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It was the same for me, I rather expected

1-pnorm(1.96,2.8,1) than pnorm(2.8,1.96,,1)

it took a while to see that the two areas under the respective bell curves are always the same, visually just reflected to the vertical axis at (2.8-1.96)/2

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Right. Oops.

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One interesting addition for the x_i in [0, 1] case is when the probability of 1 differs from 0.5. I believe the s.e. should increase for the interaction as you move away from p = 0.5 in either direction too.

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I think this solution is mistaken.

In particular, suppose there is a *non-zero* interaction effect (which we have to be). If we are powered at 0.80 to detect a main effect in a model in which we’ve excluded the interaction effect, then the interaction effect gets absorbed into sigma. So sigma_mainEffectOnly can be arbitrarily larger than sigma_withInteractions. In fact, it’s theoretically possible to have power 0.80 with the main effect and power 1.00 when we include the interaction with the same sample size (i.e. the pathological case in which all the error came from excluding the interaction effect).

So under this interpretation of your problem, which I think is quite reasonable, the answer is undefined.

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See comment for what I’d been thinking of.

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Right, but to give a statement like “You need 16 times the sample size to estimate an interaction than to estimate a main effect”, you need to add in the assumption that the ratio of interaction effect over sigma approaches 0 (assuming you’re looking at a Gaussian response variable)…which is a pretty depressing assumption. Also note that this assumption means the main effect size you are looking at has roughly the same ratio.

If you’re willing to make the assumption that the estimates of the main + interaction effects are normally distributed (not too strong an assumption), then I think the required sample size ratio for the interaction effect should actually be a function of the original required sample size and the distribution of interaction variable (which we have stated is binary with p = 0.5)? I.e., if a small sample size is required, then the main effect must be large relative to sigma_mainEffectOnly, and so sigma_withInteraction should be very small (as presented in my pathological case above, you can actually make the sample size required *smaller* than the no interaction effect sample size!). But it’s not really clear to me that this function would be consistent across different response distributions (i.e. I think you get a different function if you’re looking a Gaussian response vs. survival analysis model etc.).

You can inject an auto-configured CouchbaseTemplate instance as you would with any other Spring Bean, provided a default CouchbaseConfigurer is available (which happens when you enable Couchbase support, as explained earlier).

The following examples shows how to inject a Couchbase bean:

There are a few beans that you can define in your own configuration to override those provided by the auto-configuration:

To avoid hard-coding those names in your own config, you can reuse BeanNames provided by Spring Data Couchbase. For instance, you can customize the converters to use, as follows:

30.9LDAP

(Lightweight Directory Access Protocol) is an open, vendor-neutral, industry standard application protocol for accessing and maintaining distributed directory information services over an IP network. Spring Boot offers auto-configuration for any compliant LDAP server as well as support for the embedded in-memory LDAP server from UnboundID .

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. There is a spring-boot-starter-data-ldap “Starter” for collecting the dependencies in a convenient way.

30.9.1Connecting to an LDAP Server

To connect to an LDAP server, make sure you declare a dependency on the spring-boot-starter-data-ldap “Starter” or spring-ldap-core and then declare the URLs of your server in your application.properties, as shown in the following example:

If you need to customize connection settings, you can use the spring.ldap.base and spring.ldap.base-environment properties.

30.9.2Spring Data LDAP Repositories

Spring Data includes repository support for LDAP. For complete details of Spring Data LDAP, refer to the reference documentation .

You can also inject an auto-configured LdapTemplate instance as you would with any other Spring Bean, as shown in the following example:

30.9.3Embedded In-memory LDAP Server

For testing purposes, Spring Boot supports auto-configuration of an in-memory LDAP server from UnboundID . To configure the server, add a dependency to com.unboundid:unboundid-ldapsdk and declare a base-dn property, as follows:

By default, the server starts on a random port and triggers the regular LDAP support. There is no need to specify a spring.ldap.urls property.

If there is a schema.ldif file on your classpath, it is used to initialize the server. If you want to load the initialization script from a different resource, you can also use the spring.ldap.embedded.ldif property.

By default, a standard schema is used to validate LDIF files. You can turn off validation altogether by setting the spring.ldap.embedded.validation.enabled property. If you have custom attributes, you can use spring.ldap.embedded.validation.schema to define your custom attribute types or object classes.

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