation coefficient of 0 indicates that there is no correlation between the two variables.

How Does Correlation Coefficient Help in My Browser App Store?

In My Browser App Store, correlation coefficient can help you make informed decisions about which apps to download. For example, let's say you're looking for a new productivity app. You can use correlation coefficient to see which apps are most closely related to productivity. You can also use correlation coefficient to see which apps have a positive or negative impact on your device's performance. By using correlation coefficient, you can make more informed decisions about which apps to download and which to avoid.

How to Calculate Correlation Coefficient?

Calculating correlation coefficient can be a bit complicated, but it's not impossible. There are several methods you can use to calculate correlation coefficient, including the Pearson correlation coefficient and the Spearman correlation coefficient. The Pearson correlation coefficient is used to measure the strength of a linear relationship between two variables, while the Spearman correlation coefficient is used to measure the strength of a non-linear relationship between two variables.

Conclusion

Correlation coefficient is an important statistical measure that can help you make informed decisions in My Browser App Store. By understanding what correlation coefficient is and how it works, you can use it to your advantage when choosing which apps to download. Whether you're looking for a productivity app or trying to improve your device's performance, correlation coefficient can be a useful tool in your decision-making proc.

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[covid-safer-hotties]

Patients With Long-COVID Show Abnormal Lung Perfusion Despite Normal CT Scans - Published Sept 12, 2024

VIENNA — Some patients who had mild COVID-19 infection during the first wave of the pandemic and continued to experience postinfection symptoms for at least 12 months after infection present abnormal perfusion despite showing normal CT scans. Researchers at the European Respiratory Society (ERS) 2024 International Congress called for more research to be done in this space to understand the underlying mechanism of the abnormalities observed and to find possible treatment options for this cohort of patients.

Laura Price, MD, PhD, a consultant respiratory physician at Royal Brompton Hospital and an honorary clinical senior lecturer at Imperial College London, London, told Medscape Medical News that this cohort of patients shows symptoms that seem to correlate with a pulmonary microangiopathy phenotype.

"Our clinics in the UK and around the world are full of people with long-COVID, persisting breathlessness, and fatigue. But it has been hard for people to put the finger on why patients experience these symptoms still," Timothy Hinks, associate professor and Wellcome Trust Career Development fellow at the Nuffield Department of Medicine, NIHR Oxford Biomedical Research Centre senior research fellow, and honorary consultant at Oxford Special Airway Service at Oxford University Hospitals, England, who was not involved in the study, told Medscape Medical News.

The Study Researchers at Imperial College London recruited 41 patients who experienced persistent post-COVID-19 infection symptoms, such as breathlessness and fatigue, but normal CT scans after a mild COVID-19 infection that did not require hospitalization. Those with pulmonary emboli or interstitial lung disease were excluded. The cohort was predominantly female (87.8%) and nonsmokers (85%), with a mean age of 44.7 years. They were assessed over 1 year after the initial infection.

Exercise intolerance was the predominant symptom, affecting 95.1% of the group. A significant proportion (46.3%) presented with myopericarditis, while a smaller subset (n = 5) exhibited dysautonomia. Echocardiography did not reveal pulmonary hypertension. Laboratory findings showed elevated angiotensin-converting enzyme and antiphospholipid antibodies. "These patients are young, female, nonsmokers, and previously healthy. This is not what you would expect to see," Price said. Baseline pulmonary function tests showed preserved spirometry with forced expiratory volume in 1 second and forced vital capacity above 100% predicted. However, diffusion capacity was impaired, with a mean diffusing capacity of the lungs for carbon monoxide (DLCO) of 74.7%. The carbon monoxide transfer coefficient (KCO) and alveolar volume were also mildly reduced. Oxygen saturation was within normal limits.

These abnormalities were through advanced imaging techniques like dual-energy CT scans and ventilation-perfusion scans. These tests revealed a non-segmental and "patchy" perfusion abnormality in the upper lungs, suggesting that the problem was vascular, Price explained.

Cardiopulmonary exercise testing revealed further abnormalities in 41% of patients. Peak oxygen uptake was slightly reduced, and a significant proportion of patients showed elevated alveolar-arterial gradient and dead space ventilation during peak exercise, suggesting a ventilation-perfusion mismatch.

Over time, there was a statistically significant improvement in DLCO, from 70.4% to 74.4%, suggesting some degree of recovery in lung function. However, DLCO values did not return to normal. The KCO also improved from 71.9% to 74.4%, though this change did not reach statistical significance. Most patients (n = 26) were treated with apixaban, potentially contributing to the observed improvement in gas transfer parameters, Price said.

The researchers identified a distinct phenotype of patients with persistent post-COVID-19 infection symptoms characterized by abnormal lung perfusion and reduced gas diffusion capacity, even when CT scans appear normal. Price explains that this pulmonary microangiopathy may explain the persistent symptoms. However, questions remain about the underlying mechanisms, potential treatments, and long-term outcomes for this patient population.

Causes and Treatments Remain a Mystery Previous studies have suggested that COVID-19 causes endothelial dysfunction, which could affect the small blood vessels in the lungs. Other viral infections, such as HIV, have also been shown to cause endothelial dysfunction. However, researchers don't fully understand how this process plays out in patients with COVID-19.

"It is possible these patients have had inflammation insults that have damaged the pulmonary vascular endothelium, which predisposes them to either clotting at a microscopic level or ongoing inflammation," said Hinks.

Some patients (10 out of 41) in the cohort studied by the Imperial College London's researchers presented with Raynaud syndrome, which might suggest a physiological link, Hinks explains. "Raynaud's is a condition of vascular control or dysregulation, and potentially, there could be a common factor contributing to both breathlessness and Raynaud's."

He said there is an encouraging signal that these patients improve over time, but their recovery might be more complex and lengthy than for other patients. "This cohort will gradually get better. But it raises questions and gives a point that there is a true physiological deficit in some people with long-COVID."

Price encouraged physicians to look beyond conventional diagnostic tools when visiting a patient whose CT scan looks normal yet experiences fatigue and breathlessness. Not knowing what causes the abnormalities observed in this group of patients makes treatment extremely challenging. "We need more research to understand the treatment implications and long-term impact of these pulmonary vascular abnormalities in patients with long-COVID," Price concluded.

[diminuel]

I think I'm as ready as I can be for my presentation. I have the slides all ready, though I still don't quite understand what I'm saying and I haven't learnt anything by heart so I'll be talking from my slide notes. And I might struggle to answer questions if there will be questions because my notes are spread over three print outs of multiple pages. X3

Also, those who know statistics, please tell me if my stupid meme below the cut makes sense X3

(I can't actually confirm that it's lower. It's a correlation coefficient of r: -0.30. But since I also have graphs with means I can see that it's lower. I just don't know if the magic of R confirms my findings or I just did a test wrong somewhere *lol*)

[myrawjcsmicasereports]

 Inhibition of EIF4E Downregulates VEGFA and CCND1 Expression to Suppress Ovarian Cancer Tumor Progression by Jing Wang in Journal of Clinical Case Reports Medical Images and Health Sciences

Abstract

This study investigates the role of EIF4E in ovarian cancer and its influence on the expression of VEGFA and CCND1. Differential expression analysis of VEGFA, CCND1, and EIF4E was conducted using SKOV3 cells in ovarian cancer patients and controls. Correlations between EIF4E and VEGFA/CCND1 were assessed, and three-dimensional cell culture experiments were performed. Comparisons of EIF4E, VEGFA, and CCND1 mRNA and protein expression between the EIF4E inhibitor 4EGI-1-treated group and controls were carried out through RT-PCR and Western blot. Our findings demonstrate elevated expression of EIF4E, VEGFA, and CCND1 in ovarian cancer patients, with positive correlations. The inhibition of EIF4E by 4EGI-1 led to decreased SKOV3 cell clustering and reduced mRNA and protein levels of VEGFA and CCND1. These results suggest that EIF4E plays a crucial role in ovarian cancer and its inhibition may modulate VEGFA and CCND1 expression, underscoring EIF4E as a potential therapeutic target for ovarian cancer treatment.

Keywords: Ovarian cancer; Eukaryotic translation initiation factor 4E; Vascular endothelial growth factor A; Cyclin D1

Introduction

Ovarian cancer ranks high among gynecological malignancies in terms of mortality, necessitating innovative therapeutic strategies [1]. Vascular endothelial growth factor (VEGF) plays a pivotal role in angiogenesis, influencing endothelial cell proliferation, migration, vascular permeability, and apoptosis regulation [2, 3]. While anti-VEGF therapies are prominent in malignancy treatment [4], the significance of cyclin D1 (CCND1) amplification in cancers, including ovarian, cannot be overlooked, as it disrupts the cell cycle, fostering tumorigenesis [5, 6]. Eukaryotic translation initiation factor 4E (EIF4E), central to translation initiation, correlates with poor prognoses in various cancers due to its dysregulated expression and activation, particularly in driving translation of growth-promoting genes like VEGF [7, 8]. Remarkably, elevated EIF4E protein levels have been observed in ovarian cancer tissue, suggesting a potential role in enhancing CCND1 translation, thereby facilitating cell cycle progression and proliferation [9]. Hence, a novel conjecture emerges: by modulating EIF4E expression, a dual impact on VEGF and CCND1 expression might be achieved. This approach introduces an innovative perspective to impede the onset and progression of ovarian cancer, distinct from existing literature, and potentially offering a unique therapeutic avenue.

Materials and Methods

Cell Culture

Human ovarian serous carcinoma cell line SKOV3 (obtained from the Cell Resource Center, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences) was cultured in DMEM medium containing 10% fetal bovine serum. Cells were maintained at 37°C with 5% CO2 in a cell culture incubator and subcultured every 2-3 days.

Three-Dimensional Spheroid Culture

SKOV3 cells were prepared as single-cell suspensions and adjusted to a concentration of 5×10^5 cells/mL. A volume of 0.5 mL of single-cell suspension was added to Corning Ultra-Low Attachment 24-well microplates and cultured at 37°C with 5% CO2 for 24 hours. Subsequently, 0.5 mL of culture medium or 0.5 mL of EIF4E inhibitor 4EGI-1 (Selleck, 40 μM) was added. After 48 hours, images were captured randomly from five different fields—upper, lower, left, right, and center—using an inverted phase-contrast microscope. The experiment was repeated three times.

GEPIA Online Analysis

The GEPIA online analysis tool (http://gepia.cancer-pku.cn/index.html) was utilized to assess the expression of VEGFA, CCND1, and EIF4E in ovarian cancer tumor samples from TCGA and normal samples from GTEx. Additionally, Pearson correlation coefficient analysis was employed to determine the correlation between VEGF and CCND1 with EIF4E.

RT-PCR

RT-PCR was employed to assess the mRNA expression levels of EIF4E, VEGF, and CCND1 in treatment and control group samples. Total RNA was extracted using the RNA extraction kit from Vazyme, followed by reverse transcription to obtain cDNA using their reverse transcription kit. Amplification was carried out using SYBR qPCR Master Mix as per the recommended conditions from Vazyme. GAPDH was used as an internal reference, and the primer sequences for PCR are shown in Table 1.

Amplification was carried out under the following conditions: an initial denaturation step at 95°C for 60 seconds, followed by cycling conditions of denaturation at 95°C for 10 seconds, annealing at 60°C for 30 seconds, repeated for a total of 40 cycles. Melting curves were determined under the corresponding conditions. Each sample was subjected to triplicate experiments. The reference gene GAPDH was used for normalization. The relative expression levels of the target genes were calculated using the 2-ΔΔCt method.

Western Blot

Western Blot technique was employed to assess the protein expression levels of EIF4E, VEGF, and CCND1 in the treatment and control groups. Initially, cell samples collected using RIPA lysis buffer were lysed, and the total protein concentration was determined using the BCA assay kit (Shanghai Biyuntian Biotechnology, Product No.: P0012S). Based on the detected concentration, 20 μg of total protein was loaded per well. Electrophoresis was carried out using 5% stacking gel and 10% separating gel. Subsequently, the following primary antibodies were used for immune reactions: rabbit anti-human polyclonal antibody against phospho-EIF4E (Beijing Boao Sen Biotechnology, Product No.: bs-2446R, dilution 1:1000), mouse anti-human monoclonal antibody against EIF4E (Wuhan Sanying Biotechnology, Product No.: 66655-1-Ig, dilution 1:5000), mouse anti-human monoclonal antibody against VEGFA (Wuhan Sanying Biotechnology, Product No.: 66828-1-Ig, dilution 1:1000), mouse anti-human monoclonal antibody against CCND1 (Wuhan Sanying Biotechnology, Product No.: 60186-1-Ig, dilution 1:5000), and mouse anti-human monoclonal antibody against GAPDH (Shanghai Biyuntian Biotechnology, Product No.: AF0006, dilution 1:1000). Subsequently, secondary antibodies conjugated with horseradish peroxidase (Shanghai Biyuntian Biotechnology, Product No.: A0216, dilution 1:1000) were used for immune reactions. Finally, super-sensitive ECL chemiluminescence reagent (Shanghai Biyuntian Biotechnology, Product No.: P0018S) was employed for visualization, and the ChemiDocTM Imaging System (Bio-Rad Laboratories, USA) was used for image analysis.

Statistical Analysis

GraphPad software was used for statistical analysis. Data were presented as (x ± s) and analyzed using the t-test for quantitative data. Pearson correlation analysis was performed for assessing correlations. A significance level of P < 0.05 was considered statistically significant.

Results

3D Cell Culture of SKOV3 Cells and Inhibitory Effect of 4EGI-1 on Aggregation

In this experiment, SKOV3 cells were subjected to 3D cell culture, and the impact of the EIF4E inhibitor 4EGI-1 on ovarian cancer cell aggregation was investigated. As depicted in Figure 1, compared to the control group (Figure 1A), the diameter of the SKOV3 cell spheres significantly decreased in the treatment group (Figure 1B) when exposed to 4EGI-1 under identical culture conditions. This observation indicates that inhibiting EIF4E expression effectively suppresses tumor aggregation.

Expression and Correlation Analysis of VEGFA, CCND1, and EIF4E in Ovarian Cancer Samples

To investigate the expression of VEGFA, CCND1, and EIF4E in ovarian cancer, we utilized the GEPIA online analysis tool and employed the Pearson correlation analysis method to compare expression differences between tumor and normal groups. As depicted in Figures 2A-C, the results indicate significantly elevated expression levels of VEGFA, CCND1, and EIF4E in the tumor group compared to the normal control group. Notably, the expression differences of VEGFA and CCND1 were statistically significant (p < 0.05). Furthermore, the correlation analysis revealed a positive correlation between VEGFA and CCND1 with EIF4E (Figures 2D-E), and this correlation exhibited significant statistical differences (p < 0.001). These findings suggest a potential pivotal role of VEGFA, CCND1, and EIF4E in the initiation and progression of ovarian cancer, indicating the presence of intricate interrelationships among them.

EIF4E, VEGFA, and CCND1 mRNA Expression in SKOV3 Cells

To investigate the function of EIF4E in SKOV3 cells, we conducted RT-PCR experiments comparing EIF4E inhibition group with the control group. As illustrated in Figure 3, treatment with 4EGI-1 significantly reduced EIF4E expression (0.58±0.09 vs. control, p < 0.01). Concurrently, mRNA expression of VEGFA (0.76±0.15 vs. control, p < 0.05) and CCND1 (0.81±0.11 vs. control, p < 0.05) also displayed a substantial decrease. These findings underscore the significant impact of EIF4E inhibition on the expression of VEGFA and CCND1, indicating statistically significant differences.

Protein Expression Profiles in SKOV3 Cells with EIF4E Inhibition and Control Group

Protein expression of EIF4E, VEGFA, and CCND1 was assessed using Western Blot in the 4EGI-1 treatment group and the control group. As presented in Figure 4, the expression of p-EIF4E was significantly lower in the 4EGI-1 treatment group compared to the control group (0.33±0.14 vs. control, p < 0.001). Simultaneously, the expression of VEGFA (0.53±0.18 vs. control, p < 0.01) and CCND1 (0.44±0.16 vs. control, p < 0.001) in the 4EGI-1 treatment group exhibited a marked reduction compared to the control group.

Discussion

EIF4E is a post-transcriptional modification factor that plays a pivotal role in protein synthesis. Recent studies have underscored its critical involvement in various cancers [10]. In the context of ovarian cancer research, elevated EIF4E expression has been observed in late-stage ovarian cancer tissues, with low EIF4E expression correlating to higher survival rates [9]. Suppression of EIF4E expression or function has been shown to inhibit ovarian cancer cell proliferation, invasion, and promote apoptosis. Various compounds and drugs that inhibit EIF4E have been identified, rendering them potential candidates for ovarian cancer treatment [11]. Based on the progressing understanding of EIF4E's role in ovarian cancer, inhibiting EIF4E has emerged as a novel therapeutic avenue for the disease. 4EGI-1, a cap-dependent translation small molecule inhibitor, has been suggested to disrupt the formation of the eIF4E complex [12]. In this study, our analysis of public databases revealed elevated EIF4E expression in ovarian cancer patients compared to normal controls. Furthermore, through treatment with 4EGI-1 in the SKOV3 ovarian cancer cell line, we observed a capacity for 4EGI-1 to inhibit SKOV3 cell spheroid formation. Concurrently, results from PCR and Western Blot analyses demonstrated effective EIF4E inhibition by 4EGI-1. Collectively, 4EGI-1 effectively suppresses EIF4E expression and may exert its effects on ovarian cancer therapy by modulating EIF4E.

Vascular Endothelial Growth Factor (VEGF) is a protein that stimulates angiogenesis and increases vascular permeability, playing a crucial role in tumor growth and metastasis [13]. In ovarian cancer, excessive release of VEGF by tumor cells leads to increased angiogenesis, forming a new vascular network to provide nutrients and oxygen to tumor cells. The formation of new blood vessels enables tumor growth, proliferation, and facilitates tumor cell dissemination into the bloodstream, contributing to distant metastasis [14]. As a significant member of the VEGF family, VEGFA has been extensively studied, and it has been reported that VEGFA expression is notably higher in ovarian cancer tumors [15], consistent with our public database analysis. Furthermore, elevated EIF4E levels have been associated with increased malignant tumor VEGF mRNA translation [16]. Through the use of the EIF4E inhibitor 4EGI-1 in ovarian cancer cell lines, we observed a downregulation in both mRNA and protein expression levels of VEGFA. This suggests that EIF4E inhibition might affect ovarian cancer cell angiogenesis capability through downregulation of VEGF expression.

Cyclin D1 (CCND1) is a cell cycle regulatory protein that participates in controlling cell entry into the S phase and the cell division process. In ovarian cancer, overexpression of CCND1 is associated with increased tumor proliferation activity and poor prognosis [17]. Elevated CCND1 levels promote cell cycle progression, leading to uncontrolled cell proliferation [18]. Additionally, CCND1 can activate cell cycle-related signaling pathways, promoting cancer cell growth and invasion capabilities [19]. Studies have shown that CCND1 gene expression is significantly higher in ovarian cancer tissues compared to normal ovarian tissues [20], potentially promoting proliferation and cell cycle progression through enhanced cyclin D1 translation [9]. Our public database analysis results confirm these observations. Furthermore, treatment with the EIF4E inhibitor 4EGI-1 in ovarian cancer cell lines resulted in varying degrees of downregulation in CCND1 mRNA and protein levels. This indicates that EIF4E inhibition might affect ovarian cancer cell proliferation and cell cycle progression through regulation of CCND1 expression.

In conclusion, overexpression of EIF4E appears to be closely associated with the clinical and pathological characteristics of ovarian cancer patients. In various tumors, EIF4E is significantly correlated with VEGF and cyclin D1, suggesting its role in the regulation of protein translation related to angiogenesis and growth [9, 21]. The correlation analysis results in our study further confirmed the positive correlation among EIF4E, VEGFA, and CCND1 in ovarian cancer. Simultaneous inhibition of EIF4E also led to downregulation of VEGFA and CCND1 expression, validating their interconnectedness. Thus, targeted therapy against EIF4E may prove to be an effective strategy for treating ovarian cancer. However, further research and clinical trials are necessary to assess the safety and efficacy of targeted EIF4E therapy, offering more effective treatment options for ovarian cancer patients.

Acknowledgments:

Funding: This study was supported by the Joint Project of Southwest Medical University and the Affiliated Traditional Chinese Medicine Hospital of Southwest Medical University (Grant No. 2020XYLH-043).

Conflict of Interest: The authors declare no conflicts of interest.

[shamira22]

To generate a correlation coefficient using Python, you can follow these steps:1. **Prepare Your Data**: Ensure you have two quantitative variables ready to analyze.2. **Load Your Data**: Use pandas to load and manage your data.3. **Calculate the Correlation Coefficient**: Use the `pearsonr` function from `scipy.stats`.4. **Interpret the Results**: Provide a brief interpretation of your findings.5. **Submit Syntax and Output**: Include the code and output in your blog entry along with your interpretation.### Example CodeHere is an example using a sample dataset:```pythonimport pandas as pdfrom scipy.stats import pearsonr# Sample datadata = {'Variable1': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 'Variable2': [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]}df = pd.DataFrame(data)# Calculate the correlation coefficientcorrelation, p_value = pearsonr(df['Variable1'], df['Variable2'])# Output resultsprint("Correlation Coefficient:", correlation)print("P-Value:", p_value)# Interpretationif p_value < 0.05: print("There is a significant linear relationship between Variable1 and Variable2.")else: print("There is no significant linear relationship between Variable1 and Variable2.")```### Output```plaintextCorrelation Coefficient: 1.0P-Value: 0.0There is a significant linear relationship between Variable1 and Variable2.```### Blog Entry Submission**Syntax Used:**```pythonimport pandas as pdfrom scipy.stats import pearsonr# Sample datadata = {'Variable1': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 'Variable2': [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]}df = pd.DataFrame(data)# Calculate the correlation coefficientcorrelation, p_value = pearsonr(df['Variable1'], df['Variable2'])# Output resultsprint("Correlation Coefficient:", correlation)print("P-Value:", p_value)# Interpretationif p_value < 0.05: print("There is a significant linear relationship between Variable1 and Variable2.")else: print("There is no significant linear relationship between Variable1 and Variable2.")```**Output:**```plaintextCorrelation Coefficient: 1.0P-Value: 0.0There is a significant linear relationship between Variable1 and Variable2.```**Interpretation:**The correlation coefficient between Variable1 and Variable2 is 1.0, indicating a perfect positive linear relationship. The p-value is 0.0, which is less than 0.05, suggesting that the relationship is statistically significant. Therefore, we can conclude that there is a significant linear relationship between Variable1 and Variable2 in this sample.This example uses a simple dataset for clarity. Make sure to adapt the data and context to fit your specific research question and dataset for your assignment.

[chemoelectric]

Originally posted to Facebook, and unaltered from that text:

----------

The 2022 Nobel Prize in Physics was awarded for what is commonly regarded as "confirmation of quantum physics" but this is muddleheaded nonsense. What it actually was awarded for is what is considered by physicists proof that no mathematics except quantum mechanics can derive the correlation coefficient of the following experiment. You have to have a clear head to see that this is the actual claim, but it assuredly and inarguably is.

Here is the experiment, and I will derive its correlation without using quantum mechanics. I am not sure anyone knew how to do this before I did, and it took me about 20 years to find.

A light source emits two photons left and right, randomly with one polarized vertically and the other horizontally. Each photon goes through a polarizing beam splitter, whose two output channels +1 and -1 are finished by photodetectors. The left PBS has angle a', the right PBS has angle b'.

There is a law of physics called the Law of Malus, where the accent is on the u in Malus. When applied to a horizontal photon in a polarizing beam splitter with angle a', it says the photon will go through the +1 channel with probability cos² a', the -1 channel with probability sin² a'. Similarly if the angle is b'. If the photon is vertical, the cos and sin are reversed. (I am leaving out all other possible angles. The full Law also accounts for them.)

This is not the traditional statement of the Law of Malus, but is what we want. When you are using quantum mechanics, the rules are written funky and probably are not called the Law of Malus, but are an obfuscated way of saying what we just said.

By a lot of tedious but routine probability theory that I will skip here, but which you can find for instance in my "How to Entangle Craytons" at https://crudfactory.com, you get that the probability of +1 detection on both sides is the same as the probability of -1 detection on both sides, and equals (1/2) sin² a' cos² b' + (1/2) cos² a' sin² b'. The probability of of +1 detection on only one side is (1/2) sin² a' sin² b' + (1/2) cos² a' cos² b'. Call the probabilities in obvious ways P++, P--, P+-, P-+. Then I can get the correlation as follows:

corr = (+1)(+1)(P++) + (-1)(-1)(P--) + (+1)(-1)(P+-) + (-1)(+1)(P-+)

= -cos 2a' cos 2b'

where I have used a double angle identity you can find in the Handbook of Mathematical Sciences, etc.

Here is where I do something that has evaded the mental capacities of Nobel Prize winning physicists.

Let it be noted that we already know that the supposedly "quantum" correlation for an experiment with PBS angles a and b is -cos 2(a - b). One thing I have never seen physicists point out about this expression, despite the bleeding obviousness once pointed out, is its invariance under in-unison rotation of the angles a and b. What this means is that you can ALWAYS rotate the problem so that one of the angles is zero, without changing the result.

This is simple mathematics. But physicists are not taught actual mathematics. They are taught a kind of pseudo-mathematics not based on theorems, proofs, or thorough reasoning.

Let us set b' = 0 and let a' = a - b, for any PBS angles a and b. In other words, we simply rotate the problem by -b to convert it to an already-solved problem for a' = anything, b' = 0. We have thus derived the correlation, without using quantum mechanics:

corr = -cos 2(a - b)

The 2022 Nobel Prize in Physics is a load of hogwash. There is no such thing as "particle entanglement", there is no such thing as "quantum non-locality", there is no "confirmation of quantum physics", and there is no such thing as a "quantum" computer.

But I have more general proofs of the matter than that, which do not even require mathematical expressions.

What I have done here is show with that Einstein was wrong that statistical mechanics was what underlay the type of experiment described. It is actually just ordinary pinball-like mechanics! Einstein never wavered in believing there was no distinct "quantum" physics, and was ostracized for it. But he was right.

But I have gone beyond that and come up with meta-mathematical arguments that are of different kind entirely. Those are for a separate rage.

A late postscript:

This derivation may be a little confusing, because why does b' have to be set to zero? Clauser inequalities treat b' as nonzero, but obviously, from the derivation above, this is wrong.

Here is an explanation—

If you do NOT set b' to zero, how can you distinguish which particle each angle apples to? You cannot. You are actually solving the wrong problem.

This is what Clauser inequalities do—they solve the wrong problem.

With b' set to zero and symmetry of cos, we solve the right problem.

Really it would be better to note the difficulty at the beginning and set b' to zero right away. Going through the motions above, however, helps illustrate where physicists err by NOT setting b' to zero, when they try to derive "classical" solutions and get incorrect results.

(That their results were incorrect should have been obvious, because any result different from that of quantum mechanics MUST have been derived incorrectly. All math methods must reach the same conclusion, or math is inconsistent. But that is for another rage.)

[canisitsnotlupus]

Investigating the relationship between inbreeding and life expectancy in dogs: mongrels live longer than pure breeds

This study aimed to investigate the establishment of relationship between inbreeding and life expectancy in dogs. A dataset of N = 30,563 dogs sourced from the VetCompass™ Program, UK was made available by the Royal Veterinary College, University of London, containing information about breed and longevity and was subject to survival analysis. A Cox regression proportional hazards model was used to differentiate survivability in three groups of dogs (mongrel, cross-bred and pure breed). The model was found highly significant (p < 0.001) and we found that mongrel dog had the highest life expectancy, followed by cross-bred dogs with only one purebred ancestor and purebred dogs had the lowest life expectancy. A second Cox regression was also found highly significant (p < 0.001) differentiating the lifespan of different dog breed and correlating positively the hazard ratio and the Genetic Illness Severity Index for Dogs (GISID). The results show that survivability is higher in mongrel dogs followed by cross-bred with one of the ancestor only as a pure breed, and pure breed dog have the highest morbidity level. Higher morbidity is associated with higher GISID scores, and therefore, higher inbreeding coefficients. These findings have important implications for dog breeders, owners, and animal welfare organizations seeking to promote healthier, longer-lived dogs.

[felidaereverse]

you want to compile datasets and create scatter plots and interpret trends you want to identify outliers and find lines of best fit and standard deviation you want to calculate pearson correlation coefficients you want to calculate p-values you want to examine a z-score chart you are in love with both one and two tailed t-tests and ANOVAs and MANOVAs and regression analysis and many many more

YOU ARE ENTERING MY BEAUTIFUL STATISTICS WORLD

[covid-safer-hotties]

Also preserved in our archive (Daily updates!)

At least the tool we kinda have is accurate...

Wastewater surveillance has gained attention as an effective method for monitoring regional infection trends. In July 2024, the National Action Plan for Novel Influenza, etc. included the regular implementation of wastewater surveillance during normal times, with results to be published periodically in Japan. However, when viral concentrations in wastewater are measured inadequately or show significant variability, the correlation with actual infection trends may weaken. This study identified the necessary methods for accurately monitoring COVID-19 infection patterns.

The research team analyzed wastewater data obtained from the city of Sapporo in northern Japan between April 2021 and September 2023. The dataset featured high sensitivity (100 times greater than the standard method) and high reproducibility (standard deviation below 0.4 at log10 values) and was supported by a substantial sample size of 15 samples per week, totaling 1,830 samples over a sufficient survey period of two and a half years. The correlation coefficient between the number of infected individuals and the viral concentration in the wastewater was 0.87, indicating that this method effectively tracks regional infection trends. Additionally, the research team concluded desirable survey frequency requires at least three samples, preferably five samples, per week.

The study provides detailed guidance on wastewater surveillance methodologies for understanding infection trends, focusing on data processing, analytical sensitivity, and survey frequency. As wastewater surveillance during normal times becomes more widely implemented and its results increasingly published, this study's findings are expected to serve as valuable resources for decision making.

Source: Osaka University

Journal reference: Murakami, M., et al. (2024) Evaluating survey techniques in wastewater-based epidemiology for accurate COVID-19 incidence estimation. The Science of the Total Environment. doi.org/10.1016/j.scitotenv.2024.176702. www.sciencedirect.com/science/article/pii/S0048969724068591?via%3Dihub

[mystery-two]

Generating a Correlation Coefficient

Topic:  Alcohol intake among young adults in the morning, afternoon, and evening on a weekly basis.

X = {categorical: morning, afternoon, evening}

Y= {1, 2, 3, 4, 5, 6… 30} number of participants.

Sample size = 30

Numerical values were assigned to the categories

Morning = 1

Afternoon= 2

Evening = 3

PARTICIPANTS

TIME OF DAY

1

1

2

2

3

3

4

1

5

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3

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2

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1

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2

11

1

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1

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1

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2

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1

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2

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2

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2

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3

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1

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28

2

29

3

30

1

Mean Calculation: 

X = first term+ last term/2 =1+30/2= 15.5

Y=  1+2 +3+1+3+3+2+2+1+2+1+3+1+1+2+1+2+2+3+2+2+3+3+1+1+3+2+2+3+1/30=65/30=2.17

Deviation Score for X and Y

X={ 1, 2, 3, ……30}

Formula 1 - mean = deviation score

X [−14.5,−13.5,−12.5,−11.5,−10.5,−9.5,−8.5,−7.5,−6.5,−5.5,−4.5,−3.5,−2.5,−1.5,−0.5,0.5,1.5,2.5,3.5,4.5,5.5,6.5,7.5,8.5,9.5,10.5,11.5,12.5,13.5,14.5]

 Y= [-1.17,−0.17,0.83,−1.17,0.83,0.83,−0.17,−0.17,−1.17,−0.17,−1.17,0.83,−1.17,−1.17,−0.17,−1.17,−0.17,−0.17,0.83,−0.17,−0.17,0.83,0.83,−1.17,−1.17,0.83,−0.17,−0.17,0.83,−1.17]

Product of Deviation Scores

Formula:- deviation score X x deviation score Y.

Example -14.5 ×-1.17=16.965

[16.965, 2.295, −10.375, 13.455, −8.715, −7.885, 1.445, 1.275, 7.605, 0.935, 5.265, -2.905, 2.925, 1.755, 0.085, −0.585, −0.255, −0.425 , 2.905 ,−0.765 ,−0.935, 5.395, 6.225 ,−9.945, −11.115, 8.715,

− 1.955,  −2 .125, 11.205, −16.965]

Positive numbers sum 

16.965 + 2.295 + 13.455 + 1.444 + 1.275 + 7.605 + 0.935 + 5.265 + 2.925 + 1.755 + 0.085 + 2.905 + 5.395 + 6.225 + 8.715 + 11.205 =88.450

Negative numbers sum

−10.375 + -8.715+ -7.885 + −2.905 + -0.585 + -0.255 + -0.425 + -0.765 + - 0.935 +- 9.945 + -11.115 + -1.955 +-2.125 + -16.965 = -74.948

Sum of the positive numbers+ negative numbers= 

88.450+(−74.948)=13.502

Standard Deviation

Square all the X values

X = 210.25 + 182.25 + 156.25 + 132.25 +110.25 + 90.25 + 72.25 + 56.25 + 42.25 + 30.25 + 20.25+ 12.25 + 6.25 + 2.25 + 0.25 + 0.25 + 2.25 + 6.25 + 12.25 + 20.25 + 30.25 + 42.25 + 56.25 + 72.25 + 90.25 + 110.25 + 132.25 + 156.25 + 182.25 + 210.25  

Sum all the values of X

2247.5/30 = 74.916

Then find the square 74.916 = 8.6554

Square all the values of Y

1.3689 + 0.0289 + 0.6889 + 1.3689 + 0.6889 + 0.6889 + 0.0289 + 0.0289 + 1.3689 + 0.0289 + 1.3689 + 0.6889 + 1.3689 + 1.3689 + 0.0289 + 1.3689 + 0..0289 + 0.0289 + 0.6889 + 0.0289 + 0.0289 + 0.6889 + 0.6889 + 1.3689 + 1.3689 + 0.6889 + 0.0289 + 0.0289 + 0.6889 + 1.3689 = 20.207

Sum of Y deviation scores/30

20.207/30= 0.6735

Then the square root= 0.8206

Find the square root of 0.6735 = 0.8206

Final calculation

The sum of the deviation = 13.502

Standard Deviation X= 8.6554

Standard Deviation Y= 0.8206

N=30

13.502/ 30-1 x  8.6554 × 0.8206

13.502/205.9760 = 0.06556

r = 0.06556  a very weak correlation

[kactusnz]

@an-gremlin above said it best. It’s not that they’re lying, it’s that they’re picking which part they choose to tell you. 

For the examples above: Mean: knowing the median would be useful information, it’d show you your starting salary was $30,000, in line with the median. Median: knowing the mean would be useful information, it’d show that your long-term investment in the fund would net you a loss. Mode: honestly you probably want to know exactly which tests your child is struggling with, so looking at the mean might indicate you need to take a closer look at the actual data. This is a small data set, so you can just look at all of it. Range: the mean, median OR mode would show that you have very few studensts within the lower income brackets. Correlation coefficient: this is more about looking into the study methodology than a specific statistic as above. Probably could do several posts on finding the actual studies behind the correlation.

but genuinely the graphs shown as an explanation of what is happening give you more of the picture than a single number does, and are a much better way to display data anyway (as long as an appropriate graph is chosen and they haven’t done anything tricky (see part 2 (I’m not actually making a part 2 but one about suppressing origins, mixing different scales, linking data sets that are unrelated/do not have a causal relationship (don’t accidentally misread that as casual like I usually do)/etc would be great)))

The thing with statistics - via

[ensafomer]

a Basic Linear Regression Model

What is linear regression?

Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.

This form of analysis estimates the coefficients of the linear equation, involving one or more independent variables that best predict the value of the dependent variable. Linear regression fits a straight line or surface that minimizes the discrepancies between predicted and actual output values. There are simple linear regression calculators that use a “least squares” method to discover the best-fit line for a set of paired data. You then estimate the value of X (dependent variable)

n statistics, simple linear regression (SLR) is a linear regression model with a single explanatory variable.[1][2][3][4][5] That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent variable. The adjective simple refers to the fact that the outcome variable is related to a single predictor.

It is common to make the additional stipulation that the ordinary least squares (OLS) method should be used: the accuracy of each predicted value is measured by its squared residual (vertical distance between the point of the data set and the fitted line), and the goal is to make the sum of these squared deviations as small as possible. In this case, the slope of the fitted line is equal to the correlation between y and x corrected by the ratio of standard deviations of these variables. The intercept of the fitted line is such that the line passes through the center of mass (x, y) of the data points.

Formulation and computation

[edit]

This relationship between the true (but unobserved) underlying parameters α and β and the data points is called a linear regression model.

Here we have introduced

x¯ and y¯ as the average of the xi and yi, respectively

Δxi and Δyi as the deviations in xi and yi with respect to their respective means.

Expanded formulas

[edit]

Interpretation

[edit]

Relationship with the sample covariance matrix

[edit]

where

rxy is the sample correlation coefficient between x and y

sx and sy are the uncorrected sample standard deviations of x and y

sx2 and sx,y are the sample variance and sample covariance, respectively

Interpretation about the slope

[edit]

Interpretation about the intercept

Interpretation about the correlation

[edit]

Numerical properties

[edit]

The regression line goes through the center of mass point, (x¯,y¯), if the model includes an intercept term (i.e., not forced through the origin).

The sum of the residuals is zero if the model includes an intercept term:∑i=1nε^i=0.

The residuals and x values are uncorrelated (whether or not there is an intercept term in the model), meaning:∑i=1nxiε^i=0

The relationship between ρxy (the correlation coefficient for the population) and the population variances of y (σy2) and the error term of ϵ (σϵ2) is:[10]: 401 σϵ2=(1−ρxy2)σy2For extreme values of ρxy this is self evident. Since when ρxy=0 then σϵ2=σy2. And when ρxy=1 then σϵ2=0.

Statistical properties

[edit]

Description of the statistical properties of estimators from the simple linear regression estimates requires the use of a statistical model. The following is based on assuming the validity of a model under which the estimates are optimal. It is also possible to evaluate the properties under other assumptions, such as inhomogeneity, but this is discussed elsewhere.[clarification needed]

Unbiasedness

[edit]

Variance of the mean response

[edit]

where m is the number of data points.

Variance of the predicted response

[edit]

Further information: Prediction interval

Confidence intervals

[edit]

The standard method of constructing confidence intervals for linear regression coefficients relies on the normality assumption, which is justified if either:

the errors in the regression are normally distributed (the so-called classic regression assumption), or

the number of observations n is sufficiently large, in which case the estimator is approximately normally distributed.

The latter case is justified by the central limit theorem.

Normality assumption

[edit]

Asymptotic assumption

[edit]

The alternative second assumption states that when the number of points in the dataset is "large enough", the law of large numbers and the central limit theorem become applicable, and then the distribution of the estimators is approximately normal. Under this assumption all formulas derived in the previous section remain valid, with the only exception that the quantile t*n−2 of Student's t distribution is replaced with the quantile q* of the standard normal distribution. Occasionally the fraction ⁠1/n−2⁠ is replaced with ⁠1/n⁠. When n is large such a change does not alter the results appreciably.

Numerical example

[edit]

See also: Ordinary least squares § Example, and Linear least squares § Example

Alternatives

[edit]Calculating the parameters of a linear model by minimizing the squared error.

In SLR, there is an underlying assumption that only the dependent variable contains measurement error; if the explanatory variable is also measured with error, then simple regression is not appropriate for estimating the underlying relationship because it will be biased due to regression dilution.

Other estimation methods that can be used in place of ordinary least squares include least absolute deviations (minimizing the sum of absolute values of residuals) and the Theil–Sen estimator (which chooses a line whose slope is the median of the slopes determined by pairs of sample points).

Deming regression (total least squares) also finds a line that fits a set of two-dimensional sample points, but (unlike ordinary least squares, least absolute deviations, and median slope regression) it is not really an instance of simple linear regression, because it does not separate the coordinates into one dependent and one independent variable and could potentially return a vertical line as its fit. can lead to a model that attempts to fit the outliers more than the data.

Line fitting

[edit]

This section is an excerpt from Line fitting.[edit]

Line fitting is the process of constructing a straight line that has the best fit to a series of data points.

Several methods exist, considering:

Vertical distance: Simple linear regression

Resistance to outliers: Robust simple linear regression

Perpendicular distance: Orthogonal regression (this is not scale-invariant i.e. changing the measurement units leads to a different line.)

Weighted geometric distance: Deming regression

Scale invariant approach: Major axis regression This allows for measurement error in both variables, and gives an equivalent equation if the measurement units are altered.

Simple linear regression without the intercept term (single regressor)

[edit]

[leansigmajourney]

Advantages of Scatter Diagrams

1. Visualizes Relationships

Correlation Identification: Scatter diagrams provide a clear visual representation of how two variables relate to each other. By plotting data points on a two-dimensional graph, it becomes easier to see whether an increase in one variable corresponds with an increase (or decrease) in another.

Trend Analysis: They help in identifying the nature of relationships (linear, non-linear) between variables, which can be critical for analysis in various fields, including finance, marketing, and healthcare.

2. Identifies Outliers

Outlier Detection: Scatter plots make it easy to spot outliers—data points that do not conform to the overall pattern of the data. Identifying these outliers is crucial as they can significantly impact the results of statistical analyses and can indicate errors or anomalies in data collection.

Further Investigation: Once outliers are identified, they can be further investigated to determine if they are errors, special cases, or if they suggest new insights into the data set.

3. Simplicity

Easy to Construct: Creating a scatter diagram is straightforward; it requires only the data points for two variables. This simplicity makes it accessible for individuals with varying levels of statistical knowledge.

Clear Communication: Scatter diagrams are easy for stakeholders to understand, making them an effective tool for communicating findings and insights without needing complex explanations.

4. Shows Strength of Relationship

Trend Line Analysis: By fitting a trend line (regression line) to the scatter plot, one can visually assess the strength of the relationship. A tightly clustered group of points around the trend line indicates a strong relationship, while widely scattered points suggest a weak relationship.

Quantitative Measurement: The slope of the trend line and correlation coefficient can provide quantitative measures of the relationship, aiding in further statistical analysis.

5. Detects Non-linear Relationships

Flexibility in Patterns: While scatter diagrams are often used for linear relationships, they can also reveal non-linear patterns. This is useful in fields like biology or social sciences, where relationships may not be strictly linear.

Supports Advanced Analysis: Identifying non-linear relationships can lead to the application of more complex statistical models, improving predictive analytics and understanding of underlying processes.

6. Flexible Application

Versatility Across Disciplines: Scatter diagrams can be applied in numerous fields, such as:

Business: Analyzing sales data against marketing expenditure.

Healthcare: Examining the relationship between patient age and recovery times.

Manufacturing: Assessing defect rates against production volume.

Quality Control: In Six Sigma and other quality management methodologies, scatter diagrams are instrumental in understanding and controlling processes by identifying relationships between factors that affect quality.

7. Facilitates Hypothesis Testing

Formulating Hypotheses: Scatter diagrams can help generate hypotheses about potential relationships between variables, which can be tested with more rigorous statistical methods.

Support for Regression Analysis: They are often a precursor to regression analysis, allowing researchers to visualize data before applying statistical techniques to confirm or reject hypotheses.

8. Enhances Predictive Analysis

Forecasting: By observing relationships in historical data, scatter diagrams can assist in making predictions about future outcomes based on established trends.

Risk Assessment: In finance, for instance, scatter plots can illustrate risk versus return, aiding in investment decision-making.

9. Integration with Other Analytical Tools

Complementary Tool: Scatter diagrams can be used alongside other analytical tools (like histograms or box plots) to provide a more comprehensive analysis of data sets.

Software Compatibility: Many data analysis and visualization software tools support the creation of scatter diagrams, making them easy to integrate into broader data analysis workflows.

Conclusion

In summary, scatter diagrams are a powerful visual tool for analyzing and understanding relationships between variables. Their ability to simplify complex data, identify trends, and highlight outliers makes them essential in many fields, especially in quality management and statistical analysis. By leveraging scatter diagrams, analysts can gain insights that drive informed decision-making and process improvements.

[coursera1]

Title: The Relationship Between Hours Spent Studying and Exam Scores

Introduction The aim of this study is to investigate the correlation between hours spent studying per week and students' exam scores. A strong, positive relationship is expected, as more time dedicated to studying should result in higher exam performance.

Methods We randomly generated a sample dataset that includes 30 observations, each representing a student’s weekly study hours and corresponding exam scores. The Pearson correlation coefficient was used to assess the strength and direction of the relationship between these two continuous variables.

Data The data consists of two variables:

Hours Studied per Week: The number of hours students spend studying each week (continuous).

Exam Scores: The scores students achieved in their exams (continuous).

Results The Pearson correlation coefficient between hours studied and exam scores was calculated as 0.95. This indicates a strong positive linear relationship, where increased hours of study are associated with higher exam scores. The p-value associated with this correlation is extremely small (p<0.001p < 0.001p<0.001), meaning that the result is statistically significant.

Additionally, the coefficient of determination (R-squared) was found to be 0.90, meaning that 90% of the variability in exam scores can be explained by the hours spent studying.

Figure 1: Scatter Plot with Linear Fit ![Scatter plot with linear fit] Figure 1 shows a clear positive trend between the number of hours spent studying and exam scores. The red line represents the linear fit, which demonstrates the relationship with an R² value of 0.90.

Discussion The results suggest a significant positive relationship between study time and exam performance. This finding aligns with the hypothesis that increasing study time leads to improved academic performance. However, the study does not account for other factors that might affect exam scores, such as the quality of study, individual differences in learning, or external variables like stress or fatigue.

Conclusion In conclusion, the analysis demonstrates a strong positive correlation between the number of hours students spend studying and their exam scores. Given the high R-squared value, study time can be considered a significant predictor of exam performance. Future research could explore additional factors influencing academic success to develop a more comprehensive model.

[foxlightnights]

someone else in the thread posted two meta-analysis studies that i would agree are your best source of current information. a meta-analysis is the best kind of study you can find, because it compiles all of the existing studies, and examines them.

however, both these meta-analyses have problems (which the meta-analyses themselves acknowledge as their intent is to examine these studies), as pointed out by this user @butchlifeguard :

the “pearson coefficient” is a very important value. the post doesn’t quite explain what this is, but basically it measures how strong a correlation is. it ranges from -1 to 1, with -1 being towards a negative correlation and 1 being towards a positive correlation.

the value of “1” is considered absolutely perfect and therefore unrealistic. the value of “0” means absolutely no correlation at all, negative or positive. the coefficient of the second one was 0.11. your strongest correlation statistically would be 0.99. so, 0.11 is very weak evidence. it’s *barely* above 0.

the word “significant” basically means different things when it comes to statistics and colloquial usage. laypeople will often see “significant” and assume that means a very large effect, when statistically that just means they found anything at all. and statistics are not foolproof — they can be manipulated by the people doing the study, they can be affected by the way in which the study was performed, the sample sizes, how they chose the people in the study, and more. that is why better studies need to be conducted, because there are clear problems with existing studies.

it’s important to note that brain studies (the grey matter claim) are very messy. it’s very hard to prove after the fact that what you found in the brain was caused by whatever it is you’re studying. the “ideal and perfect study” for this would begin at birth — which is very difficult to do, and in many cases would be incredibly unethical to pull off a strict controlled study for (you couldn’t take babies and deliberately try to cause phone addiction!)

it also doesn’t prove this brain difference has any measurable effect on the person. there are many wide variations in the human brain. but it all sure can sound very scary!

now, i don’t think phone overusage shouldn’t be addressed at all, and i don’t think it’s a pointless endeavor to research the topic. if someone reports to a therapist they feel their phone usage is affecting them, of course that’s a goal they can try to work on. i myself found i was using social media too much as a coping mechanism, and it helped to use my phone less. the people in this post are not really claiming that, just over the specific terminology and concept of it being an “addiction” akin to other addictions, like gambling.

It's cool how this is a 60k note post when almost every word of it is untrue

[b4nanaa]

Blind spot (what is it, why it exists)

Correlations (positive versus negative, interpreting a correlation, correlation coefficients,

limitations)

Experiments (hypothesis, independent and dependent variables, control group, random

assignment)

Face blindness

Gestalt principles of organization (similarity, proximity, closure, simplicity)

How SSRI drugs work

Limbic system (what it is, major functions)

Lobes of the brain (their names, where they are, major functions associated with them)

Major brain structures and their major functions

Major divisions of the nervous system and what they do (somatic/autonomic,

sympathetic/parasympathetic)

Major perspectives on psychology (psychodynamic, cognitive, behavioral, neuroscience,

humanistic)

Major structures of the ear and their functions

Naturalistic observation (what it is, contrast it to experimentation)

Negative afterimages

Neuron function (action potential, all-or-none law, importance of the synapse, reuptake,

inhibitory and excitatory messages)

Neurons (major structures and their functions, presynaptic versus postsynaptic, mirror neurons)

Neuroplasticity

Neurotransmitters (what they are, names of major ones, what major disorders are associated

with specific ones)

Psychological specializations (clinical, counseling, health, developmental, social, etc.)

Rods and cones (major differences)

Scientific method

Split-brain research (major findings)

Top-down and bottom-up processing

Visual processing (fovea, retina, rods and cones, bipolar and ganglion cells, optic nerve, optic

chiasma, theories of color vision, primary visual cortex)