How many independent variables?

1. The purpose of this presentation is to assist you in determining the number of independent variables in the problem you are working on.

2. Here are your options:

3. Here are your options: 0 Independent Variables 1 Independent Variable 2+ Independent Variables

4. As you may remember from previous instruction, in statistics we are generally attempting to determine what causes what?

5. In statistics we are generally attempting to determine what causes what?

6. In statistics we are generally attempting to determine what causes what? Cause

7. In statistics we are generally attempting to determine what causes what? Cause

8. In statistics we are generally attempting to determine what causes what? Cause Effect

9. Or what influences what?

10. Or what influences what? Influencer Influenced

13. Simply put, in the cause and effect model, the cause side of the equation is known as the independent variable.

14. Simply put, in the cause and effect model, the cause side of the equation is known as the independent variable. Effect Cause

15. Simply put, in the cause and effect model, the cause side of the equation is known as the independent variable. Effect Cause

16. Simply put, in the cause and effect model, the cause side of the equation is known as the independent variable. Effect Cause Independent Variable

17. Or in the influencer / influenced model, the influencer side of the equation is also known as the independent variable.

18. Or in the influencer / influenced model, the influencer side of the equation is also known as the independent variable. Influencer Influenced

19. Or in the influencer / influenced model, the influencer side of the equation is also known as the independent variable. Influencer Influenced

20. Or in the influencer / influenced model, the influencer side of the equation is also known as the independent variable. Influencer Influenced Independent Variable

21. Let’s look at an example

22. A researcher wishes to determine the degree to which test scores are influenced by amount of study time.

23. A researcher wishes to determine the degree to which test scores are influenced by amount of study time. What is being influenced here?

24. A researcher wishes to determine the degree to which test scores are influenced by amount of study time. What is being influenced here?

25. A researcher wishes to determine the degree to which test scores are influenced by amount of study time. This is the Dependent Variable

26. A researcher wishes to determine the degree to which test scores are influenced by amount of study time. What is the influencer?

27. A researcher wishes to determine the degree to which test scores are influenced by amount of study time. What is the influencer?

28. A researcher wishes to determine the degree to which test scores are influenced by amount of study time. This is the Independent Variable

29. A researcher wishes to determine the degree to which test scores are influenced by amount of study time.

30. A researcher wishes to determine the degree to which test scores are influenced by amount of study time. Influencer Influenced

31. A researcher wishes to determine the degree to which test scores are influenced by amount of study time. Dependent Variable Influencer

32. A researcher wishes to determine the degree to which test scores are influenced by amount of study time. Dependent Variable Independent Variable

33. Let’s look at another example almost identical to the last one.

34. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

35. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. What is being influenced here?

36. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. What is being influenced here?

37. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. This is the Dependent Variable

38. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. What is the influencer?

39. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. What is the influencer?

40. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. This is the Independent Variable

41. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep.

42. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. Influencer Influenced

43. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. Influencer Influenced

44. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. Influencer Test Scores

45. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. Influencer Test Scores The Dependent Variable

46. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. Influencer Test Scores

47. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. Test Scores Amount of Sleep

48. A researcher wishes to determine the degree to which test scores are influenced by amount of sleep. Test Scores Amount of Sleep The Independent Variable

49. Let’s see how this question could be worded as an actual study.

50. Researchers wish to determine if the amount of sleep can have an effect on test scores.

51. Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups.

52. Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep.

53. Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences.

54. Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences. What is being influenced here?

55. Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences. What is being influenced here?

56. Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences. This is the DEPENDENT VARIABLE

57. Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences. What is doing the influencing?

58. Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences. What is doing the influencing?

59. Researchers wish to determine if the amount of sleep can have an effect on test scores. So, they randomly select two similar groups. They ensure that one group gets 6-8 hours of sleep and a second group gets only 3-4 hours of sleep. That morning both groups are administered an academic test. The results are examined for differences. This is the Independent Variable

60. See if you can identify the independent variable and the dependent variable in the following research studies.

61. Scientist wish to determine if - - good nutrition results in increased longevity. - time on social media impacts verbal skills. - exercise effects heart health - an instructional software helps students overcome conceptual gaps.

63. Scientist wish to determine if - - good nutrition results in increased longevity. - time on social media impacts verbal skills. - exercise effects heart health - an instructional software helps students overcome conceptual gaps. This is the INDEPENDENT VARIABLE

64. Scientist wish to determine if - - good nutrition results in increased longevity. - time on social media impacts verbal skills. - exercise effects heart health - an instructional software helps students overcome conceptual gaps. This is the DEPENDENT VARIABLE

68. Scientist wish to determine if - - good nutrition results in increased longevity. - time on social media impacts verbal skills. - exercise effects heart health. - an instructional software helps students overcome conceptual gaps.

71. Scientist wish to determine if - - good nutrition results in increased longevity. - time on social media impacts verbal skills. - exercise effects heart health. - an instructional software helps students overcome conceptual gaps.

74. Now, see if you can identify the independent and dependent variables in the following word problems:

75. A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period.

76. A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set:

77. A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set: Amount of Stress Negligible stress Minimal stress Moderate stress Sever stress Number of viral infections 2 4 6 5 1 3 5 7 4 2 7 8 1 3 5 4

78. A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set: What is being influenced here? Amount of Stress Negligible stress Minimal stress Moderate stress Sever stress Number of viral infections 2 4 6 5 1 3 5 7 4 2 7 8 1 3 5 4

79. A researcher investigated the number of viral infections people contract as a function of the amount of stress they experienced during a six-month period. She obtained the following data set: What is being influenced here? Amount of Stress Negligible stress Minimal stress Moderate stress Sever stress Number of viral infections 2 4 6 5 1 3 5 7 4 2 7 8 1 3 5 4

80. A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set: What is being influenced here? Amount of Stress Negligible stress Minimal stress Moderate stress Sever stress Number of viral infections 2 4 6 5 1 3 5 7 4 2 7 8 1 3 5 4

81. A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set: This is the DEPENDENT VARIABLE Amount of Stress Negligible stress Minimal stress Moderate stress Sever stress Number of viral infections 2 4 6 5 1 3 5 7 4 2 7 8 1 3 5 4

82. A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set: What is doing the influencing? Amount of Stress Negligible stress Minimal stress Moderate stress Sever stress Number of viral infections 2 4 6 5 1 3 5 7 4 2 7 8 1 3 5 4

83. A researcher investigated the number of viral infections people contract as function of the amount of stress they experienced during a six-month period. She obtained the following data set: What is doing the influencing? Amount of Stress Negligible stress Minimal stress Moderate stress Sever stress Number of viral infections 2 4 6 5 1 3 5 7 4 2 7 8 1 3 5 4

84. Next example:

85. A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task.

86. A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data:

87. A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data: Levels of Volume Low Volume Moderate Volume High Volume Number of errors 2 4 6 1 3 5 4 2 7 1 3 5

88. A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data: What is being influenced here? Levels of Volume Low Volume Moderate Volume High Volume Number of errors 2 4 6 1 3 5 4 2 7 1 3 5

91. A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data: This is the DEPENDENT VARIABLE Levels of Volume Low Volume Moderate Volume High Volume Number of errors 2 4 6 1 3 5 4 2 7 1 3 5

92. A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data: What is doing the influencing? Levels of Volume Low Volume Moderate Volume High Volume Number of errors 2 4 6 1 3 5 4 2 7 1 3 5

95. A researcher investigated the effect of volume background noise on participant’s error rates while performing a boring task. She tested three groups of randomly selected students and obtained the following error data: This is the Independent Variable Levels of Volume Low Volume Moderate Volume High Volume Number of errors 2 4 6 1 3 5 4 2 7 1 3 5

96. All of the examples shown so far are examples of problems with only one independent variable.

97. What does a word problem look like with more than one independent variable?

98. Here are some examples:

99. A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility.

100. A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility. What is being influenced here?

101. A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility. What is being influenced here?

102. A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility. This is the DEPENDENT VARIABLE

103. A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility. In this case there are two influencers

104. A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility. 1st Independent Variable In this case there are two influencers

105. A researcher investigated the effects of (1) whether participants meditate, and (2) the degree of introversion they exhibit on hypnotic suggestibility. 2nd Independent Variable In this case there are two influencers

106. Next problem:

107. You have been asked to determine the degree to which the amount of sleep and study time both effect student test scores.

108. You have been asked to determine the degree to which the amount of sleep and study time both effect student test scores. What is being influenced here?

109. You have been asked to determine the degree to which the amount of sleep and study time both effect student test scores. What is being influenced here?

110. You have been asked to determine the degree to which the amount of sleep and study time both effect student test scores. What is doing the influencing?

111. You have been asked to determine the degree to which the amount of sleep and study time both effect student test scores. 1st Independent Variable What is doing the influencing?

112. You have been asked to determine the degree to which the amount of sleep and study time both effect student test scores. 2nd Independent Variable What is doing the influencing?

113. Next example:

114. You have been asked to determine how the processes known as fracking and hydraulic propulsion impact the subterranean as well as the above ground environments.

115. You have been asked to determine how the processes known as fracking and hydraulic propulsion impact the subterranean as well as the above ground environments. What is being influenced here?

116. You have been asked to determine how the processes known as fracking and hydraulic propulsion impact the subterranean as well as the above ground environments. 1st Dependent Variable What is being influenced here?

117. You have been asked to determine how the processes known as fracking and hydraulic propulsion impact the subterranean as well as the above ground environments. 2nd Dependent Variable What is being influenced here?

118. You have been asked to determine how the processes known as fracking and hydraulic propulsion impact the subterranean as well as the above ground environments. What is doing the influencing?

119. You have been asked to determine how the processes known as fracking and hydraulic propulsion impact the subterranean as well as the above ground environments. 1st Independent Variable What is doing the influencing?

120. You have been asked to determine how the processes known as fracking and hydraulic propulsion impact the subterranean as well as the above ground environments. 2nd Independent Variable What is doing the influencing?

121. Quick note -

122. Quick note – there will be some research questions that only have a dependent variable and no independent variable. You will find that there are questions that focus on the degree to which a sample is similar to a population. Their similarity will be based on the dependent variable, but no influencer will be present.

123. Quick note – there will be some research questions that only have a dependent variable and no independent variable. These usually take the form of questions that focus on the degree to which a sample is similar to a population. Their similarity will be based on the dependent variable, but no influencer will be present.

124. Quick note – there will be some research questions that only have a dependent variable and no independent variable. These usually take the form of questions that focus on the degree to which a sample is similar to a population. Their similarity will be based on the dependent variable, but no independent variable will be present.

125. Here is an example:

126. A random sample of 22 fifth grade pupils have a grade point average of 3.6.

127. A random sample of 22 fifth grade pupils have a grade point average of 3.6. The grade point average (GPA) of all fifth grade pupils of the last five years is 3.4.

128. A random sample of 22 fifth grade pupils have a grade point average of 3.6. The grade point average (GPA) of all fifth grade pupils of the last five years is 3.4. Is the GPA of the 22 pupils significantly different from the populations’ GPA?

129. A random sample of 22 fifth grade pupils have a grade point average of 3.6. The grade point average (GPA) of all fifth grade pupils of the last five years is 3.4. Is the GPA of the 22 pupils significantly different from the populations’ GPA? In this case, the dependent variable is GPA. This type of analysis is generally a preliminary step. If the sample GPA is shown to be representative of the population GPA, then studies showing the impact of some independent variable (e.g., study habits, instructional software) are then conducted.

134. In this course, only a few problems will be like this.

135. Here is another issue to consider:

136. There can be some confusion as to what an independent variable is when you read some word problems.

137. Here is an example of this possible confusion:

138. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting.

139. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. As you know the Dependent Variable is pizza slices

140. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. At this point, some might think that there are three independent variables: Football, Basketball, and Soccer Players

141. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. However, there is really only one Independent Variable: Type of Athlete

142. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. What you will learn at the next decision point is that independent variables have at least two levels

143. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. So, here is a way to visualize this:

144. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. Football Players

145. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. Football Players Basketball Players

146. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. Football Players Basketball Players Soccer Players

147. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. Independent Variable: Football Players Basketball Players Soccer Players Type of Athlete

148. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. Independent Variable: Football Players Basketball Players Soccer Players Type of Athlete A Group

149. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. Independent Variable: Football Players Type of Athlete Basketball Players Soccer Players Group A Group B

150. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. Independent Variable: Football Players Basketball Players Soccer Players Type of Athlete Group A Group B Group C

151. Here is another example:

152. Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not.

153. Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not. The Dependent Variable is test scores

154. Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not. The Levels are

155. Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not. The Levels are Group using Software

156. Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not. The Levels are Group using Software

157. Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not. The Levels are Group using Software Group NOT using Software

158. Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not. The Independent Variable is Group using Software Group NOT using Software

159. Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not. The Independent Variable is INSTRUCTION TYPE Group using Software Group NOT using Software

160. Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not. The Independent Variable is INSTRUCTION TYPE Group using Software Group NOT using Software Group 1

161. Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not. The Independent Variable is INSTRUCTION TYPE Group 1 Group 2 Group using Software Group NOT using Software

162. Educational researchers wish to investigate if there is a difference in test scores between a group that received instruction using an innovative software and another group that did not. INSTRUCTION TYPE Notice that the expression instruction type does not show up any where in the problem. So, what you do is look at the levels and come up with a descriptive word or words that describe the independent variable.

163. Other examples

164. Problem #1

165. Problem #1 Dependent Variable: Degree of Anxiety

166. Problem #1 Dependent Variable: Degree of Anxiety Levels:

167. Problem #1 Dependent Variable: Degree of Anxiety Levels: • Group 1 – takes anxiety medication

168. Problem #1 Dependent Variable: Degree of Anxiety Levels: • Group 1 – takes anxiety medication • Group 2 – does not take anxiety medication

169. Problem #1 Dependent Variable: Degree of Anxiety Levels: • Group 1 – takes anxiety medication • Group 2 – does not take anxiety medication What shall we call the Independent Variable?

170. Problem #1 Dependent Variable: Degree of Anxiety Levels: • Group 1 – takes anxiety medication • Group 2 – does not take anxiety medication Independent Variable: Medication Status

171. Problem #2

172. Problem #2 Dependent Variable:

173. Problem #2 Dependent Variable: Bowling performance

174. Problem #2 Dependent Variable: Bowling performance Levels:

175. Problem #2 Dependent Variable: Bowling performance Levels: • Group 1 – use a specialty glove

176. Problem #2 Dependent Variable: Bowling performance Levels: • Group 1 – use a specialty glove • Group 2 – does not use a specialty glove

177. Problem #2 Dependent Variable: Bowling performance Levels: • Group 1 – use a specialty glove • Group 2 – does not use a specialty glove What shall we call the Independent Variable?

178. Problem #2 Dependent Variable: Bowling performance Levels: • Group 1 – use a specialty glove • Group 2 – does not use a specialty glove Independent Variable: Glove Type

179. Sometimes the independent variable is time.

180. Here is an example:

181. A class of 30 students are given a pre-class test to determine their level of statistical knowledge.

182. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test.

183. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test.

184. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test. The dependent variable is the test scores

185. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test. The independent variable is the times the test was given

186. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test. The independent variable is the times the test was given

187. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test. The independent variable is the times the test was given Pre-class test

188. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test. The independent variable is the times the test was given Pre-class test First Test

189. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test. The independent variable is the times the test was given Pre-class test 1st Test

190. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test. The independent variable is the times the test was given Pre-class test 1st Test 2nd Test End-term test

191. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test. The independent variable is the times the test was given Pre-class test 1st Test 2nd Test End-term test

192. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test. The independent variable is the times the test was given Pre-class test End-term test Post-term test 1st Test 2nd Test 3rd Level

193. Once again, time is the independent variable with three levels. A class of 30 students are given a pre-class test to determine their level of statistical knowledge. At the end of the term they are given an end of the term test. And then, three months after the course is over, they take post-term test. The independent variable is the times the test was given Pre-class test End-term test Post-term test 1st Test 2nd Test 3rd Level

194. Finally,

195. Finally, some problems will have what are called covariates.

196. You will learn more about covariates later.

197. Here is what a problem looks like with a covariate:

198. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to control for gender in order to see the unique effect of player type minus the gender factor.

201. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to control for gender in order to see the unique effect of player type minus the gender factor. Gender is what we call the covariate in this problem

202. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to control for gender in order to see the unique effect of player type minus the gender factor. You will be able to recognize it because it will use words like, control for, eliminate the effect, etc.

203. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to control for gender in order to see the unique effect of player type minus the gender factor. You will be able to recognize it because it will use words like, control for, eliminate the effect, etc.

204. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to eliminate the effect of gender in order to see the unique effect of player type minus the gender factor. You will be able to recognize it because it will use words like, control for, eliminate the effect of, hold constant.etc.

205. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to hold gender constant in order to see the unique effect of player type minus the gender factor. You will be able to recognize it because it will use words like, control for, eliminate the effect of, or hold constant.

206. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to control for gender in order to see the unique effect of player type minus the gender factor. In either case, you may think that you are working with two independent variables: Player type and Gender.

207. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to control for gender in order to see the unique effect of player type minus the gender factor. In this case, you may think that you are working with two independent variables: Player type and Gender.

208. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to control for gender in order to see the unique effect of player type minus the gender factor. In this case, you may think that you are working with two independent variables: Player type and Gender.

209. A pizza café owner wishes to know who to market her pizza to: Football, Basketball, or Soccer players. So, she conducts a study to determine which group eats more pizza slices in one sitting. She also wants to control for gender in order to see the unique effect of player type minus the gender factor. However, there is really only one independent variable that is of concern to us: Player type. Gender is just an additional analysis.

212. As with the previous scenario you will not run into a problem like this very often.

213. In Summary

214. Main Points:

215. Main Points: – The independent variable does the influencing or the causing in a word problem. – The independent variable may not be stated in the word problem, but you can determine it by coming up with an expression that ties to the two or more levels together.

216. Main Points: – The independent variable does the influencing or the causing in a word problem. – The independent variable may not be stated in the For example, if the study asks if study habits have an effect on test scores, then Study habits will be in the word problem, but you can determine it by coming up with an expression that ties to the two or more levels together. influencer and thus the independent variable.

217. Main Points: – The independent variable does the influencing or the causing in a word problem. – The independent variable may not be stated in the word problem, but you can determine it by coming up with an expression that ties the two or more levels together.

218. Main Points: – The independent variable does the influencing or the causing in a word problem. – The independent variable may not be stated in the word problem, but you can determine it by coming up with an expression that ties the two or more levels together. For example, if the study examines who eats more pizza slices, football, basketball, or soccer players. The dependent variable will be pizza slices and the independent variable will be something that ties these three levels together, like Player Type

221. Main Points: – The independent variable does the influencing or the causing in a word problem. – The independent variable may not be stated in the word problem, but you can determine it by coming up with an expression that ties the two or more levels together. Or, if one group receives a treatment (like a medication) and the other does not, then the two levels would be (1) receiving treatment and the other (2) not receiving treatment. The independent variable could be: Treatment Status

222. Main Points: – The independent variable does the influencing or the causing in a word problem. – The independent variable may not be stated in the word problem, but you can determine it by coming up with an expression that ties the two or more levels together. Or, if one group receives a treatment (like a medication) and the other does not, then the two levels would be (1) receiving treatment and the other (2) not receiving treatment. The independent variable could be: Treatment Status

223. Main Points: – The independent variable does the influencing or the causing in a word problem. – The independent variable may not be stated in the word problem, but you can determine it by coming up with an expression that ties the two or more levels together. Or, if one group receives a treatment (like a medication) and the other group does not, then the two levels would be (1) group receiving treatment and the other (2) group not receiving treatment. The independent variable could be: Treatment Status

224. Main Points: – The independent variable does the influencing or the causing in a word problem. – The independent variable may not be stated in the word problem, but you can determine it by coming up with an expression that ties the two or more levels together. Or, if one group receives a treatment (like a medication) and the other group does not, then the two levels would be (1) group receiving treatment and the other (2) group not receiving treatment. The independent variable could be: Treatment Status

225. Main Points: – The independent variable does the influencing or the causing in a word problem. – The independent variable may not be stated in the word problem, but you can determine it by coming up with an expression that ties the two or more levels together. Or, if one group receives a treatment (like a medication) and the other group does not, then the two levels would be: (1) group receiving treatment and the other (2) group not receiving treatment. The independent variable could be: Treatment Status

231. Additional Points-

232. Additional Points- – There can be more than one independent variable.

233. Additional Points- – There can be more than one independent variable. For example, test scores being influenced by a combination of (1) hours of sleep and (2) study time

234. Additional Points- – There can be more than one independent variable. – In a few cases, when dealing with difference questions,

235. Additional Points- – There can be more than one independent variable. – In a few cases, when dealing with difference questions, • one problem type does not have an independent variable.

236. Additional Points- – There can be more than one independent variable. – In a few cases, when dealing with difference questions, • one problem type does not have an independent variable. For example, when you simply want to see if the sample you are about to study is statistically similar to the population based on some dependent variable like test scores, level of anxiety, or amount of pizza eaten. In this case we do not have an independent variable yet to test to see what influence it has on the dependent variable.

240. Additional Points- – There can be more than one independent variable. – In a few cases, when dealing with difference questions, • one problem type does not have a independent variable. • another problem type has a covariate which is not counted as an independent variable.

241. Additional Points- – There can be more than one independent variable. – In a few cases, when dealing with difference questions, • one problem type does not have a independent variable. • another problem type has a covariate which is not counted as an independent variable. For example, if you are comparing football players and soccer players in terms of the amount of pizza they eat. And then run an additional analysis eliminating the effect of gender to determine if gender plays a role in the amount of pizza eaten as well.

242. Additional Points- – There can be more than one independent variable. – In a few cases, when dealing with difference questions, • one problem type does not have a independent variable. • another problem type has a covariate which is not counted as an independent variable. For example, if you are comparing football players and soccer players in terms of the amount of pizza they eat. And then run an additional analysis eliminating the effect of gender to determine if gender plays a role in the amount of pizza eaten as well.

243. Now, determine the number of independent variables in the problem you are working on. 0 Independent Variables 1 Independent Variable 2+ Independent Variables

How many independent variables?

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