Computing_NN1 intervals_NN2 using_VVG replaced-dns_NN2 
Appendix_NN1 1_CRD gives_VVZ output_NN1 from_PRP the_AT0 provided_VVN software_NN1 (_PUL see_VVB Software_NN1 section_NN1 at_PRP end_NN1 of_PRF Methods_NN2 )_PUR for_PRP the_AT0 example_NN1 given_VVN in_PRP Fig._NN1 1b_NN1 (_PUL see_VVB Example_NN1 1_CRD in_PRP the_AT0 user_NN1 's_POS notes_NN2 )_PUR ._SENT The_AT0 problem_NN1 is_VBZ to_TO0 find_VVI 95_CRD %_NN0 confidence_NN1 intervals_NN2 for_PRP both_DT0 the_AT0 Hedges_NN2 &_NP0 Olkin_NP0 and_CJC Steiger_NP0 &_NP0 Fouladi_NP0 methods_NN2 ,_PUN each_DT0 based_VVN on_PRP either_AV0 d_ZZ0 or_CJC g_ZZ0 (_PUL i.e._AV0 ,_PUN 4_CRD separate_AJ0 intervals_NN2 )_PUR ,_PUN when_CJS d_ZZ0 =_NN1 1.0_CRD and_CJC ν_CRD =_NP0 16._CRD The_AT0 program_NN1 reads_VVZ the_AT0 instructions_NN2 from_PRP the_AT0 input_NN1 file_NN1 and_CJC writes_VVZ an_AT0 output_NN1 text_NN1 file_NN1 that_CJT can_VM0 be_VBI opened_VVN with_PRP a_AT0 text_NN1 editor_NN1 or_CJC spreadsheet_NN1 (_PUL see_VVB Appendix_NN1 1_CRD )_PUR ._SENT The_AT0 output_NN1 contains_VVZ the_AT0 mean_AJ0 difference_NN1 ,_PUN lower_AJC and_CJC upper_AJ0 limits_NN2 ,_PUN lower_AJC and_CJC upper_AJ0 segments_NN2 (_PUL the_AT0 distance_NN1 between_PRP the_AT0 non-centrality_AJ0 parameter_NN1 and_CJC the_AT0 respective_AJ0 upper_AJ0 and_CJC lower_AJC confidence_NN1 limits_NN2 )_PUR ,_PUN and_CJC the_AT0 full_AJ0 width_NN1 of_PRF the_AT0 interval_NN1 for_PRP both_DT0 the_AT0 standardized_AJ0 biased_AJ0 scaling_NN1 and_CJC the_AT0 standardized_AJ0 unbiased_AJ0 scaling_NN1 for_PRP both_DT0 the_AT0 Hedges_NN2 &_NP0 Olkin_NP0 and_CJC Steiger_NP0 &_NP0 Fouladi_NP0 methods_NN2 ._SENT The_AT0 d-scaled_AJ0 confidence_NN1 intervals_NN2 from_PRP Fig._NN1 1b_NN1 are_VBB given_VVN under_PRP "_PUQ Standardized_AJ0 Biased_AJ0 Scaling_NN1 "_PUQ for_PRP Hedges_NP0 &_NP0 Olkin_NP0 and_CJC Steiger_NP0 &_NP0 Fouladi_NP0 confidence_NN1 intervals_NN2 ._SENT 
Supplement_NN1 1_CRD gives_VVZ detailed_AJ0 example_NN1 calculations_NN2 for_PRP each_DT0 of_PRF the_AT0 four_CRD methods_NN2 used_VVN in_PRP this_DT0 paper_NN1 ._SENT 
Predicting_VVG coverages_NN2 for_PRP confidence_NN1 intervals_NN2 
It_PNP is_VBZ obvious_AJ0 from_PRP Fig._NN1 1_CRD that_CJT the_AT0 Hedges_NN2 &_NP0 Olkin_NP0 and_CJC Steiger_NP0 &_NP0 Fouladi_NP0 methods_NN2 differ_VVB ,_PUN and_CJC it_PNP is_VBZ important_AJ0 to_TO0 understand_VVI how_AVQ they_PNP differ_VVB in_PRP order_NN1 to_TO0 predict_VVI and_CJC compare_VVI the_AT0 coverages_NN2 of_PRF the_AT0 two_CRD methods_NN2 ._SENT When_CJS the_AT0 d_ZZ0 is_VBZ 0.0_CRD ,_PUN both_DT0 methods_NN2 produce_VVB symmetrical_AJ0 confidence_NN1 intervals_NN2 ,_PUN and_CJC in_PRP that_DT0 characteristic_NN1 ,_PUN they_PNP are_VBB similar_AJ0 to_PRP central_AJ0 t_ZZ0 confidence_NN1 intervals_NN2 which_DTQ can_VM0 be_VBI expressed_VVN as_PRP a_AT0 mean_AJ0 value_NN1 plus_PRP and_CJC minus_PRP a_AT0 calculated_AJ0 half_NN1 width_NN1 ._SENT 
When_CJS the_AT0 d_ZZ0 is_VBZ nonzero_NN1 ,_PUN such_DT0 as_PRP 1.0_CRD ,_PUN all_DT0 three_CRD distributions_NN2 in_PRP Fig._NN1 1a_NN1 are_VBB positively_AV0 skewed_VVN ,_PUN and_CJC the_AT0 distances_NN2 from_PRP the_AT0 non-centrality_AJ0 parameter_NN1 to_PRP the_AT0 confidence_NN1 limits_NN2 differ_VVB on_PRP the_AT0 right_AJ0 and_CJC left_AJ0 sides_NN2 ._SENT I_PNP will_VM0 call_VVI these_DT0 unequal_AJ0 distances_NN2 segments_NN2 ._SENT With_PRP the_AT0 Hedges_NN2 &_NP0 Olkin_NP0 method_NN1 ,_PUN the_AT0 wider_AJC segment_NN1 is_VBZ always_AV0 on_PRP the_AT0 same_DT0 side_NN1 as_PRP the_AT0 direction_NN1 of_PRF skewness_NN1 ;_PUN that_DT0 is_VBZ ,_PUN a_AT0 positively_AV0 skewed_AJ0 distribution_NN1 will_VM0 have_VHI a_AT0 wider_AJC right_AJ0 segment_NN1 and_CJC a_AT0 negatively_AV0 skewed_AJ0 distribution_NN1 will_VM0 have_VHI a_AT0 wider_AJC left_AJ0 segment_NN1 ._SENT With_PRP the_AT0 Steiger_NP0 &_NP0 Fouladi_NP0 method_NN1 ,_PUN the_AT0 reverse_NN1 is_VBZ true_AJ0 :_PUN a_AT0 positively_AV0 skewed_AJ0 distribution_NN1 will_VM0 have_VHI a_AT0 wider_AJC left_AJ0 segment_NN1 and_CJC a_AT0 negatively_AV0 skewed_AJ0 distribution_NN1 will_VM0 have_VHI a_AT0 wider_AJC right_AJ0 segment_NN1 ._SENT We_PNP can_VM0 see_VVI in_PRP the_AT0 example_NN1 for_PRP d_CRD =_NP0 1.0_CRD in_PRP Fig._NN1 1b_NN1 that_CJT the_AT0 wider_AJC segment_NN1 for_PRP the_AT0 Hedges_NN2 &_NP0 Olkin_NP0 method_NN1 is_VBZ obviously_AV0 in_PRP the_AT0 direction_NN1 of_PRF skewness_NN1 to_PRP the_AT0 right_NN1 ,_PUN and_CJC is_VBZ less_AV0 obviously_AV0 in_PRP the_AT0 opposite_AJ0 direction_NN1 for_PRP the_AT0 Steiger_NP0 &_NP0 Fouladi_NP0 method_NN1 (_PUL i.e._AV0 ,_PUN 1.0_CRD –_PUN .001_CRD =_NP0 .999_CRD on_PRP the_AT0 left_NN1 and_CJC 1.972_CRD –_PUN 1.0_CRD =_NP0 .972_CRD on_PRP the_AT0 right_NN1 ,_PUN see_VVB segment_NN1 widths_NN2 in_PRP Appendix_NN1 1_CRD )_PUR ._SENT The_AT0 confidence_NN1 interval_NN1 for_PRP a_AT0 d_ZZ0 of_PRF –_PUN 1.0_CRD would_VM0 simply_AV0 be_VBI the_AT0 mirror_NN1 image_NN1 of_PRF this_DT0 graph_NN1 in_PRP the_AT0 negative_AJ0 direction_NN1 ._SENT 
The_AT0 difference_NN1 in_PRP the_AT0 direction_NN1 of_PRF the_AT0 wider_AJC segment_NN1 for_PRP Hedges_NP0 &_NP0 Olkin_NP0 and_CJC Steiger_NP0 &_NP0 Fouladi_NP0 methods_NN2 has_VHZ implications_NN2 for_PRP the_AT0 coverages_NN2 of_PRF the_AT0 intervals_NN2 ._SENT With_PRP effect_NN1 size_NN1 0_CRD (_PUL Fig._NN1 1a_CRD )_PUR ,_PUN the_AT0 symmetrical_AJ0 Hedges_NN2 &_NP0 Olkin_NP0 interval_NN1 is_VBZ wider_AJC than_CJS the_AT0 symmetrical_AJ0 Steiger_NP0 &_NP0 Fouladi_NP0 interval_NN1 ._SENT This_DT0 implies_VVZ greater_AJC coverage_NN1 for_PRP the_AT0 Hedges_NN2 &_NP0 Olkin_NP0 interval_NN1 with_PRP δ_NN1 at_PRP or_CJC near_PRP 0._CRD As_CJS the_AT0 effect_NN1 size_NN1 increases_VVZ to_PRP a_AT0 value_NN1 such_DT0 as_PRP 1.0_CRD in_PRP Fig._NN1 1b_NN1 ,_PUN the_AT0 Hedges_NN2 &_NP0 Olkin_NP0 interval_NN1 is_VBZ wider_AJC in_PRP the_AT0 direction_NN1 of_PRF skewness_NN1 toward_PRP the_AT0 tails_NN2 ,_PUN where_CJS there_EX0 is_VBZ a_AT0 smaller_AJC probability_NN1 density_NN1 ._SENT The_AT0 Steiger_NP0 &_NP0 Fouladi_NP0 interval_NN1 is_VBZ wider_AJC toward_PRP the_AT0 center_NN1 of_PRF the_AT0 distribution_NN1 ,_PUN where_CJS there_EX0 is_VBZ a_AT0 larger_AJC probability_NN1 density_NN1 ._SENT Thus_AV0 ,_PUN a_AT0 small_AJ0 increase_NN1 in_PRP the_AT0 wider_AJC segment_NN1 of_PRF a_AT0 Steiger_NP0 &_NP0 Fouladi_NP0 interval_NN1 will_VM0 add_VVI more_DT0 coverage_NN1 probability_NN1 than_CJS an_AT0 equal_AJ0 increase_NN1 in_PRP the_AT0 wider_AJC segment_NN1 of_PRF a_AT0 Hedges_NN2 &_NP0 Olkin_NP0 interval_NN1 ._SENT Steiger_NP0 &_NP0 Fouladi_NP0 intervals_NN2 with_PRP moderate_AJ0 to_PRP large_AJ0 effect_NN1 sizes_NN2 can_VM0 be_VBI narrower_AJC (_PUL more_AV0 precise_AJ0 )_PUR and_CJC yet_AV0 have_VHB higher_AJC coverage_NN1 than_CJS Hedges_NP0 &_NP0 Olkin_NP0 intervals_NN2 ._SENT 
Overview_NN1 and_CJC method_NN1 of_PRF predictions_NN2 
Before_CJS proceeding_VVG to_PRP the_AT0 technical_AJ0 details_NN2 ,_PUN let_VVB us_PNP examine_VVI the_AT0 output_NN1 of_PRF the_AT0 provided_VVN software_NN1 to_TO0 calculate_VVI the_AT0 expected_AJ0 coverages_NN2 for_PRP all_DT0 four_CRD confidence_NN1 intervals_NN2 using_VVG d_ZZ0 or_CJC g_ZZ0 and_CJC using_VVG the_AT0 Hedges_NN2 &_NP0 Olkin_NP0 or_CJC Steiger_NP0 &_NP0 Fouladi_NP0 methods_NN2 ._SENT The_AT0 procedure_NN1 is_VBZ given_VVN in_PRP Example_NN1 3_CRD in_PRP the_AT0 user_NN1 's_POS notes_NN2 and_CJC the_AT0 output_NN1 for_PRP 16_CRD degrees_NN2 of_PRF freedom_NN1 rounded_VVN to_PRP three_CRD decimal_AJ0 digits_NN2 is_VBZ displayed_VVN in_PRP Table_NN1 1._CRD Ignoring_VVG the_AT0 intermediate_AJ0 calculations_NN2 and_CJC examining_VVG the_AT0 expected_AJ0 coverages_NN2 in_PRP the_AT0 far_AV0 right_AJ0 column_NN1 ,_PUN we_PNP see_VVB that_DT0 coverage_NN1 for_PRP Hedges_NP0 &_NP0 Olkin_NP0 using_VVG d_ZZ0 (_PUL Hd_NP0 )_PUR is_VBZ .930_CRD ,_PUN Hedges_VVZ &_NP0 Olkin_NP0 using_VVG g_NN0 (_PUL Hg_NP0 )_PUR is_VBZ .944_CRD ,_PUN Steiger_NP0 &_NP0 Fouladi_NP0 using_VVG d_ZZ0 (_PUL Sd_NN0 )_PUR is_VBZ .950_CRD ,_PUN and_CJC Steiger_NP0 &_NP0 Fouladi_NP0 using_VVG g_NN0 (_PUL Sg_NP0 )_PUR is_VBZ .957_CRD ._SENT 
The_AT0 expected_AJ0 coverage_NN1 in_PRP Table_NN1 1_CRD is_VBZ the_AT0 probability_NN1 of_PRF sampling_VVG a_AT0 d_ZZ0 value_NN1 between_PRP two_CRD boundary_NN1 d_ZZ0 values_NN2 ._SENT These_DT0 boundaries_NN2 for_PRP d_ZZ0 are_VBB called_VVN "_PUQ leftd_AJ0 "_PUQ and_CJC "_PUQ rightd_NN1 "_PUQ in_PRP the_AT0 text_NN1 output_NN1 in_PRP Table_NN1 1._CRD These_DT0 d_ZZ0 values_NN2 are_VBB converted_VVN to_PRP t_ZZ0 values_NN2 called_VVD 𝜆̂𝑑_NP0 ,_PUN 𝑙𝑒𝑓𝑡_NP0 and_CJC 𝜆̂𝑑_NP0 ,_PUN 𝑟𝑖𝑔ℎ𝑡_NP0 using_VVG Eq._NP0 9b_NN1 ._SENT These_DT0 t_ZZ0 boundaries_NN2 are_VBB selected_VVN to_TO0 represent_VVI the_AT0 most_AV0 extreme_AJ0 possible_AJ0 d_ZZ0 value_NN1 in_PRP that_DT0 direction_NN1 (_PUL left_AJ0 or_CJC right_AJ0 )_PUR that_DT0 could_VM0 have_VHI a_AT0 confidence_NN1 interval_NN1 of_PRF the_AT0 given_AJ0 type_NN1 that_CJT still_AV0 includes_VVZ δ_NN1 ._SENT That_DT0 is_VBZ to_TO0 say_VVI ,_PUN all_DT0 d_ZZ0 values_NN2 to_PRP the_AT0 left_NN1 of_PRF leftd_NN1 will_VM0 have_VHI confidence_NN1 intervals_NN2 of_PRF that_DT0 type_NN1 that_CJT do_VDB not_XX0 include_VVI δ_NN1 ,_PUN and_CJC all_DT0 d_ZZ0 values_NN2 to_PRP the_AT0 right_NN1 of_PRF rightd_NN1 will_VM0 also_AV0 have_VHI confidence_NN1 intervals_NN2 of_PRF that_DT0 type_NN1 that_CJT do_VDB not_XX0 include_VVI δ_NN1 ._SENT The_AT0 probability_NN1 of_PRF a_AT0 𝜆̂𝑑_AJ0 value_NN1 to_PRP the_AT0 left_NN1 of_PRF 𝜆̂𝑑_NP0 ,_PUN 𝑙𝑒𝑓𝑡_NP0 (_PUL called_VVN 𝛼̂𝑙𝑒𝑓𝑡_NP0 )_PUR or_CJC to_PRP the_AT0 right_NN1 of_PRF 𝜆̂𝑑_NP0 ,_PUN 𝑟𝑖𝑔ℎ𝑡_NP0 (_PUL 𝛼̂𝑟𝑖𝑔ℎ𝑡_NP0 )_PUR can_VM0 be_VBI determined_VVN directly_AV0 from_PRP the_AT0 cumulative_AJ0 distribution_NN1 function_NN1 of_PRF the_AT0 corresponding_AJ0 noncentral_AJ0 t_ZZ0 distribution_NN1 with_PRP non-centrality_AJ0 parameter_NN1 𝜆𝛿_NP0 =_NP0 𝛿𝐴_NP0 ‾_NP0 ‾_NP0 √_NP0 and_CJC ν_AJ0 as_CJS given_VVN in_PRP Eqs_NN2 ._SENT 10_CRD and_CJC 11._CRD The_AT0 sum_NN1 of_PRF these_DT0 two_CRD tail_NN1 probabilities_NN2 (_PUL "_PUQ ltail_NN1 "_PUQ and_CJC "_PUQ rtail_NN1 "_PUQ in_PRP Table_NN1 1_CRD )_PUR is_VBZ the_AT0 total_AJ0 probability_NN1 of_PRF sampling_VVG a_AT0 d_ZZ0 that_CJT does_VDZ not_XX0 include_VVI δ_NN1 (_PUL 𝛼̂_NP0 =_NP0 𝛼̂𝑙𝑒𝑓𝑡_NP0 +_NP0 𝛼̂𝑟𝑖𝑔ℎ𝑡_NP0 )_PUR ._SENT The_AT0 complement_NN1 ,_PUN 1_CRD −_NP0 𝛼̂_NP0 ,_PUN is_VBZ the_AT0 expected_AJ0 coverage_NN1 of_PRF the_AT0 confidence_NN1 interval_NN1 as_CJS given_VVN in_PRP the_AT0 far_AV0 right_AJ0 column_NN1 in_PRP Table_NN1 1._CRD 
For_PRP Hd_NP0 and_CJC Sd_NN0 ,_PUN the_AT0 d_ZZ0 boundaries_NN2 (_PUL leftd_AJ0 and_CJC rightd_AJ0 in_PRP Table_NN1 1_CRD )_PUR are_VBB determined_VVN by_PRP a_AT0 process_NN1 using_VVG Hd_NP0 and_CJC Sd_NN0 confidence_NN1 intervals_NN2 directly_AV0 ._SENT For_PRP Hg_NP0 and_CJC Sg_NP0 ,_PUN the_AT0 d_ZZ0 boundaries_NN2 (_PUL leftd_AJ0 and_CJC rightd_AJ0 )_PUR are_VBB determined_VVN by_PRP a_AT0 two-step_AJ0 process_NN1 :_PUN (_PUL 1_CRD )_PUR use_VVB Hg_NP0 and_CJC Sg_NP0 confidence_NN1 intervals_NN2 to_TO0 determine_VVI g_NN0 boundaries_NN2 ,_PUN then_AV0 (_PUL 2_CRD )_PUR convert_NN1 g_ZZ0 boundaries_NN2 to_PRP d_ZZ0 boundaries_NN2 by_PRP dividing_VVG the_AT0 g_NN0 boundaries_NN2 by_PRP J_NP0 (_PUL ν_CRD )_PUR ._SENT For_PRP example_NN1 ,_PUN rightd_NN1 for_PRP method_NN1 Hg_NP0 is_VBZ computed_VVN as_PRP rightd_NP0 =_NP0 rightg_NP0 /_PUN J_NP0 (_PUL ν_CRD )_PUR =_NP0 1.972_CRD /_PUN .95225_CRD =_NP0 2.071_CRD ._SENT The_AT0 leftg_NN1 and_CJC rightg_NN1 values_NN2 have_VHB been_VBN calculated_VVN but_CJC are_VBB not_XX0 needed_VVN for_PRP methods_NN2 Hd_NP0 and_CJC Sd_NN0 ._SENT 
The_AT0 process_NN1 for_PRP discovering_VVG these_DT0 d_ZZ0 boundaries_NN2 involves_VVZ a_AT0 computer_NN1 search_NN1 for_PRP a_AT0 confidence_NN1 interval_NN1 of_PRF a_AT0 given_AJ0 type_NN1 that_CJT has_VHZ one_PNI of_PRF the_AT0 standardized_AJ0 limits_NN2 equal_AJ0 to_PRP the_AT0 standardized_AJ0 population_NN1 effect_NN1 size_NN1 ,_PUN δ_NP0 ._SENT The_AT0 standardized_AJ0 limits_NN2 of_PRF a_AT0 confidence_NN1 interval_NN1 are_VBB determined_VVN with_PRP respect_NN1 to_PRP a_AT0 corresponding_AJ0 t-scaled_AJ0 non-centrality_NN1 parameter_NN1 ,_PUN and_CJC the_AT0 non-centrality_AJ0 parameter_NN1 to_TO0 be_VBI used_VVN depends_VVZ on_PRP whether_CJS the_AT0 confidence_NN1 interval_NN1 is_VBZ a_AT0 d_ZZ0 interval_NN1 (_PUL 𝜆̂𝑑_NP0 ,_PUN Eq._NP0 9b_NN1 )_PUR or_CJC a_AT0 g_ZZ0 interval_NN1 (_PUL 𝜆̂𝑔_NP0 ,_PUN Eq._NP0 9c_NN1 )_PUR ._SENT The_AT0 left_AJ0 d_ZZ0 boundary_NN1 for_PRP determining_VVG the_AT0 expected_AJ0 coverage_NN1 of_PRF Hd_NP0 or_CJC Sd_NN0 confidence_NN1 intervals_NN2 is_VBZ a_AT0 d_ZZ0 whose_DTQ Hd_NP0 or_CJC Sd_NN0 standardized_AJ0 confidence_NN1 interval_NN1 has_VHZ an_AT0 upper_AJ0 limit_NN1 of_PRF δ_NN1 ._SENT The_AT0 left_AJ0 d_ZZ0 boundary_NN1 for_PRP determining_VVG coverage_NN1 of_PRF Hg_NP0 or_CJC Sg_NP0 confidence_NN1 intervals_NN2 is_VBZ a_AT0 d_ZZ0 whose_DTQ associated_VVD Hg_NP0 or_CJC Sg_NP0 standardized_AJ0 confidence_NN1 interval_NN1 has_VHZ an_AT0 upper_AJ0 limit_NN1 of_PRF δ_NN1 ._SENT Note_VVB that_CJT we_PNP do_VDB not_XX0 rescale_NN1 δ_NN1 for_PRP use_NN1 with_PRP a_AT0 g_NN0 interval_NN1 ._SENT In_PRP either_DT0 case_NN1 ,_PUN there_EX0 can_VM0 be_VBI no_AT0 d_ZZ0 value_NN1 to_PRP the_AT0 left_NN1 of_PRF the_AT0 selected_AJ0 boundary_NN1 that_CJT has_VHZ a_AT0 confidence_NN1 interval_NN1 of_PRF the_AT0 same_DT0 type_NN1 that_CJT includes_VVZ δ_NN1 ._SENT For_PRP the_AT0 Hg_NP0 and_CJC Sg_NP0 confidence_NN1 intervals_NN2 ,_PUN this_DT0 involves_VVZ converting_VVG the_AT0 d_ZZ0 to_PRP a_AT0 g_NN0 ,_PUN searching_VVG for_PRP the_AT0 g_NN0 boundary_NN1 that_CJT has_VHZ an_AT0 upper_AJ0 limit_NN1 of_PRF δ_NN1 ,_PUN and_CJC then_AV0 converting_VVG that_CJT g_ZZ0 boundary_NN1 back_AVP to_PRP a_AT0 d_ZZ0 boundary_NN1 ._SENT Any_DT0 d_ZZ0 to_PRP the_AT0 left_NN1 of_PRF that_DT0 d_ZZ0 boundary_NN1 would_VM0 have_VHI a_AT0 corresponding_AJ0 g_NN0 that_CJT is_VBZ to_PRP the_AT0 left_NN1 of_PRF its_DPS g_NN0 boundary_NN1 ._SENT The_AT0 d_ZZ0 boundary_NN1 generated_VVN by_PRP a_AT0 Hg_NP0 or_CJC Sg_NP0 confidence_NN1 interval_NN1 method_NN1 will_VM0 not_XX0 be_VBI the_AT0 same_DT0 as_CJS the_AT0 d_ZZ0 boundary_NN1 generated_VVN by_PRP a_AT0 Hd_NP0 or_CJC Sd_NN0 confidence_NN1 interval_NN1 method_NN1 ._SENT 
Computation_NN1 of_PRF d_ZZ0 boundaries_NN2 is_VBZ done_VDN by_PRP a_AT0 computer_NN1 search_NN1 algorithm_NN1 ,_PUN but_CJC the_AT0 equivalent_AJ0 hand_NN1 calculation_NN1 could_VM0 be_VBI done_VDN with_PRP much_DT0 effort_NN1 by_PRP trial_NN1 and_CJC error_NN1 ._SENT Suppose_VVB we_PNP wish_VVB to_TO0 calculate_VVI the_AT0 lower_AJC d_ZZ0 boundary_NN1 ,_PUN leftd_NN1 ,_PUN for_PRP the_AT0 Sd_NN0 method_NN1 ._SENT A_AT0 standardized_AJ0 confidence_NN1 interval_NN1 of_PRF the_AT0 Sd_NN0 type_NN1 around_PRP this_DT0 d_ZZ0 boundary_NN1 should_VM0 have_VHI an_AT0 upper_AJ0 limit_NN1 δ_NN1 (_PUL i.e._AV0 ,_PUN the_AT0 population_NN1 standardized_AJ0 effect_NN1 size_NN1 )_PUR ,_PUN so_CJS that_DT0 is_VBZ our_DPS target_NN1 d_ZZ0 ._SENT We_PNP select_VVB an_AT0 initial_AJ0 educated_AJ0 guess_NN1 as_CJS to_PRP the_AT0 d_ZZ0 boundary_NN1 ,_PUN dguess_NN1 (_PUL it_PNP must_VM0 be_VBI less_AV0 than_CJS δ_AJ0 if_CJS the_AT0 right_AJ0 limit_NN1 will_VM0 be_VBI δ_AJ0 )_PUR ,_PUN then_AV0 search_NN1 for_PRP a_AT0 Sd_NN0 confidence_NN1 interval_NN1 for_PRP dguess_NN1 and_CJC examine_VVB the_AT0 upper_AJ0 limit_NN1 ._SENT If_CJS it_PNP is_VBZ greater_AJC than_CJS δ_NN1 ,_PUN reduce_VVB the_AT0 size_NN1 of_PRF dguess_NN1 and_CJC try_VVB again_AV0 ._SENT If_CJS it_PNP is_VBZ less_AV0 than_CJS δ_NN1 ,_PUN increase_VVB the_AT0 size_NN1 of_PRF dguess_NN1 and_CJC try_VVB again_AV0 ._SENT Stop_VVB when_AVQ the_AT0 value_NN1 of_PRF dguess_NN1 generates_VVZ a_AT0 confidence_NN1 interval_NN1 suitably_AV0 close_AJ0 to_PRP δ_NN1 ._SENT The_AT0 computer_NN1 does_VDZ this_DT0 to_PRP eight_CRD decimal_AJ0 digits_NN2 ._SENT Note_VVB that_CJT similar_AJ0 searches_NN2 are_VBB required_VVN for_PRP repeatedly_AV0 computing_NN1 Steiger_NP0 &_NP0 Fouladi_NP0 confidence_NN1 intervals_NN2 on_PRP the_AT0 way_NN1 to_PRP determining_VVG that_DT0 boundary_NN1 ,_PUN so_AV0 the_AT0 searching_NN1 is_VBZ onerous_AJ0 indeed_AV0 ._SENT There_EX0 are_VBB shortcuts_NN2 to_PRP this_DT0 end_NN1 ,_PUN discussed_VVN later_AV0 ,_PUN but_CJC the_AT0 computer_NN1 always_AV0 calculates_VVZ the_AT0 value_NN1 from_PRP this_DT0 basic_AJ0 principle_NN1 ._SENT 
Pseudo-algorithm_NN1 used_VVN by_PRP computer_NN1 program_NN1 
The_AT0 procedure_NN1 used_VVN by_PRP my_DPS computer_NN1 program_NN1 for_PRP determining_VVG the_AT0 expected_AJ0 coverage_NN1 of_PRF a_AT0 d_ZZ0 or_CJC g_ZZ0 confidence_NN1 interval_NN1 for_PRP either_DT0 method_NN1 follows_VVZ ._SENT Steps_NN2 beginning_VVG "_PUQ Search_VVB for_PRP ..._PUN "_PUQ are_VBB done_VDN using_VVG specialized_AJ0 search_NN1 functions_NN2 written_VVN for_PRP that_DT0 purpose_NN1 ._SENT 
1._CRD Calculate_VVB 𝜆𝛿_NP0 =_NP0 𝛿𝐴_NP0 ‾_NP0 ‾_NP0 √_NN1 and_CJC ν_NN1 (_PUL Eqs_NN2 ._SENT 9a_NN1 to_PRP 11_CRD )_PUR ._SENT 
2._CRD If_CJS finding_VVG the_AT0 boundaries_NN2 for_PRP Hd_NP0 or_CJC Sd_NN0 use_NN1 Step_NN1 2a_NN1 ._SENT If_CJS finding_VVG the_AT0 boundaries_NN2 for_PRP Hg_NP0 or_CJC Sg_NP0 use_NN1 Step_NN1 2b_NN1 ._SENT For_PRP each_DT0 instance_NN1 of_PRF the_AT0 word_NN1 "_PUQ [_PUL Method_NN1 ]_PUR ,_PUN "_PUQ substitute_NN1 "_PUQ Hedges_VVZ &_NP0 Olkin_NP0 Method_NN1 "_PUQ if_CJS finding_VVG the_AT0 coverage_NN1 of_PRF Hd_NP0 or_CJC Hg_NP0 confidence_NN1 intervals_NN2 or_CJC substitute_NN1 "_PUQ Steiger_NP0 &_NP0 Fouladi_NP0 Method_NN1 "_PUQ if_CJS finding_VVG the_AT0 coverage_NN1 of_PRF Sd_NN0 or_CJC Sg_NP0 confidence_NN1 intervals_NN2 ._SENT 
2a_NN1 ._SENT Hd_NN0 or_CJC Sd_NN0 procedure_NN1 
i_CRD ._SENT Search_NN1 for_PRP the_AT0 left_AJ0 t_ZZ0 boundary_NN1 ,_PUN 𝜆̂𝑑_NP0 ,_PUN 𝑙𝑒𝑓𝑡_NP0 ,_PUN which_DTQ is_VBZ the_AT0 non-centrality_AJ0 parameter_NN1 of_PRF the_AT0 [_PUL Method_NN1 ]_PUR confidence_NN1 interval_NN1 to_PRP the_AT0 left_NN1 of_PRF λδ_NP0 =_NP0 𝛿𝐴_NP0 ‾_NP0 ‾_NN1 √_NN1 that_CJT includes_VVZ λδ_NN1 as_PRP the_AT0 right-hand_AJ0 confidence_NN1 limit_NN1 ._SENT 
ii_CRD ._SENT Search_NN1 for_PRP the_AT0 right_AJ0 t_ZZ0 boundary_NN1 ,_PUN 𝜆̂𝑑_NP0 ,_PUN 𝑟𝑖𝑔ℎ𝑡_NP0 ,_PUN which_DTQ is_VBZ the_AT0 non-centrality_AJ0 parameter_NN1 of_PRF the_AT0 [_PUL Method_NN1 ]_PUR confidence_NN1 interval_NN1 to_PRP the_AT0 right_NN1 of_PRF λδ_NP0 =_NP0 𝛿𝐴_NP0 ‾_NP0 ‾_NN1 √_NN1 that_CJT includes_VVZ λδ_NN1 as_PRP the_AT0 left-hand_AJ0 confidence_NN1 limit_NN1 ._SENT 
2b_AJ0 ._SENT Hg_NP0 or_CJC Sg_NP0 procedure_NN1 
i_CRD ._SENT Search_NN1 for_PRP the_AT0 left_AJ0 t_ZZ0 boundary_NN1 ,_PUN 𝜆̂𝑔_NP0 ,_PUN 𝑙𝑒𝑓𝑡_NP0 ,_PUN which_DTQ is_VBZ the_AT0 non-centrality_AJ0 parameter_NN1 of_PRF the_AT0 [_PUL Method_NN1 ]_PUR confidence_NN1 interval_NN1 to_PRP the_AT0 left_NN1 of_PRF λδ_NP0 =_NP0 𝛿𝐴_NP0 ‾_NP0 ‾_NN1 √_NN1 that_CJT includes_VVZ λδ_NN1 as_PRP the_AT0 right-hand_AJ0 confidence_NN1 limit_NN1 ._SENT Note_VVB that_CJT we_PNP do_VDB not_XX0 rescale_NN1 λδ_NN1 by_PRP the_AT0 bias_NN1 correction_NN1 factor_NN1 because_CJS the_AT0 population_NN1 value_NN1 is_VBZ not_XX0 biased_AJ0 ._SENT 
ii_CRD ._SENT Search_NN1 for_PRP the_AT0 right_AJ0 t_ZZ0 boundary_NN1 ,_PUN 𝜆̂𝑔_NP0 ,_PUN 𝑟𝑖𝑔ℎ𝑡_NP0 ,_PUN which_DTQ is_VBZ the_AT0 non-centrality_AJ0 parameter_NN1 of_PRF the_AT0 [_PUL Method_NN1 ]_PUR confidence_NN1 interval_NN1 to_PRP the_AT0 right_NN1 of_PRF λδ_NP0 =_NP0 𝛿𝐴_NP0 ‾_NP0 ‾_NN1 √_NN1 that_CJT includes_VVZ λδ_NN1 as_PRP the_AT0 left-hand_AJ0 confidence_NN1 limit_NN1 ._SENT 
iii_CRD ._SENT Calculate_VVB 𝜆̂𝑑_NP0 ,_PUN 𝑙𝑒𝑓𝑡_NP0 =_NP0 𝜆̂𝑔_NP0 ,_PUN 𝑙𝑒𝑓𝑡_NP0 /_PUN J_NP0 (_PUL ν_CRD )_PUR and_CJC 𝜆̂𝑑_NP0 ,_PUN 𝑟𝑖𝑔ℎ𝑡_NP0 =_NP0 𝜆̂𝑔_NP0 ,_PUN 𝑟𝑖𝑔ℎ𝑡_NP0 /_PUN J_NP0 (_PUL ν_CRD )_PUR ._SENT 
3._CRD Using_VVG the_AT0 noncentral_AJ0 t_ZZ0 distribution_NN1 for_PRP λδ_NN1 and_CJC ν_NN1 determine_VVB the_AT0 cumulative_AJ0 probability_NN1 ,_PUN pleft_NN1 ,_PUN of_PRF 𝜆̂𝑑_NP0 ,_PUN 𝑙𝑒𝑓𝑡_NP0 and_CJC assign_VVB 𝛼̂𝑙𝑒𝑓𝑡_NP0 =_NP0 pleft_NN1 ._SENT Do_VDB the_AT0 same_DT0 for_PRP the_AT0 other_AJ0 tail_NN1 to_TO0 compute_VVI pright_NN1 based_VVN on_PRP 𝜆̂𝑑_NP0 ,_PUN 𝑟𝑖𝑔ℎ𝑡_NP0 and_CJC assign_VVB 𝛼̂𝑟𝑖𝑔ℎ𝑡_NP0 =_NP0 1_CRD –_PUN pright_NN1 ._SENT 
4._CRD Calculate_VVB 𝛼̂_NP0 =_NP0 𝛼̂𝑙𝑒𝑓𝑡_NP0 +_NP0 𝛼̂𝑟𝑖𝑔ℎ𝑡_NP0 ._SENT 
5._CRD Calculate_VVB expected_AJ0 coverage_NN1 =_NN1 1_CRD –_PUN 𝛼̂_NP0 ._SENT 
Supplement_NN1 1_CRD gives_VVZ examples_NN2 of_PRF how_AVQ to_TO0 calculate_VVI expected_AJ0 coverages_NN2 for_PRP both_DT0 the_AT0 Hedges_NN2 &_NP0 Olkin_NP0 and_CJC Steiger_NP0 and_CJC Fouladi_NP0 methods_NN2 used_VVN in_PRP this_DT0 paper_NN1 ._SENT 
Comments_NN2 and_CJC shortcuts_NN2 for_PRP predicting_VVG coverage_NN1 
These_DT0 d_ZZ0 boundaries_NN2 are_VBB not_XX0 confidence_NN1 intervals_NN2 ,_PUN although_CJS they_PNP can_VM0 be_VBI interpreted_VVN in_PRP a_AT0 fashion_NN1 similar_AJ0 to_PRP confidence_NN1 intervals_NN2 ._SENT That_DT0 is_VBZ ,_PUN the_AT0 tail_NN1 probabilities_NN2 represent_VVB d_ZZ0 values_NN2 that_CJT have_VHB confidence_NN1 intervals_NN2 that_CJT exclude_VVB δ_NN1 ,_PUN and_CJC the_AT0 probabilities_NN2 between_PRP the_AT0 boundaries_NN2 represent_VVB d_ZZ0 values_NN2 that_CJT have_VHB confidence_NN1 intervals_NN2 that_CJT include_VVB δ_NN1 ._SENT However_AV0 ,_PUN 𝛼̂_NP0 is_VBZ a_AT0 dependent_AJ0 variable_NN1 in_PRP this_DT0 process_NN1 rather_AV0 that_CJT an_AT0 independent_AJ0 variable_NN1 ._SENT 
