📚 Edexcel Maths Skills for WJEC Psychology: Statistical Foundations | Edexcel 数学技能与 WJEC 心理学：统计基础
Edexcel A-Level Mathematics develops the core numerical and statistical skills that appear throughout WJEC Psychology research methods. Understanding these mathematical foundations helps you analyse psychological data accurately and write stronger exam answers.
Edexcel A-Level 数学培养学生的核心数值与统计技能，这些技能贯穿 WJEC 心理学研究方法。理解这些数学基础有助于你准确分析心理学数据，并写出更高质量的考试答案。
This article reviews the key statistical techniques from an Edexcel maths perspective and links each one to typical WJEC Psychology data tasks. You will see how probability, distributions, and hypothesis testing work together in psychological research.
本文从 Edexcel 数学角度复习关键统计技术，并将每个技术与 WJEC 心理学中常见的数据任务联系起来。你将看到概率、分布和假设检验如何在心理学研究中协同工作。
1. Understanding Data Types and Measurement Scales | 理解数据类型与测量尺度
In Edexcel maths, you must first decide whether a variable is qualitative or quantitative before choosing a suitable diagram or test. WJEC Psychology studies record the same kinds of variables when measuring behaviour, memory, or attitude.
在 Edexcel 数学中，你必须先判断变量是定性变量还是定量变量，然后再选择合适的图表或检验方法。WJEC 心理学研究在测量行为、记忆或态度时也会记录相同类型的变量。
Qualitative variables are non-numerical categories, such as gender or eye colour. Quantitative variables are numerical and can be discrete or continuous. Psychology experiments also use nominal, ordinal, or interval data to describe the level of measurement.
定性变量是非数字类别，例如性别或眼睛颜色。定量变量是数值型的，可以是离散型或连续型。心理学实验还使用名义数据、顺序数据或等距数据来描述测量水平。
Nominal data: categories with no order. Ordinal data: ordered but not equally spaced. Interval data: equal intervals, no true zero.
名义数据：无顺序的类别。顺序数据：有顺序但不等距。等距数据：等距间隔，没有真实零点。
| Data type | Meaning | Psychology example |
| Nominal | Labels without order | Handedness, diagnostic group |
| Ordinal | Ordered ranks, unequal gaps | Likert scale responses |
| Interval | Equal gaps, no true zero | IQ score, temperature |
2. Measures of Central Tendency | 集中趋势量数
The mean is the arithmetic average and is strongly affected by outliers. The median is the middle value and is more robust, while the mode is the most frequent value in the data set.
平均数是算术平均值，受异常值影响较大。中位数是位于中间位置的数值，更加稳健，而众数是数据集中出现频率最高的数值。
x̄ = Σx / n
In WJEC Psychology, the mean is commonly reported for interval data, while the median is often used for skewed reaction-time data. The mode is useful for nominal data where a mean is not meaningful.
在 WJEC 心理学中，平均数通常用于等距数据，而中位数常用于偏态的反应时数据。众数适用于名义数据，因为此时计算平均数没有意义。
The mean is best for roughly symmetric interval data.
平均数最适合近似对称的等距数据。
The median is better when outliers or skew are present.
当存在异常值或偏态时，中位数更好。
The mode is the only measure for nominal categories.
众数是唯一适用于名义类别的集中趋势量数。
3. Measures of Dispersion | 离散程度量数
The range is the difference between the largest and smallest values. It is easy to calculate but ignores all the middle data points.
极差是最大值与最小值之间的差值。它计算简单，但忽略了所有中间数据点。
The interquartile range IQR = Q3 - Q1 gives the spread of the middle 50% ess affected by outliers. Standard deviation measures the average deviation from the mean.
四分位距 IQR = Q3 - Q1 表示中间 50% 数据的离散程度，受异常值影响较小。标准差测量数据偏离平均数的平均程度。
s = √[ Σ(x - x̄)² / (n - 1) ]
Find the mean x̄.
求出平均数 x̄。
Square each deviation x - x̄.
将每个离差 x - x̄ 平方。
Add the squared deviations, divide by n - 1, then take the square root.
将平方后的离差相加，除以 n - 1，再取平方根。
A larger standard deviation indicates greater variability in the results. In psychology experiments, high variability can weaken the evidence for an effect.
标准差越大，说明结果的变异性越大。在心理学实验中，高变异性会削弱效应存在的证据。
4. Probability Basics for Research | 研究中的概率基础
n Edexcel maths, P(A) = number of successful outcomes / total number of possible outcomes.
概率是用来衡量事件发生可能性的数值，取值范围在 0 到 1 之间。在 Edexcel 数学中，P(A) = 成功结果的数量 / 所有可能结果的数量。
(A) × P(B). For any two events, the addition rule is P(A or B) = P(A) + P(B) - P(A and B).
如果两个事件互不影响，则它们是独立事件。对于独立事件，P(A 且 B) = P(A) × P(B)。对于任意两个事件，加法法则为 P(A 或 B) = P(A) + P(B) - P(A 且 B)。
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
In WJEC Psychology, probability appears as the p-value. The p-value is the probability of obtaining the observed result, or one more extreme, if the null hypothesis is true.
在 WJEC 心理学中，概率以 p 值的形式出现。p 值是在零假设为真的情况下，获得当前结果或更极端结果的概率。
5. The Binomial Distribution | 二
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