Writing Hypotheses

Quick reference

• 00:04 Hello, I'm Ray Sheen.
• 00:06 Let's take a few minutes now and discuss hypotheses.
• 00:10 A well-written hypothesis statement is at the core of successful hypothesis testing.
• 00:16 >> So let's discuss the principles for writing a hypothesis.
• 00:20 Writing a hypothesis creates focus for the rest of the hypothesis testing analysis.
• 00:25 The hypothesis should both define the population of data or
• 00:28 information to be used in the analysis and the parameter of interest.
• 00:32 When writing the hypothesis,
• 00:34 first start by stating in practical terms what you want to investigate.
• 00:38 It could be something like, does the value of this process characteristic make any
• 00:42 difference in how the process performs?
• 00:44 Or, does this change in the process improve the quality of the process
• 00:48 results?
• 00:50 Now, we convert the question into two practical statements that can be expressed
• 00:54 using mathematical equations.
• 00:56 These equations will involve a parameter of the datasets.
• 00:59 So for the first statement, does the value of this process characteristic make
• 01:03 a difference in how the process performs, we could create an equation that states
• 01:07 that the mean of the total dataset of the process performance equals or
• 01:11 does not equal the mean of the dataset when this process characteristic is
• 01:14 at one extreme value.
• 01:16 And when considering the question, does this change in the process improve
• 01:20 the quality of the process results, we could create an equation, for
• 01:24 the case where the mean of the process quality metric is lower after the change
• 01:27 was put in place, and the mean stayed the same after the change was put in place.
• 01:32 Notice that we're creating two equations, one for when the effect occurs, and
• 01:36 one for when the effect does not occur.
• 01:39 I find often it's easier to write the equation for
• 01:42 the alternative hypothesis first.
• 01:44 This is the equation for when the effect I'm trying to prove or disprove occurs.
• 01:48 So in the first case, it is that the mean of the full dataset does not equal
• 01:52 the mean of the data when the process characteristic is at the extreme value.
• 01:56 And for the second one, it is the mean of the process quality metric is lower after
• 02:00 the change has been put into the process.
• 02:03 The null hypothesis then would occur if the effect did not make a difference.
• 02:08 In both of these examples,
• 02:09 it would be that the mean of the two data sets are equal.
• 02:12 As you can see, often the null and alternative hypothesis are opposite
• 02:16 answers with respect to the question that is being asked.
• 02:20 Let's look at the formal definition of the two parts of the hypothesis.
• 02:24 The null hypothesis is designated as H sub 0.
• 02:28 It always represents the status quo.
• 02:30 It is saying that whatever change we are seeing between the statistical metrics of
• 02:34 the data set is just based upon the normal variation that occurs.
• 02:37 It's like our commute to work, each day it's a little longer or shorter,
• 02:41 depending upon traffic or the weather.
• 02:43 However, unless there's some major accident or other event that changes
• 02:46 traffic patterns and schedules, the variation from day to day is just random.
• 02:51 There's nothing worth looking at here, nothing significant is happening.
• 02:54 And our hypothesis testing approach we'll start by assuming that this is the case.
• 02:59 That means that the data has to prove that something significant is happening.
• 03:04 We don't start by assuming that there is a major change, and
• 03:07 the data has to prove that there isn't a difference.
• 03:09 More about that in another lesson.
• 03:11 The final result of our hypothesis test is that we accept or
• 03:15 reject the null hypothesis.
• 03:17 And just to be clear,
• 03:18 we accept the null hypothesis unless we can prove that we should reject it.
• 03:23 Now let's consider the alternative hypothesis.
• 03:26 This is represented by the symbol H sub a.
• 03:29 The hypothesis describes the differences we are attempting to prove.
• 03:33 Recall I said that the hypothesis testing is using data to prove what we
• 03:37 think we know.
• 03:38 This is what we think we know.
• 03:40 This is the difference we think exists in the data.
• 03:43 The hypothesis testing will prove whether that difference is statistically
• 03:47 significant or just due to random chance,.
• 03:49 It will validate whether there is a real difference or not.
• 03:53 Let's go through some more examples, and
• 03:54 you should definitely do the exercises to practice writing the hypotheses.
• 03:58 A well-written hypothesis will easily convert to an equation.
• 04:02 Remember, the hypothesis is a pair of statements that expresses two different
• 04:05 mathematical relationships for the data sets.
• 04:08 That is because it clearly spells out the population being investigated.
• 04:12 Therefore, we know what subset of data to use.
• 04:14 It identifies the dependent variable and independent variable that helps us to
• 04:18 determine the data characteristic to be measured, which is the dependent variable,
• 04:22 and the screening or differentiation of that data population to be used,
• 04:26 which is the independent variable.
• 04:29 Finally, the type of relationship or direction of the relationship is clear.
• 04:33 Do we just want to find out if there is a difference, or do we want to show that
• 04:37 the parameter for one data set is larger or smaller than for the other data sets?
• 04:41 Let's look at an example.
• 04:43 I'll start with the alternative hypothesis since that is
• 04:45 often the one we write first.
• 04:47 Production line A has a lower incidence of test defects than production line B.
• 04:52 Notice that it tells us that the population we are dealing with,
• 04:56 our production lines, it tells us the dependent variable which is the defect,
• 05:00 and the independent variable which is line A and line B.
• 05:03 And it gives us a direction for the relationship, line A is lower than line B.
• 05:07 Mathematically, this hypothesis statement would be that the average defect value for
• 05:12 line A is less than the average defect value for line B.
• 05:17 The null hypothesis is the opposite position.
• 05:19 There is no significant difference in test defects between data from production
• 05:24 line A and production line B.
• 05:26 Mathematically, this would be that the average defect value for
• 05:29 both lines is equal.
• 05:32 Let's look at another example.
• 05:33 The alternative hypothesis states there is a higher incidence of repair when using
• 05:38 materials from supplier A rather than material from supplier B.
• 05:42 The population we're looking at is our repair process.
• 05:45 The dependent variable is the incidence of repair, not the repair time or
• 05:49 the repair cost.
• 05:50 The independent variable is the material, either supplier A or supplier B, and
• 05:55 the relationship is at the rate of repair with supplier a material is
• 05:58 greater than supplier B material.
• 06:00 Since we're talking about the incidence or rate of repair, we need to normalize
• 06:04 the repair numbers based on the amount of product with each type of material.
• 06:08 Mathematically, we would state that the normalized average number of units being
• 06:12 repaired of material A is greater than the normalized average number of units with
• 06:17 material B.
• 06:18 And of course the null hypothesis is, there is no statistically significant
• 06:22 difference in repair rates between products made with supplier A material and
• 06:26 supplier B material.
• 06:27 Mathematically, we would say that the normalized average repair rate for
• 06:33 both material types is the same.
• 06:35 >> Writing a clear null and alternative hypothesis will focus your analysis and
• 06:40 lead to a clear answer to the question you're investigating.
• 06:44 But you must follow that null and alternative hypothesis format.
• 06:48 All of the tests are structured to either accept or reject the null hypothesis.

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