Statistical Reasoning
Statistical Reasoning is an important tool in descriptive, correlational, and experimental analysis, helping us explain patterns and relationships that may not be immediately obvious to the unaided eye Researchers. Michael Norton and Dan Ariely (2011) demonstrated in a study as poor statistical assumptions can lead to widespread misconceptions. Reasonable such inaccuracies are common when people rely on rough estimates rather than accurate data, often incorrect data.
By the end of this section, you should know about:
- Statistical Reasoning in Everyday Life
- The Normal Curve and Standard Deviation
- Significant Differences
Let’s Take a closer look at them.
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Statistical Reasoning in Everyday Life
Examples include the false belief that 10 percent of the population is gay or that we only use 10 percent of our brains. Which misleads society. Clear and accurate statistics can help correct such misconceptions. For example, when the U.S. Secretary of State John Kerry gave the exact numbers—1,429 Syrians killed, including 426 children—his argument for chemical attacks gained credibility. It caused widespread public panic even though the risk was minimal.
Statistical Reasoning: Describing Data
After collecting data, researchers use descriptive statistics to organize and present it in a meaningful way. The most common format is bar graphs, but caution is needed when interpreting graphs, as the format makes differences appear larger or smaller than they are The vertical scale of the graph (y-axis). can be changed to reduce or exaggerate the data, so examine this entry carefully. Important. Another important aspect of data description is through the measure of central tendency, which summarizes the data with a single number. Commonly used measures are mode (maximum decrease in value), mean (average), and mean (mean value over a series of data).
Statistical Reasoning: Measures of Central Tendency and Variation
The mean and median provide useful information about the focus of a data set, but do not capture variation or spread in the data. Measures of variance—such as range (the difference between the highest and lowest values) and standard deviation (the spread of the values from the mean)—are important for understanding data variability. A large variation indicates whether the mean is approximately less reliable as a predictor. For example, a basketball player whose score consistently ranges from 13 to 17 points is more predictable than someone who scores between 5 and 25. Standard deviation is particularly helpful because it takes into account every point in the data set, and it allows changes to be detected.
The Normal Curve and Standard Deviation
In many biological data sets, such as height, weight, or IQ scores, the data form a symmetric, bell-shaped distribution known as a normal curve On this curve most data points are closely clustered, with a few cases where you obviously go too far. An important feature of the normal curve is that approximately 68 percent of all data points fall within a single interval of the midline. This characteristic is particularly useful in understanding the distribution of the data and predicting future discoveries in a given group.
Significant Differences
When researchers find differences between groups, the key question is whether these differences are meaningful or coincidental. We rely on statistical measures to determine whether the differences we have observed can be generalized to a population. These statistics help us assess reliability and significance in terms of variance, and help us decide whether the results will reflect a real effect in the general population, or just chance based on studied observations on the research.
Statistical Reasoning: When is an observed difference reliable?
There are three main principles to consider when determining whether observed differences can be generalized.
Representative samples are better than biased samples: The best conclusions come from samples that represent the general population. Ideally, researchers should draw samples that reflect the diversity of the population they wish to study.
Low variability observations are more reliable than discrete classifications: the average reliability increases when the data points are more accurate (low variability) e.g., as a basketball player in-game scores are relatively stable, their average scores are more reliable than if the player fluctuates wildly Change means greater confidence in the reliability of the results.
More cases are better than fewer: Larger samples provide more reliable estimates of the true population parameters than smaller samples. A few anecdotes or observations, such as a student attending only a couple of classes. May not provide a reliable picture of the larger trend. Larger samples are generally more likely to reflect the true population, leading to more trustworthy conclusions.
Statistical Reasoning: When is the observed difference significant?
Even if we look at the differences between the two groups, such as the scores of men and women on a fitness test, how do we know if these differences are real or due to chance? Statistical testing helps answer this question.
The main argument is that if the two sample averages are reliable (i.e. based on many observations with little variation). And the difference between the averages is large. Then it is noticeable that the differences would reflect real differences in the population, not chance. This is called mathematical logic. Statistically significant results indicate that the observed differences are unlikely to have occurred by chance.
To judge statistical significance, researchers often use a criterion called a p-value, which indicates the degree to which an outcome is more likely to occur by chance Most psychologists calculate a p-value less than 0.05 (5%) as severe enough to reject null hypothesis (the concept with no real difference). If it does, then the result Is considered statistically significant.
Mode the most frequently occurring score(s) in a distribution.
Mean the arithmetic average of a distribution, obtained by adding the scores and then dividing by the number of scores.
Median the middle score in a distribution; half the scores are above it and half are below it.
Range the difference between the highest and lowest scores in a distribution.
Standard deviation is a computed measure of how much scores vary around the mean score.
Normal curve (normal distribution) a symmetrical, bell-shaped curve that describes the distribution of many types of data; most scores fall near the mean (about 68 percent fall within one standard deviation of it) and fewer and fewer near the extremes.
Statistical significance a statistical statement of how likely it is that an obtained result occurred by chance.
Statistical Reasoning: What is useful is mathematical logic
It is important to remember that statistical significance does not necessarily mean that the observed differences are necessarily meaningful. For example, a study might show a statistically significant difference in intelligence test scores between first-born and late-born children. While the difference may be statistically significant. The actual score difference (usually only 1-3 points) may not have much practical meaning.
In other words, although a statistically significant result indicates that the observed effect is real. And not likely to occur by chance, it does not always indicate that the result is meaningful.
Statistical Reasoning: The Point to Remember
- Statistical significance measures the likelihood that an observed result happened by chance. It doesn’t, however, tell us how important or impactful the result is in practical terms.
- Be cautious about generalizing from small, biased samples, and always consider the size of the effect when interpreting statistical significance.
The chapter primarily focuses on various aspects of the nervous system, brain functions, and neurotransmitters. Phrenology (historically linked to the idea that the brain’s shape could indicate personality traits) cannot be attributed to the division of the brain into two hemispheres. Plasticity refers to the brain’s ability to adapt and change in response to experience. Such as the changes in spatial memory in Kareem’s brain. Neurons, the fundamental units of the nervous system, are best described as cells. And action potentials are temporary electrical charges that travel through neurons. Reuptake and the blocking of serotonin reuptake can influence neurotransmitter levels in the synaptic gap. Endorphins are natural neurotransmitters related to pain control, while Botox works by blocking acetylcholine. The sympathetic nervous system is responsible for physiological changes like increased heart rate and sweating. Motor neurons relay signals for movement, and most neurons in the body are interneurons. The sympathetic nervous system helps arouse and expend energy, influencing blood sugar levels and pupil dilation. Such as oxytocin, which facilitates childbirth and milk flow.