{"id":335,"date":"2021-10-17T14:53:03","date_gmt":"2021-10-17T18:53:03","guid":{"rendered":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/?p=335"},"modified":"2021-10-17T14:53:03","modified_gmt":"2021-10-17T18:53:03","slug":"chapter-15","status":"publish","type":"post","link":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/2021\/10\/17\/chapter-15\/","title":{"rendered":"Chapter 15"},"content":{"rendered":"

 <\/p>\n

Chapter 15 Quantitative Analysis: Inferential Statistics<\/p>\n

In this chapter we see this idea that theories can never be proven only disproved. As described in this chapter with the example of the sun, we accept that it will rise again tomorrow because it has everyday so far but that does not mean we can actually prove it to be fact. We cannot prove theories because we do not know everything, therefore it could be that we have not found the evidence that disproves the theory, only those that support it. This is what inferential statistics is used for, allowing you to make predictions such as, the sun will rise again tomorrow.<\/p>\n

In order to make these predictions, we use things such as the P-Value and the Sampling distribution. The P-Value shows if a value is statistically significant if the probability of that value is less than 5%. The Sampling distribution is defined as the theoretical distribution of an infinite number of samples from the population. There will always be some error which is considered the standard error, if it is small, then it can be accepted as a good estimate for the sample. How close that estimate is for the data set gives us the confidence interval. \u00a0of out sample estimates is defined as the confidence interval. This allows us to see the accuracy, if the value falls within the limits of the confidence interval we know this value is appropriate. The goal of the p-value and the confidence interval allow us to see the probability of our result and how close in terms of value.<\/p>\n

General Linear Model<\/strong><\/p>\n

In this section, we look various linear models. The general linear model is said to be used to represent linear patterns of relationships in observed data.<\/p>\n

\"page139image21772928\"<\/div>\n

Most examine the relationship between one independent variable and one dependent variable. We can use the GLM to determine slope and intercept using this equation: y = \u03b20 + \u03b21 x + \u03b5. Slope plus intercept, plus error. A line that describes the relationship between two or more variables is called a regression line, which is seen above.<\/p>\n

y = \u03b20 + \u03b21 x1 + \u03b22 x2 + \u03b23 x3 + … + \u03b2n xn + \u03b5.<\/p>\n

Two-Group Comparison<\/strong><\/p>\n

In this section, we looked at the t-test which is defined as examining whether the means of two groups are statistically different from each other, or whether one group has a statistically larger mean than the other.<\/p>\n

\"page142image21875344\"<\/div>\n

The denominator is the standard error which can be calculated using this formula below.<\/p>\n

\"page142image21873264\"<\/div>\n

The degrees of freedom can be calculated using this formula:<\/p>\n

\"page142image21882000\"<\/div>\n

The degree of freedom is considered the number of values that can vary freely in the calculation of the statistic. It is the number of values that can be assigned to a statistical distribution.<\/p>\n","protected":false},"excerpt":{"rendered":"

  Chapter 15 Quantitative Analysis: Inferential Statistics In this chapter we see this idea that theories can never be proven only disproved. As described in this chapter with the example of the sun, we accept that it will rise again tomorrow because it has everyday so far but that does not mean we can actually prove it to be fact…. Read more »<\/a><\/p>\n","protected":false},"author":3492,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[177784],"tags":[],"class_list":["post-335","post","type-post","status-publish","format-standard","hentry","category-chapter-summary"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/wp-json\/wp\/v2\/posts\/335","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/wp-json\/wp\/v2\/users\/3492"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/wp-json\/wp\/v2\/comments?post=335"}],"version-history":[{"count":1,"href":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/wp-json\/wp\/v2\/posts\/335\/revisions"}],"predecessor-version":[{"id":336,"href":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/wp-json\/wp\/v2\/posts\/335\/revisions\/336"}],"wp:attachment":[{"href":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/wp-json\/wp\/v2\/media?parent=335"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/wp-json\/wp\/v2\/categories?post=335"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.richmond.edu\/researchmethods-fall2021\/wp-json\/wp\/v2\/tags?post=335"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}