背景
我希望比较两个时期的菜单销售组合比率。
菜单定义为产品集合。 （即汉堡包，三明治等）
销售组合比率被定义为相对于销售的菜单单元总数（即，销售100个菜单项目）的单位（即，20个汉堡包）的产品销售量。 在汉堡包的例子中，汉堡包的销售混合比例是20％（20个汉堡/ 100个菜单项）。 这代表了菜单总销售额的份额。
期间定义为用于比较目的的时间范围（即午餐与晚餐，周一与周五等）。
我对卷的整体变化不感兴趣（我不在乎我是否在一个时期内卖出20个汉堡包而在另一个时期卖出了25个汉堡包）。 我只对比率分布的变化感兴趣（我销售的单位的20％是一个时期的汉堡包，25％是另一个时期的汉堡包）。
由于销售组合占整体的份额，因此每个时期的平均值将相同; 期间的平均差异始终为0％; 并且，每组数据的总和将始终为100％。
目的：
测试销售分布（每个菜单项相对于其他菜单项的销售组合百分比）是否从一个时期到另一个时段发生了显着变化。
零假设： A期客户的购买模式和偏好与B期客户的购买模式和偏好相同。
潜在数据输入示例：
[Menu Item] [Period A] [Period B] Hamburger 25% 28% Cheeseburger 25% 20% Salad 20% 25% Club Sandwich 30% 27%题：
是否存在常用方法来测试两组数据之间的总份额分布是否存在显着差异？
如果我测量的是实际销售单位数量的变化，那么配对的T-Test就会起作用，但是（我相信）不会改变总单位的份额。
我一直在网上和一些教科书上搜索一段时间没有运气。 我可能正在寻找错误的术语。
任何方向，无论是搜索术语还是（最好）实际名称的适当测试，都是值得赞赏的。
谢谢，
安德鲁
编辑：我正在考虑将Pearson Correlation测试作为一种可能的解决方案 - 忘记每一行数据都是独立的菜单项，数学不应该关心。 完美匹配（相同的销售组合）将获得系数1，变化越大，系数越低。 一个潜在的问题是，与常规相关性测试不同，这些变化可能会被放大，因为对一个数字的任何更改都会自动影响其他数字。 这是一个可行的解决方案？ 如果是这样，有没有办法缓和放大问题？
Background
I wish to compare menu sales mix ratios for two periods.
A menu is defined as a collection of products. (i.e., a hamburger, a club sandwich, etc.)
A sales mix ratio is defined as a product's sales volume in units (i.e., 20 hamburgers) relative to the total number of menu units sold (i.e., 100 menu items were sold). In the hamburger example, the sales mix ratio for hamburgers is 20% (20 burgers / 100 menu items). This represents the share of total menu unit sales.
A period is defined as a time range used for comparative purposes (i.e., lunch versus dinner, Mondays versus Fridays, etc.).
I am not interested in overall changes in the volume (I don't care whether I sold 20 hamburgers in one period and 25 in another). I am only interested in changes in the distribution of the ratios (20% of my units sold were hamburgers in one period and 25% were hamburgers in another period).
Because the sales mix represents a share of the whole, the mean average for each period will be the same; the mean difference between the periods will always be 0%; and, the sum total for each set of data will always be 100%.
Objective:
Test whether the sales distribution (sales mix percentage of each menu item relative to other menu items) changed significantly from one period to another.
Null Hypothesis: the purchase patterns and preferences of customers in period A are the same as those for customers in period B.
Example of potential data input:
[Menu Item] [Period A] [Period B] Hamburger 25% 28% Cheeseburger 25% 20% Salad 20% 25% Club Sandwich 30% 27%Question:
Do common methods exist to test whether the distribution of share-of-total is significantly different between two sets of data?
A paired T-Test would have worked if I was measuring a change in the number of actual units sold, but not (I believe) for a change in share of total units.
I've been searching online and a few text books for a while with no luck. I may be looking for the wrong terminology.
Any direction, be it search terms or (preferably) the actual names appropriate tests, are appreciated.
Thanks,
Andrew
EDIT: I am considering a Pearson Correlation test as a possible solution - forgetting that each row of data are independent menu items, the math shouldn't care. A perfect match (identical sales mix) would receive a coefficient of 1 and the greater the change the lower the coefficient would be. One potential issue is that unlike a regular correlation test, the changes may be amplified because any change to one number automatically impacts the others. Is this a viable solution? If so, is there a way to temper the amplification issue?
最满意答案
考虑使用Chi Squared拟合优度测试作为此问题的简单解决方案：
H0：月份B的菜单项比例与月份A相同
Ha：B月的菜单项中至少有一个比例与A月不同
这里有一个很好的教程 。
Consider using a Chi Squared Goodness-of-Fit test as a simple solution to this problem:
H0: the proportion of menu items for month B is the same as month A
Ha: at least one of the proportions of menu items for month B is different to month A
There is a nice tutorial here.
更多推荐
发布评论